Identifier
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
Mp00092: Perfect matchings —to set partition⟶ Set partitions
Mp00220: Set partitions —Yip⟶ Set partitions
Images
=>
Cc0005;cc-rep-0Cc0012;cc-rep-1Cc0009;cc-rep-2Cc0009;cc-rep-3
[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}}=>{{1,2,4,6},{3},{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}}=>{{1,3,5},{2},{4,6}} [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}}=>{{1,2,4,6,8},{3},{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}}=>{{1,2,4,7},{3,8},{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}}=>{{1,2,5,8},{3,6},{4},{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}}=>{{1,2,5,7},{3},{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}}=>{{1,3,6,8},{2,4},{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}}=>{{1,3,5,8},{2},{4,6},{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}}=>{{1,3,5,7},{2},{4},{6,8}} [1,1,0,1,1,0,0,0]=>[(1,8),(2,3),(4,7),(5,6)]=>{{1,8},{2,3},{4,7},{5,6}}=>{{1,3,6},{2,7},{4},{5,8}} [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}}=>{{1,4,7},{2,5},{3},{6,8}} [1,1,1,0,1,0,0,0]=>[(1,8),(2,7),(3,4),(5,6)]=>{{1,8},{2,7},{3,4},{5,6}}=>{{1,4,6},{2},{3,7},{5,8}} [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}}=>{{1,2,4,6,8,10},{3},{5},{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}}=>{{1,2,4,6,9},{3,10},{5},{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}}=>{{1,2,4,7,10},{3,8},{5},{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}}=>{{1,2,4,7,9},{3},{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}}=>{{1,2,4,8},{3,9},{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}}=>{{1,2,5,8,10},{3,6},{4},{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}}=>{{1,2,5,9},{3,6,10},{4},{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}}=>{{1,2,5,7,10},{3},{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}}=>{{1,2,5,7,9},{3},{4},{6,10},{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}}=>{{1,2,5,8},{3,9},{4},{6,10},{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}}=>{{1,2,6,10},{3,7},{4,8},{5},{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}}=>{{1,2,6,9},{3,7},{4},{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}}=>{{1,2,6,8},{3},{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}}=>{{1,3,6,8,10},{2,4},{5},{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}}=>{{1,3,6,9},{2,4,10},{5},{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}}=>{{1,3,7,10},{2,4,8},{5},{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}}=>{{1,3,7,9},{2,4},{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}}=>{{1,3,5,8,10},{2},{4,6},{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}}=>{{1,3,5,9},{2},{4,6,10},{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}}=>{{1,3,5,7,10},{2},{4},{6,8},{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}}=>{{1,3,5,7,9},{2},{4},{6},{8,10}} [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}}=>{{1,3,5,8},{2,9},{4},{6},{7,10}} [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}}=>{{1,3,6,10},{2,7},{4},{5,8},{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}}=>{{1,3,6,9},{2,7},{4},{5},{8,10}} [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}}=>{{1,3,6,8},{2},{4,9},{5},{7,10}} [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}}=>{{1,3,7},{2,8},{4,9},{5},{6,10}} [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}}=>{{1,4,8,10},{2,5},{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}}=>{{1,4,7,10},{2,5},{3},{6,8},{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}}=>{{1,4,7,9},{2,5},{3},{6},{8,10}} [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}}=>{{1,4,8},{2,5,9},{3},{6},{7,10}} [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}}=>{{1,4,6,10},{2},{3,7},{5,8},{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}}=>{{1,4,6,9},{2},{3,7},{5},{8,10}} [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}}=>{{1,4,6,8},{2},{3},{5,9},{7,10}} [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}}=>{{1,4,7},{2,8},{3},{5,9},{6,10}} [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}}=>{{1,5,9},{2,6},{3,7},{4},{8,10}} [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}}=>{{1,5,8},{2,6},{3},{4,9},{7,10}} [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}}=>{{1,5,7},{2},{3,8},{4,9},{6,10}} [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}}=>{{1,2,4,6,8,10,12},{3},{5},{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}}=>{{1,2,4,6,8,11},{3,12},{5},{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}}=>{{1,2,4,6,9,12},{3,10},{5},{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}}=>{{1,2,4,6,9,11},{3},{5,12},{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}}=>{{1,2,4,6,10},{3,11},{5,12},{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}}=>{{1,2,4,7,10,12},{3,8},{5},{6},{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}}=>{{1,2,4,7,11},{3,8,12},{5},{6},{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}}=>{{1,2,4,7,9,12},{3},{5,10},{6},{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}}=>{{1,2,4,7,9,11},{3},{5},{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}}=>{{1,2,4,7,10},{3,11},{5},{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}}=>{{1,2,4,8,12},{3,9},{5,10},{6},{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}}=>{{1,2,4,8,11},{3,9},{5},{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}}=>{{1,2,4,8,10},{3},{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}}=>{{1,2,4,9},{3,10},{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}}=>{{1,2,5,8,10,12},{3,6},{4},{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}}=>{{1,2,5,8,11},{3,6,12},{4},{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}}=>{{1,2,5,9,12},{3,6,10},{4},{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}}=>{{1,2,5,9,11},{3,6},{4,12},{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}}=>{{1,2,5,10},{3,6,11},{4,12},{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}}=>{{1,2,5,7,10,12},{3},{4,8},{6},{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}}=>{{1,2,5,7,11},{3},{4,8,12},{6},{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}}=>{{1,2,5,7,9,12},{3},{4},{6,10},{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}}=>{{1,2,5,7,9,11},{3},{4},{6},{8,12},{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}}=>{{1,2,5,7,10},{3,11},{4},{6},{8,12},{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}}=>{{1,2,5,8,12},{3,9},{4},{6,10},{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}}=>{{1,2,5,8,11},{3,9},{4},{6},{7,12},{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}}=>{{1,2,5,8,10},{3},{4,11},{6},{7,12},{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}}=>{{1,2,5,9},{3,10},{4,11},{6},{7,12},{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}}=>{{1,2,6,10,12},{3,7},{4,8},{5},{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}}=>{{1,2,6,11},{3,7,12},{4,8},{5},{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}}=>{{1,2,6,9,12},{3,7},{4},{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}}=>{{1,2,6,9,11},{3,7},{4},{5},{8,12},{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}}=>{{1,2,6,10},{3,7,11},{4},{5},{8,12},{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}}=>{{1,2,6,8,12},{3},{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}}=>{{1,2,6,8,11},{3},{4,9},{5},{7,12},{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}}=>{{1,2,6,8,10},{3},{4},{5,11},{7,12},{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}}=>{{1,2,6,9},{3,10},{4},{5,11},{7,12},{8}} [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}}=>{{1,2,7,12},{3,8},{4,9},{5,10},{6},{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}}=>{{1,2,7,11},{3,8},{4,9},{5},{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}}=>{{1,2,7,10},{3,8},{4},{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}}=>{{1,2,7,9},{3},{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}}=>{{1,3,6,8,10,12},{2,4},{5},{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}}=>{{1,3,6,8,11},{2,4,12},{5},{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}}=>{{1,3,6,9,12},{2,4,10},{5},{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}}=>{{1,3,6,9,11},{2,4},{5,12},{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}}=>{{1,3,6,10},{2,4,11},{5,12},{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}}=>{{1,3,7,10,12},{2,4,8},{5},{6},{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}}=>{{1,3,7,11},{2,4,8,12},{5},{6},{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}}=>{{1,3,7,9,12},{2,4},{5,10},{6},{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}}=>{{1,3,7,9,11},{2,4},{5},{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}}=>{{1,3,7,10},{2,4,11},{5},{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}}=>{{1,3,8,12},{2,4,9},{5,10},{6},{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}}=>{{1,3,8,11},{2,4,9},{5},{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}}=>{{1,3,8,10},{2,4},{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}}=>{{1,3,5,8,10,12},{2},{4,6},{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}}=>{{1,3,5,8,11},{2},{4,6,12},{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}}=>{{1,3,5,9,12},{2},{4,6,10},{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}}=>{{1,3,5,9,11},{2,12},{4,6},{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}}=>{{1,3,5,10},{2,12},{4,6,11},{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}}=>{{1,3,5,7,10,12},{2},{4},{6,8},{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}}=>{{1,3,5,7,11},{2},{4},{6,8,12},{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}}=>{{1,3,5,7,9,12},{2},{4},{6},{8,10},{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}}=>{{1,3,5,7,9,11},{2},{4},{6},{8},{10,12}} [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}}=>{{1,3,5,7,10},{2,11},{4},{6},{8},{9,12}} [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}}=>{{1,3,5,8,12},{2,9},{4},{6},{7,10},{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}}=>{{1,3,5,8,11},{2,9},{4},{6},{7},{10,12}} [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}}=>{{1,3,5,8,10},{2},{4,11},{6},{7},{9,12}} [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}}=>{{1,3,5,9},{2,10},{4,11},{6},{7},{8,12}} [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}}=>{{1,3,6,10,12},{2,7},{4},{5,8},{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}}=>{{1,3,6,11},{2,7,12},{4},{5,8},{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}}=>{{1,3,6,9,12},{2,7},{4},{5},{8,10},{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}}=>{{1,3,6,9,11},{2,7},{4},{5},{8},{10,12}} [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}}=>{{1,3,6,10},{2,7,11},{4},{5},{8},{9,12}} [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}}=>{{1,3,6,8,12},{2},{4,9},{5},{7,10},{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}}=>{{1,3,6,8,11},{2},{4,9},{5},{7},{10,12}} [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}}=>{{1,3,6,8,10},{2},{4},{5,11},{7},{9,12}} [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}}=>{{1,3,6,9},{2,10},{4},{5,11},{7},{8,12}} [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}}=>{{1,3,7,12},{2,8},{4,9},{5},{6,10},{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}}=>{{1,3,7,11},{2,8},{4,9},{5},{6},{10,12}} [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}}=>{{1,3,7,10},{2,8},{4},{5,11},{6},{9,12}} [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}}=>{{1,3,7,9},{2},{4,10},{5,11},{6},{8,12}} [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}}=>{{1,3,8},{2,9},{4,10},{5,11},{6},{7,12}} [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}}=>{{1,4,8,10,12},{2,5},{3,6},{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}}=>{{1,4,8,11},{2,5,12},{3,6},{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}}=>{{1,4,9,12},{2,5,10},{3,6},{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}}=>{{1,4,9,11},{2,5},{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}}=>{{1,4,7,10,12},{2,5},{3},{6,8},{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}}=>{{1,4,7,11},{2,5,12},{3},{6,8},{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}}=>{{1,4,7,9,12},{2,5},{3},{6},{8,10},{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}}=>{{1,4,7,9,11},{2,5},{3},{6},{8},{10,12}} [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}}=>{{1,4,7,10},{2,5,11},{3},{6},{8},{9,12}} [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}}=>{{1,4,8,12},{2,5,9},{3},{6},{7,10},{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}}=>{{1,4,8,11},{2,5,9},{3},{6},{7},{10,12}} [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}}=>{{1,4,8,10},{2,5},{3,11},{6},{7},{9,12}} [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}}=>{{1,4,9},{2,5,10},{3,11},{6},{7},{8,12}} [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}}=>{{1,4,6,10,12},{2},{3,7},{5,8},{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}}=>{{1,4,6,11},{2},{3,7,12},{5,8},{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}}=>{{1,4,6,9,12},{2},{3,7},{5},{8,10},{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}}=>{{1,4,6,9,11},{2},{3,7},{5},{8},{10,12}} [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}}=>{{1,4,6,10},{2},{3,7,11},{5},{8},{9,12}} [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}}=>{{1,4,6,8,12},{2},{3},{5,9},{7,10},{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}}=>{{1,4,6,8,11},{2},{3},{5,9},{7},{10,12}} [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}}=>{{1,4,6,8,10},{2},{3},{5},{7,11},{9,12}} [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}}=>{{1,4,6,9},{2,10},{3},{5},{7,11},{8,12}} [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}}=>{{1,4,7,12},{2,8},{3},{5,9},{6,10},{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}}=>{{1,4,7,11},{2,8},{3},{5,9},{6},{10,12}} [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}}=>{{1,4,7,10},{2,8},{3},{5},{6,11},{9,12}} [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}}=>{{1,4,7,9},{2},{3,10},{5},{6,11},{8,12}} [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}}=>{{1,4,8},{2,9},{3,10},{5},{6,11},{7,12}} [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}}=>{{1,5,10,12},{2,6},{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}}=>{{1,5,9,12},{2,6},{3,7},{4},{8,10},{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}}=>{{1,5,9,11},{2,6},{3,7},{4},{8},{10,12}} [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}}=>{{1,5,10},{2,6,11},{3,7},{4},{8},{9,12}} [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}}=>{{1,5,8,12},{2,6},{3},{4,9},{7,10},{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}}=>{{1,5,8,11},{2,6},{3},{4,9},{7},{10,12}} [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}}=>{{1,5,8,10},{2,6},{3},{4},{7,11},{9,12}} [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}}=>{{1,5,9},{2,6,10},{3},{4},{7,11},{8,12}} [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}}=>{{1,5,7,12},{2},{3,8},{4,9},{6,10},{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}}=>{{1,5,7,11},{2},{3,8},{4,9},{6},{10,12}} [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}}=>{{1,5,7,10},{2},{3,8},{4},{6,11},{9,12}} [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}}=>{{1,5,7,9},{2},{3},{4,10},{6,11},{8,12}} [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}}=>{{1,5,8},{2,9},{3},{4,10},{6,11},{7,12}} [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}}=>{{1,6,11},{2,7},{3,8},{4,9},{5},{10,12}} [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}}=>{{1,6,10},{2,7},{3,8},{4},{5,11},{9,12}} [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}}=>{{1,6,9},{2,7},{3},{4,10},{5,11},{8,12}} [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}}=>{{1,6,8},{2},{3,9},{4,10},{5,11},{7,12}} [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}}=>{{1,2,4,6,8,10,12,14},{3},{5},{7},{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}}=>{{1,2,4,6,8,10,13},{3,14},{5},{7},{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}}=>{{1,2,4,6,8,11,13},{3},{5,14},{7},{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}}=>{{1,2,4,6,8,12},{3,13},{5,14},{7},{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}}=>{{1,2,4,6,9,11,13},{3},{5},{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}}=>{{1,2,4,6,10,13},{3,11},{5},{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}}=>{{1,2,4,6,10,12},{3},{5,13},{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}}=>{{1,2,4,6,11},{3,12},{5,13},{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}}=>{{1,2,4,7,9,11,13},{3},{5},{6},{8,14},{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}}=>{{1,2,4,8,11,13},{3,9},{5},{6},{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}}=>{{1,2,4,8,10,13},{3},{5,11},{6},{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}}=>{{1,2,4,8,10,12},{3},{5},{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}}=>{{1,2,4,8,11},{3,12},{5},{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}}=>{{1,2,4,9,13},{3,10},{5,11},{6},{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}}=>{{1,2,4,9,11},{3},{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}}=>{{1,2,5,7,9,11,13},{3},{4},{6},{8},{10,14},{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}}=>{{1,2,5,10},{3,11},{4,12},{6,13},{7},{8,14},{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}}=>{{1,2,6,9,11,13},{3,7},{4},{5},{8},{10,14},{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}}=>{{1,2,6,8,11,13},{3},{4,9},{5},{7},{10,14},{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}}=>{{1,2,6,8,10,13},{3},{4},{5,11},{7},{9,14},{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}}=>{{1,2,6,9,13},{3,10},{4},{5,11},{7},{8,14},{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}}=>{{1,2,6,9,11},{3},{4,12},{5},{7,13},{8,14},{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}}=>{{1,2,6,10},{3,11},{4,12},{5},{7,13},{8,14},{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}}=>{{1,2,7,11,13},{3,8},{4,9},{5},{6},{10,14},{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}}=>{{1,2,7,11},{3,8,12},{4},{5},{6,13},{9,14},{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}}=>{{1,2,7,9,13},{3},{4,10},{5,11},{6},{8,14},{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}}=>{{1,2,7,9,12},{3},{4,10},{5},{6,13},{8,14},{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}}=>{{1,2,7,9,11},{3},{4},{5,12},{6,13},{8,14},{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}}=>{{1,2,7,10},{3,11},{4},{5,12},{6,13},{8,14},{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}}=>{{1,2,8,13},{3,9},{4,10},{5,11},{6},{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}}=>{{1,2,8,12},{3,9},{4,10},{5},{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}}=>{{1,2,8,11},{3,9},{4},{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}}=>{{1,2,8,10},{3},{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}}=>{{1,3,5,7,9,11,13},{2},{4},{6},{8},{10},{12,14}} [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}}=>{{1,3,5,7,9,12},{2,13},{4},{6},{8},{10},{11,14}} [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}}=>{{1,3,5,7,10,13},{2,11},{4},{6},{8},{9},{12,14}} [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}}=>{{1,3,5,7,10,12},{2},{4,13},{6},{8},{9},{11,14}} [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}}=>{{1,3,5,7,11},{2,12},{4,13},{6},{8},{9},{10,14}} [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}}=>{{1,3,5,8,11,13},{2,9},{4},{6},{7},{10},{12,14}} [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}}=>{{1,3,5,8,12},{2,9,13},{4},{6},{7},{10},{11,14}} [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}}=>{{1,3,5,8,10,13},{2},{4,11},{6},{7},{9},{12,14}} [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}}=>{{1,3,5,8,10,12},{2},{4},{6,13},{7},{9},{11,14}} [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}}=>{{1,3,5,8,11},{2,12},{4},{6,13},{7},{9},{10,14}} [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}}=>{{1,3,5,9,13},{2,10},{4,11},{6},{7},{8},{12,14}} [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}}=>{{1,3,5,9,12},{2,10},{4},{6,13},{7},{8},{11,14}} [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}}=>{{1,3,5,9,11},{2},{4,12},{6,13},{7},{8},{10,14}} [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}}=>{{1,3,5,10},{2,11},{4,12},{6,13},{7},{8},{9,14}} [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}}=>{{1,3,6,9,11,13},{2,7},{4},{5},{8},{10},{12,14}} [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}}=>{{1,3,6,9,12},{2,7,13},{4},{5},{8},{10},{11,14}} [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}}=>{{1,3,6,10,13},{2,7,11},{4},{5},{8},{9},{12,14}} [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}}=>{{1,3,6,10,12},{2,7},{4,13},{5},{8},{9},{11,14}} [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}}=>{{1,3,6,11},{2,7,12},{4,13},{5},{8},{9},{10,14}} [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}}=>{{1,3,6,8,11,13},{2},{4,9},{5},{7},{10},{12,14}} [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}}=>{{1,3,6,8,12},{2},{4,9,13},{5},{7},{10},{11,14}} [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}}=>{{1,3,6,8,10,13},{2},{4},{5,11},{7},{9},{12,14}} [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}}=>{{1,3,6,8,10,12},{2},{4},{5},{7,13},{9},{11,14}} [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}}=>{{1,3,6,8,11},{2,12},{4},{5},{7,13},{9},{10,14}} [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}}=>{{1,3,6,9,13},{2,10},{4},{5,11},{7},{8},{12,14}} [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}}=>{{1,3,6,9,12},{2,10},{4},{5},{7,13},{8},{11,14}} [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}}=>{{1,3,6,9,11},{2},{4,12},{5},{7,13},{8},{10,14}} [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}}=>{{1,3,6,10},{2,11},{4,12},{5},{7,13},{8},{9,14}} [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}}=>{{1,3,7,11,13},{2,8},{4,9},{5},{6},{10},{12,14}} [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}}=>{{1,3,7,12},{2,8,13},{4,9},{5},{6},{10},{11,14}} [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}}=>{{1,3,7,10,13},{2,8},{4},{5,11},{6},{9},{12,14}} [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}}=>{{1,3,7,10,12},{2,8},{4},{5},{6,13},{9},{11,14}} [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}}=>{{1,3,7,11},{2,8,12},{4},{5},{6,13},{9},{10,14}} [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}}=>{{1,3,7,9,13},{2},{4,10},{5,11},{6},{8},{12,14}} [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}}=>{{1,3,7,9,12},{2},{4,10},{5},{6,13},{8},{11,14}} [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}}=>{{1,3,7,9,11},{2},{4},{5,12},{6,13},{8},{10,14}} [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}}=>{{1,3,7,10},{2,11},{4},{5,12},{6,13},{8},{9,14}} [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}}=>{{1,3,8,14},{2,9},{4,10},{5,11},{6},{7,12},{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}}=>{{1,3,8,13},{2,9},{4,10},{5,11},{6},{7},{12,14}} [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}}=>{{1,3,8,12},{2,9},{4,10},{5},{6,13},{7},{11,14}} [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}}=>{{1,3,8,11},{2,9},{4},{5,12},{6,13},{7},{10,14}} [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}}=>{{1,3,8,10},{2},{4,11},{5,12},{6,13},{7},{9,14}} [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}}=>{{1,3,9},{2,10},{4,11},{5,12},{6,13},{7},{8,14}} [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}}=>{{1,4,7,9,11,13},{2,5},{3},{6},{8},{10},{12,14}} [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}}=>{{1,4,7,9,12},{2,5,13},{3},{6},{8},{10},{11,14}} [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}}=>{{1,4,7,10,13},{2,5,11},{3},{6},{8},{9},{12,14}} [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}}=>{{1,4,7,10,12},{2,5},{3,13},{6},{8},{9},{11,14}} [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}}=>{{1,4,7,11},{2,5,12},{3,13},{6},{8},{9},{10,14}} [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}}=>{{1,4,8,11,13},{2,5,9},{3},{6},{7},{10},{12,14}} [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}}=>{{1,4,8,12},{2,5,9,13},{3},{6},{7},{10},{11,14}} [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}}=>{{1,4,8,10,13},{2,5},{3,11},{6},{7},{9},{12,14}} [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}}=>{{1,4,8,10,12},{2,5},{3},{6,13},{7},{9},{11,14}} [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}}=>{{1,4,8,11},{2,5,12},{3},{6,13},{7},{9},{10,14}} [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}}=>{{1,4,9,13},{2,5,10},{3,11},{6},{7},{8},{12,14}} [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}}=>{{1,4,9,12},{2,5,10},{3},{6,13},{7},{8},{11,14}} [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}}=>{{1,4,9,11},{2,5},{3,12},{6,13},{7},{8},{10,14}} [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}}=>{{1,4,10},{2,5,11},{3,12},{6,13},{7},{8},{9,14}} [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}}=>{{1,4,6,9,11,13},{2},{3,7},{5},{8},{10},{12,14}} [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}}=>{{1,4,6,9,12},{2},{3,7,13},{5},{8},{10},{11,14}} [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}}=>{{1,4,6,10,13},{2},{3,7,11},{5},{8},{9},{12,14}} [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}}=>{{1,4,6,10,12},{2,13},{3,7},{5},{8},{9},{11,14}} [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}}=>{{1,4,6,11},{2,13},{3,7,12},{5},{8},{9},{10,14}} [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}}=>{{1,4,6,8,11,13},{2},{3},{5,9},{7},{10},{12,14}} [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}}=>{{1,4,6,8,12},{2},{3},{5,9,13},{7},{10},{11,14}} [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}}=>{{1,4,6,8,10,13},{2},{3},{5},{7,11},{9},{12,14}} [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}}=>{{1,4,6,8,10,12},{2},{3},{5},{7},{9,13},{11,14}} [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}}=>{{1,4,6,8,11},{2,12},{3},{5},{7},{9,13},{10,14}} [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}}=>{{1,4,6,9,13},{2,10},{3},{5},{7,11},{8},{12,14}} [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}}=>{{1,4,6,9,12},{2,10},{3},{5},{7},{8,13},{11,14}} [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}}=>{{1,4,6,9,11},{2},{3,12},{5},{7},{8,13},{10,14}} [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}}=>{{1,4,6,10},{2,11},{3,12},{5},{7},{8,13},{9,14}} [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}}=>{{1,4,7,11,13},{2,8},{3},{5,9},{6},{10},{12,14}} [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}}=>{{1,4,7,12},{2,8,13},{3},{5,9},{6},{10},{11,14}} [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}}=>{{1,4,7,10,13},{2,8},{3},{5},{6,11},{9},{12,14}} [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}}=>{{1,4,7,10,12},{2,8},{3},{5},{6},{9,13},{11,14}} [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}}=>{{1,4,7,11},{2,8,12},{3},{5},{6},{9,13},{10,14}} [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}}=>{{1,4,7,9,14},{2},{3,10},{5},{6,11},{8,12},{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}}=>{{1,4,7,9,13},{2},{3,10},{5},{6,11},{8},{12,14}} [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}}=>{{1,4,7,9,12},{2},{3,10},{5},{6},{8,13},{11,14}} [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}}=>{{1,4,7,9,11},{2},{3},{5,12},{6},{8,13},{10,14}} [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}}=>{{1,4,7,10},{2,11},{3},{5,12},{6},{8,13},{9,14}} [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}}=>{{1,4,8,14},{2,9},{3,10},{5},{6,11},{7,12},{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}}=>{{1,4,8,13},{2,9},{3,10},{5},{6,11},{7},{12,14}} [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}}=>{{1,4,8,12},{2,9},{3,10},{5},{6},{7,13},{11,14}} [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}}=>{{1,4,8,11},{2,9},{3},{5,12},{6},{7,13},{10,14}} [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}}=>{{1,4,8,10},{2},{3,11},{5,12},{6},{7,13},{9,14}} [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}}=>{{1,4,9},{2,10},{3,11},{5,12},{6},{7,13},{8,14}} [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}}=>{{1,5,9,11,13},{2,6},{3,7},{4},{8},{10},{12,14}} [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}}=>{{1,5,9,12},{2,6,13},{3,7},{4},{8},{10},{11,14}} [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}}=>{{1,5,10,13},{2,6,11},{3,7},{4},{8},{9},{12,14}} [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}}=>{{1,5,10,12},{2,6},{3,7,13},{4},{8},{9},{11,14}} [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}}=>{{1,5,11},{2,6,12},{3,7,13},{4},{8},{9},{10,14}} [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}}=>{{1,5,8,11,13},{2,6},{3},{4,9},{7},{10},{12,14}} [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}}=>{{1,5,8,12},{2,6,13},{3},{4,9},{7},{10},{11,14}} [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}}=>{{1,5,8,10,13},{2,6},{3},{4},{7,11},{9},{12,14}} [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}}=>{{1,5,8,10,12},{2,6},{3},{4},{7},{9,13},{11,14}} [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}}=>{{1,5,8,11},{2,6,12},{3},{4},{7},{9,13},{10,14}} [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}}=>{{1,5,9,14},{2,6,10},{3},{4},{7,11},{8,12},{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}}=>{{1,5,9,13},{2,6,10},{3},{4},{7,11},{8},{12,14}} [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}}=>{{1,5,9,12},{2,6,10},{3},{4},{7},{8,13},{11,14}} [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}}=>{{1,5,9,11},{2,6},{3,12},{4},{7},{8,13},{10,14}} [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}}=>{{1,5,10},{2,6,11},{3,12},{4},{7},{8,13},{9,14}} [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}}=>{{1,5,7,11,13},{2},{3,8},{4,9},{6},{10},{12,14}} [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}}=>{{1,5,7,12},{2},{3,8,13},{4,9},{6},{10},{11,14}} [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}}=>{{1,5,7,10,14},{2},{3,8},{4},{6,11},{9,12},{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}}=>{{1,5,7,10,13},{2},{3,8},{4},{6,11},{9},{12,14}} [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}}=>{{1,5,7,10,12},{2},{3,8},{4},{6},{9,13},{11,14}} [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}}=>{{1,5,7,11},{2},{3,8,12},{4},{6},{9,13},{10,14}} [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}}=>{{1,5,7,9,14},{2},{3},{4,10},{6,11},{8,12},{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}}=>{{1,5,7,9,13},{2},{3},{4,10},{6,11},{8},{12,14}} [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}}=>{{1,5,7,9,12},{2},{3},{4,10},{6},{8,13},{11,14}} [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}}=>{{1,5,7,9,11},{2},{3},{4},{6,12},{8,13},{10,14}} [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}}=>{{1,5,7,10},{2,11},{3},{4},{6,12},{8,13},{9,14}} [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}}=>{{1,5,8,14},{2,9},{3},{4,10},{6,11},{7,12},{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}}=>{{1,5,8,13},{2,9},{3},{4,10},{6,11},{7},{12,14}} [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}}=>{{1,5,8,12},{2,9},{3},{4,10},{6},{7,13},{11,14}} [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}}=>{{1,5,8,11},{2,9},{3},{4},{6,12},{7,13},{10,14}} [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}}=>{{1,5,8,10},{2},{3,11},{4},{6,12},{7,13},{9,14}} [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}}=>{{1,5,9},{2,10},{3,11},{4},{6,12},{7,13},{8,14}} [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}}=>{{1,6,11,14},{2,7},{3,8},{4,9},{5},{10,12},{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}}=>{{1,6,11,13},{2,7},{3,8},{4,9},{5},{10},{12,14}} [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}}=>{{1,6,12},{2,7,13},{3,8},{4,9},{5},{10},{11,14}} [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}}=>{{1,6,10,14},{2,7},{3,8},{4},{5,11},{9,12},{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}}=>{{1,6,10,13},{2,7},{3,8},{4},{5,11},{9},{12,14}} [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}}=>{{1,6,10,12},{2,7},{3,8},{4},{5},{9,13},{11,14}} [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}}=>{{1,6,11},{2,7,12},{3,8},{4},{5},{9,13},{10,14}} [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}}=>{{1,6,9,14},{2,7},{3},{4,10},{5,11},{8,12},{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}}=>{{1,6,9,13},{2,7},{3},{4,10},{5,11},{8},{12,14}} [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}}=>{{1,6,9,12},{2,7},{3},{4,10},{5},{8,13},{11,14}} [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}}=>{{1,6,9,11},{2,7},{3},{4},{5,12},{8,13},{10,14}} [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}}=>{{1,6,10},{2,7,11},{3},{4},{5,12},{8,13},{9,14}} [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}}=>{{1,6,8,14},{2},{3,9},{4,10},{5,11},{7,12},{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}}=>{{1,6,8,13},{2},{3,9},{4,10},{5,11},{7},{12,14}} [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}}=>{{1,6,8,12},{2},{3,9},{4,10},{5},{7,13},{11,14}} [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}}=>{{1,6,8,11},{2},{3,9},{4},{5,12},{7,13},{10,14}} [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}}=>{{1,6,8,10},{2},{3},{4,11},{5,12},{7,13},{9,14}} [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}}=>{{1,6,9},{2,10},{3},{4,11},{5,12},{7,13},{8,14}} [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}}=>{{1,7,13},{2,8},{3,9},{4,10},{5,11},{6},{12,14}} [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}}=>{{1,7,12},{2,8},{3,9},{4,10},{5},{6,13},{11,14}} [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}}=>{{1,7,11},{2,8},{3,9},{4},{5,12},{6,13},{10,14}} [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}}=>{{1,7,10},{2,8},{3},{4,11},{5,12},{6,13},{9,14}} [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}}=>{{1,7,9},{2},{3,10},{4,11},{5,12},{6,13},{8,14}} [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}}=>{{1,2,4,6,8,10,12,14,16},{3},{5},{7},{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}}=>{{1,2,4,6,8,10,12,15},{3,16},{5},{7},{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}}=>{{1,2,4,6,8,10,13,15},{3},{5,16},{7},{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}}=>{{1,2,4,6,8,10,14},{3,15},{5,16},{7},{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}}=>{{1,2,4,6,8,11,13,15},{3},{5},{7,16},{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}}=>{{1,2,4,6,8,12,15},{3,13},{5},{7,16},{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}}=>{{1,2,4,6,8,12,14},{3},{5,15},{7,16},{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}}=>{{1,2,4,6,8,13},{3,14},{5,15},{7,16},{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}}=>{{1,2,4,6,9,11,13,15},{3},{5},{7},{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}}=>{{1,2,4,6,10,13,15},{3,11},{5},{7},{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}}=>{{1,2,4,6,10,12,15},{3},{5,13},{7},{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}}=>{{1,2,4,6,11,15},{3,12},{5,13},{7},{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}}=>{{1,2,4,7,9,11,13,15},{3},{5},{6},{8},{10,16},{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}}=>{{1,2,4,8,11,13,15},{3,9},{5},{6},{7},{10,16},{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}}=>{{1,2,4,8,10,13,15},{3},{5,11},{6},{7},{9,16},{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}}=>{{1,2,4,9,13,15},{3,10},{5,11},{6},{7},{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}}=>{{1,2,5,7,9,11,13,15},{3},{4},{6},{8},{10},{12,16},{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}}=>{{1,2,6,9,11,13,15},{3,7},{4},{5},{8},{10},{12,16},{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}}=>{{1,2,6,8,11,13,15},{3},{4,9},{5},{7},{10},{12,16},{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}}=>{{1,2,7,11,13,15},{3,8},{4,9},{5},{6},{10},{12,16},{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}}=>{{1,2,7,11},{3,12},{4,13},{5},{6,14},{8,15},{9,16},{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}}=>{{1,2,8,10,12},{3},{4},{5,13},{6,14},{7,15},{9,16},{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}}=>{{1,2,8,11},{3,12},{4},{5,13},{6,14},{7,15},{9,16},{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}}=>{{1,2,9,13},{3,10},{4,11},{5},{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}}=>{{1,2,9,12},{3,10},{4},{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}}=>{{1,2,9,11},{3},{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}}=>{{1,3,5,7,9,11,13,15},{2},{4},{6},{8},{10},{12},{14,16}} [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}}=>{{1,4,7,9,11,13,15},{2,5},{3},{6},{8},{10},{12},{14,16}} [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}}=>{{1,4,6,9,11,13,15},{2},{3,7},{5},{8},{10},{12},{14,16}} [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}}=>{{1,5,9,11,13,15},{2,6},{3,7},{4},{8},{10},{12},{14,16}} [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}}=>{{1,5,9,16},{2,10},{3,11},{4},{6,12},{7,13},{8,14},{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}}=>{{1,6,8,10,16},{2},{3},{4,11},{5,12},{7,13},{9,14},{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}}=>{{1,6,9,16},{2,10},{3},{4,11},{5,12},{7,13},{8,14},{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}}=>{{1,7,11,16},{2,8},{3,9},{4},{5,12},{6,13},{10,14},{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}}=>{{1,7,10,16},{2,8},{3},{4,11},{5,12},{6,13},{9,14},{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}}=>{{1,7,9,16},{2},{3,10},{4,11},{5,12},{6,13},{8,14},{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}}=>{{1,8,10,18},{2},{3,11},{4,12},{5,13},{6,14},{7,15},{9,16},{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}}=>{{1,2,10,12},{3},{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}}=>{{1,9,11,20},{2},{3,12},{4,13},{5,14},{6,15},{7,16},{8,17},{10,18},{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}}=>{{1,8,11,18},{2,9},{3},{4,12},{5,13},{6,14},{7,15},{10,16},{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}}=>{{1,7,10,18},{2,11},{3},{4,12},{5,13},{6,14},{8,15},{9,16},{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}}=>{{1,2,10,13},{3,11},{4},{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}}=>{{1,2,9,12},{3,13},{4},{5,14},{6,15},{7,16},{8,17},{10,18},{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}}=>{{1,2,11,13},{3},{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}}=>{{1,3,5,7,9,11,13,15,17},{2},{4},{6},{8},{10},{12},{14},{16,18}} [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}}=>{{1,4,7,9,11,13,15,17},{2,5},{3},{6},{8},{10},{12},{14},{16,18}} [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}}=>{{1,2,4,6,8,10,12,14,16,18},{3},{5},{7},{9},{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}}=>{{1,2,4,6,8,10,12,14,17},{3,18},{5},{7},{9},{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}}=>{{1,2,4,6,8,10,12,15,17},{3},{5,18},{7},{9},{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}}=>{{1,2,4,6,8,10,13,15,17},{3},{5},{7,18},{9},{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}}=>{{1,2,4,6,8,11,13,15,17},{3},{5},{7},{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}}=>{{1,2,4,6,9,11,13,15,17},{3},{5},{7},{8},{10,18},{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}}=>{{1,2,4,7,9,11,13,15,17},{3},{5},{6},{8},{10},{12,18},{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}}=>{{1,2,5,7,9,11,13,15,17},{3},{4},{6},{8},{10},{12},{14,18},{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}}=>{{1,2,4,6,8,10,12,14,16,18,20},{3},{5},{7},{9},{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}}=>{{1,2,4,6,8,10,12,14,16,19},{3,20},{5},{7},{9},{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}}=>{{1,2,4,6,8,10,12,16},{3,17},{5,18},{7},{9},{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}}=>{{1,2,4,6,8,10,12,14,17,19},{3},{5,20},{7},{9},{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}}=>{{1,2,4,6,8,10,14,17},{3,15},{5},{7,18},{9},{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}}=>{{1,2,4,6,8,10,12,15,17,19},{3},{5},{7,20},{9},{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}}=>{{1,2,4,6,8,12,15,17},{3,13},{5},{7},{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}}=>{{1,2,4,6,8,10,13,15,17,19},{3},{5},{7},{9,20},{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}}=>{{1,2,4,6,10,13,15,17},{3,11},{5},{7},{8},{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}}=>{{1,2,4,6,8,11,13,15,17,19},{3},{5},{7},{9},{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}}=>{{1,2,4,8,11,13,15,17},{3,9},{5},{6},{7},{10},{12,18},{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}}=>{{1,2,4,6,9,11,13,15,17,19},{3},{5},{7},{8},{10},{12,20},{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}}=>{{1,2,6,9,11,13,15,17},{3,7},{4},{5},{8},{10},{12},{14,18},{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}}=>{{1,2,4,7,9,11,13,15,17,19},{3},{5},{6},{8},{10},{12},{14,20},{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}}=>{{1,2,5,7,9,11,13,15,17,19},{3},{4},{6},{8},{10},{12},{14},{16,20},{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}}=>{{1,3,5,7,9,11,13,15,17,19},{2},{4},{6},{8},{10},{12},{14},{16},{18,20}}
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
Yip
Description
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 $\psi$.