Identifier
Mp00231: Integer compositions bounce pathDyck paths
Mp00138: Dyck paths to noncrossing partitionSet partitions
Mp00220: Set partitions Yip Set partitions
Images
=>
Cc0005;cc-rep-1Cc0009;cc-rep-2Cc0009;cc-rep-3
[1]=>[1,0]=>{{1}}=>{{1}} [1,1]=>[1,0,1,0]=>{{1},{2}}=>{{1},{2}} [2]=>[1,1,0,0]=>{{1,2}}=>{{1,2}} [1,1,1]=>[1,0,1,0,1,0]=>{{1},{2},{3}}=>{{1},{2},{3}} [1,2]=>[1,0,1,1,0,0]=>{{1},{2,3}}=>{{1,3},{2}} [2,1]=>[1,1,0,0,1,0]=>{{1,2},{3}}=>{{1,2},{3}} [3]=>[1,1,1,0,0,0]=>{{1,2,3}}=>{{1,2,3}} [1,1,1,1]=>[1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4}}=>{{1},{2},{3},{4}} [1,1,2]=>[1,0,1,0,1,1,0,0]=>{{1},{2},{3,4}}=>{{1,4},{2},{3}} [1,2,1]=>[1,0,1,1,0,0,1,0]=>{{1},{2,3},{4}}=>{{1,3},{2},{4}} [1,3]=>[1,0,1,1,1,0,0,0]=>{{1},{2,3,4}}=>{{1,3,4},{2}} [2,1,1]=>[1,1,0,0,1,0,1,0]=>{{1,2},{3},{4}}=>{{1,2},{3},{4}} [2,2]=>[1,1,0,0,1,1,0,0]=>{{1,2},{3,4}}=>{{1,2,4},{3}} [3,1]=>[1,1,1,0,0,0,1,0]=>{{1,2,3},{4}}=>{{1,2,3},{4}} [4]=>[1,1,1,1,0,0,0,0]=>{{1,2,3,4}}=>{{1,2,3,4}} [1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5}}=>{{1},{2},{3},{4},{5}} [1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4,5}}=>{{1,5},{2},{3},{4}} [1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5}}=>{{1,4},{2},{3},{5}} [1,1,3]=>[1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3,4,5}}=>{{1,4,5},{2},{3}} [1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4},{5}}=>{{1,3},{2},{4},{5}} [1,2,2]=>[1,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5}}=>{{1,3,5},{2},{4}} [1,3,1]=>[1,0,1,1,1,0,0,0,1,0]=>{{1},{2,3,4},{5}}=>{{1,3,4},{2},{5}} [1,4]=>[1,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4,5}}=>{{1,3,4,5},{2}} [2,1,1,1]=>[1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5}}=>{{1,2},{3},{4},{5}} [2,1,2]=>[1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3},{4,5}}=>{{1,2,5},{3},{4}} [2,2,1]=>[1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5}}=>{{1,2,4},{3},{5}} [2,3]=>[1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5}}=>{{1,2,4,5},{3}} [3,1,1]=>[1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4},{5}}=>{{1,2,3},{4},{5}} [3,2]=>[1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5}}=>{{1,2,3,5},{4}} [4,1]=>[1,1,1,1,0,0,0,0,1,0]=>{{1,2,3,4},{5}}=>{{1,2,3,4},{5}} [5]=>[1,1,1,1,1,0,0,0,0,0]=>{{1,2,3,4,5}}=>{{1,2,3,4,5}} [1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6}}=>{{1},{2},{3},{4},{5},{6}} [1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6}}=>{{1,6},{2},{3},{4},{5}} [1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6}}=>{{1,5},{2},{3},{4},{6}} [1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5,6}}=>{{1,5,6},{2},{3},{4}} [1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6}}=>{{1,4},{2},{3},{5},{6}} [1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6}}=>{{1,4,6},{2},{3},{5}} [1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3,4,5},{6}}=>{{1,4,5},{2},{3},{6}} [1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3,4,5,6}}=>{{1,4,5,6},{2},{3}} [1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6}}=>{{1,3},{2},{4},{5},{6}} [1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5,6}}=>{{1,3,6},{2},{4},{5}} [1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6}}=>{{1,3,5},{2},{4},{6}} [1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}}=>{{1,3,5,6},{2},{4}} [1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2,3,4},{5},{6}}=>{{1,3,4},{2},{5},{6}} [1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}}=>{{1,3,4,6},{2},{5}} [1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2,3,4,5},{6}}=>{{1,3,4,5},{2},{6}} [1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3,4,5,6}}=>{{1,3,4,5,6},{2}} [2,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6}}=>{{1,2},{3},{4},{5},{6}} [2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5,6}}=>{{1,2,6},{3},{4},{5}} [2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4,5},{6}}=>{{1,2,5},{3},{4},{6}} [2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5,6}}=>{{1,2,5,6},{3},{4}} [2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>{{1,2},{3,4},{5},{6}}=>{{1,2,4},{3},{5},{6}} [2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6}}=>{{1,2,4,6},{3},{5}} [2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>{{1,2},{3,4,5},{6}}=>{{1,2,4,5},{3},{6}} [2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6}}=>{{1,2,4,5,6},{3}} [3,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6}}=>{{1,2,3},{4},{5},{6}} [3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5,6}}=>{{1,2,3,6},{4},{5}} [3,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6}}=>{{1,2,3,5},{4},{6}} [3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5,6}}=>{{1,2,3,5,6},{4}} [4,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>{{1,2,3,4},{5},{6}}=>{{1,2,3,4},{5},{6}} [4,2]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2,3,4},{5,6}}=>{{1,2,3,4,6},{5}} [5,1]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2,3,4,5},{6}}=>{{1,2,3,4,5},{6}} [6]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}}=>{{1,2,3,4,5,6}} [1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7}}=>{{1},{2},{3},{4},{5},{6},{7}} [1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6,7}}=>{{1,7},{2},{3},{4},{5},{6}} [1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5,6},{7}}=>{{1,6},{2},{3},{4},{5},{7}} [1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6,7}}=>{{1,6,7},{2},{3},{4},{5}} [1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3},{4,5},{6},{7}}=>{{1,5},{2},{3},{4},{6},{7}} [1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4,5},{6,7}}=>{{1,5,7},{2},{3},{4},{6}} [1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3},{4,5,6},{7}}=>{{1,5,6},{2},{3},{4},{7}} [1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4,5,6,7}}=>{{1,5,6,7},{2},{3},{4}} [1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6},{7}}=>{{1,4},{2},{3},{5},{6},{7}} [1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2},{3,4},{5},{6,7}}=>{{1,4,7},{2},{3},{5},{6}} [1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5,6},{7}}=>{{1,4,6},{2},{3},{5},{7}} [1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4},{5,6,7}}=>{{1,4,6,7},{2},{3},{5}} [1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2},{3,4,5},{6},{7}}=>{{1,4,5},{2},{3},{6},{7}} [1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7}}=>{{1,4,5,7},{2},{3},{6}} [1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2},{3,4,5,6},{7}}=>{{1,4,5,6},{2},{3},{7}} [1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7}}=>{{1,4,5,6,7},{2},{3}} [1,2,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6},{7}}=>{{1,3},{2},{4},{5},{6},{7}} [1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5},{6,7}}=>{{1,3,7},{2},{4},{5},{6}} [1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>{{1},{2,3},{4},{5,6},{7}}=>{{1,3,6},{2},{4},{5},{7}} [1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5,6,7}}=>{{1,3,6,7},{2},{4},{5}} [1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7}}=>{{1,3,5},{2},{4},{6},{7}} [1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>{{1,3,5,7},{2},{4},{6}} [1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4,5,6},{7}}=>{{1,3,5,6},{2},{4},{7}} [1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>{{1,3,5,6,7},{2},{4}} [1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>{{1},{2,3,4},{5},{6},{7}}=>{{1,3,4},{2},{5},{6},{7}} [1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4},{5},{6,7}}=>{{1,3,4,7},{2},{5},{6}} [1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5,6},{7}}=>{{1,3,4,6},{2},{5},{7}} [1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>{{1,3,4,6,7},{2},{5}} [1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7}}=>{{1,3,4,5},{2},{6},{7}} [1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>{{1,3,4,5,7},{2},{6}} [1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6},{7}}=>{{1,3,4,5,6},{2},{7}} [1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}}=>{{1,3,4,5,6,7},{2}} [2,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6},{7}}=>{{1,2},{3},{4},{5},{6},{7}} [2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5},{6,7}}=>{{1,2,7},{3},{4},{5},{6}} [2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4},{5,6},{7}}=>{{1,2,6},{3},{4},{5},{7}} [2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4},{5,6,7}}=>{{1,2,6,7},{3},{4},{5}} [2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>{{1,2},{3},{4,5},{6},{7}}=>{{1,2,5},{3},{4},{6},{7}} [2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2},{3},{4,5},{6,7}}=>{{1,2,5,7},{3},{4},{6}} [2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>{{1,2},{3},{4,5,6},{7}}=>{{1,2,5,6},{3},{4},{7}} [2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2},{3},{4,5,6,7}}=>{{1,2,5,6,7},{3},{4}} [2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7}}=>{{1,2,4},{3},{5},{6},{7}} [2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3,4},{5},{6,7}}=>{{1,2,4,7},{3},{5},{6}} [2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5,6},{7}}=>{{1,2,4,6},{3},{5},{7}} [2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>{{1,2,4,6,7},{3},{5}} [2,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2},{3,4,5},{6},{7}}=>{{1,2,4,5},{3},{6},{7}} [2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>{{1,2,4,5,7},{3},{6}} [2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3,4,5,6},{7}}=>{{1,2,4,5,6},{3},{7}} [2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>{{1,2,4,5,6,7},{3}} [3,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6},{7}}=>{{1,2,3},{4},{5},{6},{7}} [3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5},{6,7}}=>{{1,2,3,7},{4},{5},{6}} [3,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>{{1,2,3},{4},{5,6},{7}}=>{{1,2,3,6},{4},{5},{7}} [3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1,2,3},{4},{5,6,7}}=>{{1,2,3,6,7},{4},{5}} [3,2,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>{{1,2,3},{4,5},{6},{7}}=>{{1,2,3,5},{4},{6},{7}} [3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}}=>{{1,2,3,5,7},{4},{6}} [3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3},{4,5,6},{7}}=>{{1,2,3,5,6},{4},{7}} [3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>{{1,2,3,5,6,7},{4}} [4,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>{{1,2,3,4},{5},{6},{7}}=>{{1,2,3,4},{5},{6},{7}} [4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1,2,3,4},{5},{6,7}}=>{{1,2,3,4,7},{5},{6}} [4,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4},{5,6},{7}}=>{{1,2,3,4,6},{5},{7}} [4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>{{1,2,3,4,6,7},{5}} [5,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,5},{6},{7}}=>{{1,2,3,4,5},{6},{7}} [5,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5},{6,7}}=>{{1,2,3,4,5,7},{6}} [6,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}}=>{{1,2,3,4,5,6},{7}} [7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}}=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7},{8}}=>{{1},{2},{3},{4},{5},{6},{7},{8}} [1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6},{7,8}}=>{{1,8},{2},{3},{4},{5},{6},{7}} [1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5},{6,7},{8}}=>{{1,7},{2},{3},{4},{5},{6},{8}} [1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5},{6,7,8}}=>{{1,7,8},{2},{3},{4},{5},{6}} [1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3},{4},{5,6},{7},{8}}=>{{1,6},{2},{3},{4},{5},{7},{8}} [1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6},{7,8}}=>{{1,6,8},{2},{3},{4},{5},{7}} [1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3},{4},{5,6,7},{8}}=>{{1,6,7},{2},{3},{4},{5},{8}} [1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4},{5,6,7,8}}=>{{1,6,7,8},{2},{3},{4},{5}} [1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2},{3},{4,5},{6},{7},{8}}=>{{1,5},{2},{3},{4},{6},{7},{8}} [1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2},{3},{4,5},{6},{7,8}}=>{{1,5,8},{2},{3},{4},{6},{7}} [1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6,7},{8}}=>{{1,5,7},{2},{3},{4},{6},{8}} [1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5},{6,7,8}}=>{{1,5,7,8},{2},{3},{4},{6}} [1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2},{3},{4,5,6},{7},{8}}=>{{1,5,6},{2},{3},{4},{7},{8}} [1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4,5,6},{7,8}}=>{{1,5,6,8},{2},{3},{4},{7}} [1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2},{3},{4,5,6,7},{8}}=>{{1,5,6,7},{2},{3},{4},{8}} [1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3},{4,5,6,7,8}}=>{{1,5,6,7,8},{2},{3},{4}} [1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3,4},{5},{6},{7,8}}=>{{1,4,8},{2},{3},{5},{6},{7}} [1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3,4},{5,6},{7},{8}}=>{{1,4,6},{2},{3},{5},{7},{8}} [1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8}}=>{{1,4,6,8},{2},{3},{5},{7}} [1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3,4},{5,6,7,8}}=>{{1,4,6,7,8},{2},{3},{5}} [1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>{{1},{2},{3,4,5},{6},{7},{8}}=>{{1,4,5},{2},{3},{6},{7},{8}} [1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4,5},{6,7,8}}=>{{1,4,5,7,8},{2},{3},{6}} [1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5,6},{7,8}}=>{{1,4,5,6,8},{2},{3},{7}} [1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2},{3,4,5,6,7},{8}}=>{{1,4,5,6,7},{2},{3},{8}} [1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8}}=>{{1,4,5,6,7,8},{2},{3}} [1,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6},{7},{8}}=>{{1,3},{2},{4},{5},{6},{7},{8}} [1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5},{6},{7,8}}=>{{1,3,8},{2},{4},{5},{6},{7}} [1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2,3},{4},{5},{6,7},{8}}=>{{1,3,7},{2},{4},{5},{6},{8}} [1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5},{6,7,8}}=>{{1,3,7,8},{2},{4},{5},{6}} [1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4},{5,6,7,8}}=>{{1,3,6,7,8},{2},{4},{5}} [1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7},{8}}=>{{1,3,5},{2},{4},{6},{7},{8}} [1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8}}=>{{1,3,5,7},{2},{4},{6},{8}} [1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7,8}}=>{{1,3,5,7,8},{2},{4},{6}} [1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2,3},{4,5,6},{7},{8}}=>{{1,3,5,6},{2},{4},{7},{8}} [1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3},{4,5,6},{7,8}}=>{{1,3,5,6,8},{2},{4},{7}} [1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2,3},{4,5,6,7},{8}}=>{{1,3,5,6,7},{2},{4},{8}} [1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8}}=>{{1,3,5,6,7,8},{2},{4}} [1,3,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>{{1},{2,3,4},{5},{6},{7},{8}}=>{{1,3,4},{2},{5},{6},{7},{8}} [1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5},{6,7},{8}}=>{{1,3,4,7},{2},{5},{6},{8}} [1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5},{6,7,8}}=>{{1,3,4,7,8},{2},{5},{6}} [1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6},{7,8}}=>{{1,3,4,6,8},{2},{5},{7}} [1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3,4},{5,6,7},{8}}=>{{1,3,4,6,7},{2},{5},{8}} [1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8}}=>{{1,3,4,6,7,8},{2},{5}} [1,4,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7},{8}}=>{{1,3,4,5},{2},{6},{7},{8}} [1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4,5},{6},{7,8}}=>{{1,3,4,5,8},{2},{6},{7}} [1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4,5},{6,7},{8}}=>{{1,3,4,5,7},{2},{6},{8}} [1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4,5},{6,7,8}}=>{{1,3,4,5,7,8},{2},{6}} [1,5,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>{{1},{2,3,4,5,6},{7},{8}}=>{{1,3,4,5,6},{2},{7},{8}} [1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6},{7,8}}=>{{1,3,4,5,6,8},{2},{7}} [1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7},{8}}=>{{1,3,4,5,6,7},{2},{8}} [1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8}}=>{{1,3,4,5,6,7,8},{2}} [2,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6},{7},{8}}=>{{1,2},{3},{4},{5},{6},{7},{8}} [2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5},{6},{7,8}}=>{{1,2,8},{3},{4},{5},{6},{7}} [2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4},{5},{6,7},{8}}=>{{1,2,7},{3},{4},{5},{6},{8}} [2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4},{5},{6,7,8}}=>{{1,2,7,8},{3},{4},{5},{6}} [2,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>{{1,2},{3},{4},{5,6},{7},{8}}=>{{1,2,6},{3},{4},{5},{7},{8}} [2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2},{3},{4},{5,6,7,8}}=>{{1,2,6,7,8},{3},{4},{5}} [2,1,2,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3},{4,5},{6},{7},{8}}=>{{1,2,5},{3},{4},{6},{7},{8}} [2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5},{6,7,8}}=>{{1,2,5,7,8},{3},{4},{6}} [2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3},{4,5,6},{7,8}}=>{{1,2,5,6,8},{3},{4},{7}} [2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3},{4,5,6,7},{8}}=>{{1,2,5,6,7},{3},{4},{8}} [2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3},{4,5,6,7,8}}=>{{1,2,5,6,7,8},{3},{4}} [2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7},{8}}=>{{1,2,4},{3},{5},{6},{7},{8}} [2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5},{6,7,8}}=>{{1,2,4,7,8},{3},{5},{6}} [2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1,2},{3,4},{5,6},{7},{8}}=>{{1,2,4,6},{3},{5},{7},{8}} [2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,6,8},{3},{5},{7}} [2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1,2},{3,4},{5,6,7},{8}}=>{{1,2,4,6,7},{3},{5},{8}} [2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8}}=>{{1,2,4,6,7,8},{3},{5}} [2,3,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>{{1,2},{3,4,5},{6},{7},{8}}=>{{1,2,4,5},{3},{6},{7},{8}} [2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>{{1,2},{3,4,5},{6},{7,8}}=>{{1,2,4,5,8},{3},{6},{7}} [2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5},{6,7,8}}=>{{1,2,4,5,7,8},{3},{6}} [2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6},{7,8}}=>{{1,2,4,5,6,8},{3},{7}} [2,5,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7},{8}}=>{{1,2,4,5,6,7},{3},{8}} [2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>{{1,2,4,5,6,7,8},{3}} [3,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6},{7},{8}}=>{{1,2,3},{4},{5},{6},{7},{8}} [3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5},{6},{7,8}}=>{{1,2,3,8},{4},{5},{6},{7}} [3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2,3},{4},{5},{6,7,8}}=>{{1,2,3,7,8},{4},{5},{6}} [3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4},{5,6},{7,8}}=>{{1,2,3,6,8},{4},{5},{7}} [3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4},{5,6,7,8}}=>{{1,2,3,6,7,8},{4},{5}} [3,2,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2,3},{4,5},{6},{7},{8}}=>{{1,2,3,5},{4},{6},{7},{8}} [3,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6,7},{8}}=>{{1,2,3,5,7},{4},{6},{8}} [3,3,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4,5,6},{7},{8}}=>{{1,2,3,5,6},{4},{7},{8}} [3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8}}=>{{1,2,3,5,6,8},{4},{7}} [3,4,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3},{4,5,6,7},{8}}=>{{1,2,3,5,6,7},{4},{8}} [3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8}}=>{{1,2,3,5,6,7,8},{4}} [4,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>{{1,2,3,4},{5},{6},{7},{8}}=>{{1,2,3,4},{5},{6},{7},{8}} [4,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>{{1,2,3,4},{5},{6},{7,8}}=>{{1,2,3,4,8},{5},{6},{7}} [4,1,2,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>{{1,2,3,4},{5},{6,7},{8}}=>{{1,2,3,4,7},{5},{6},{8}} [4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>{{1,2,3,4},{5},{6,7,8}}=>{{1,2,3,4,7,8},{5},{6}} [4,2,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>{{1,2,3,4},{5,6},{7},{8}}=>{{1,2,3,4,6},{5},{7},{8}} [4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8}}=>{{1,2,3,4,6,8},{5},{7}} [4,3,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3,4},{5,6,7},{8}}=>{{1,2,3,4,6,7},{5},{8}} [4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6,7,8}}=>{{1,2,3,4,6,7,8},{5}} [5,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>{{1,2,3,4,5},{6},{7},{8}}=>{{1,2,3,4,5},{6},{7},{8}} [5,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>{{1,2,3,4,5},{6},{7,8}}=>{{1,2,3,4,5,8},{6},{7}} [5,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4,5},{6,7},{8}}=>{{1,2,3,4,5,7},{6},{8}} [5,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5},{6,7,8}}=>{{1,2,3,4,5,7,8},{6}} [6,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,5,6},{7},{8}}=>{{1,2,3,4,5,6},{7},{8}} [6,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6},{7,8}}=>{{1,2,3,4,5,6,8},{7}} [7,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6,7},{8}}=>{{1,2,3,4,5,6,7},{8}} [8]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7,8}}=>{{1,2,3,4,5,6,7,8}} [1,1,1,1,1,1,1,1,1]=>[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}}=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}} [1,1,1,1,1,1,1,2]=>[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}}=>{{1,9},{2},{3},{4},{5},{6},{7},{8}} [1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7,8},{9}}=>{{1,8},{2},{3},{4},{5},{6},{7},{9}} [1,1,1,1,1,1,3]=>[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}}=>{{1,8,9},{2},{3},{4},{5},{6},{7}} [1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6,7},{8,9}}=>{{1,7,9},{2},{3},{4},{5},{6},{8}} [1,1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3},{4},{5},{6,7,8},{9}}=>{{1,7,8},{2},{3},{4},{5},{6},{9}} [1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4},{5},{6,7,8,9}}=>{{1,7,8,9},{2},{3},{4},{5},{6}} [1,1,1,1,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6},{7,8,9}}=>{{1,6,8,9},{2},{3},{4},{5},{7}} [1,1,1,1,3,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6,7},{8,9}}=>{{1,6,7,9},{2},{3},{4},{5},{8}} [1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3},{4},{5,6,7,8,9}}=>{{1,6,7,8,9},{2},{3},{4},{5}} [1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4,5},{6},{7},{8},{9}}=>{{1,5},{2},{3},{4},{6},{7},{8},{9}} [1,1,1,2,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4,5},{6,7},{8,9}}=>{{1,5,7,9},{2},{3},{4},{6},{8}} [1,1,1,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4,5},{6,7,8,9}}=>{{1,5,7,8,9},{2},{3},{4},{6}} [1,1,1,3,3]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5,6},{7,8,9}}=>{{1,5,6,8,9},{2},{3},{4},{7}} [1,1,1,6]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2},{3},{4,5,6,7,8,9}}=>{{1,5,6,7,8,9},{2},{3},{4}} [1,1,2,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6},{7},{8},{9}}=>{{1,4},{2},{3},{5},{6},{7},{8},{9}} [1,1,2,2,3]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4},{5,6},{7,8,9}}=>{{1,4,6,8,9},{2},{3},{5},{7}} [1,1,2,5]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4},{5,6,7,8,9}}=>{{1,4,6,7,8,9},{2},{3},{5}} [1,1,3,2,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7},{8,9}}=>{{1,4,5,7,9},{2},{3},{6},{8}} [1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8,9}}=>{{1,4,5,6,7,8,9},{2},{3}} [1,2,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6},{7},{8},{9}}=>{{1,3},{2},{4},{5},{6},{7},{8},{9}} [1,2,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5},{6},{7},{8,9}}=>{{1,3,9},{2},{4},{5},{6},{7},{8}} [1,2,2,1,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7},{8},{9}}=>{{1,3,5},{2},{4},{6},{7},{8},{9}} [1,2,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7},{8,9}}=>{{1,3,5,7,9},{2},{4},{6},{8}} [1,2,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5},{6,7,8,9}}=>{{1,3,5,7,8,9},{2},{4},{6}} [1,2,3,3]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6},{7,8,9}}=>{{1,3,5,6,8,9},{2},{4},{7}} [1,2,6]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8,9}}=>{{1,3,5,6,7,8,9},{2},{4}} [1,3,1,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2,3,4},{5},{6},{7},{8},{9}}=>{{1,3,4},{2},{5},{6},{7},{8},{9}} [1,3,5]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8,9}}=>{{1,3,4,6,7,8,9},{2},{5}} [1,4,4]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4,5},{6,7,8,9}}=>{{1,3,4,5,7,8,9},{2},{6}} [1,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5,6,7},{8,9}}=>{{1,3,4,5,6,7,9},{2},{8}} [1,7,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7,8},{9}}=>{{1,3,4,5,6,7,8},{2},{9}} [1,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8,9}}=>{{1,3,4,5,6,7,8,9},{2}} [2,1,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6},{7},{8},{9}}=>{{1,2},{3},{4},{5},{6},{7},{8},{9}} [2,1,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5},{6},{7},{8,9}}=>{{1,2,9},{3},{4},{5},{6},{7},{8}} [2,1,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4},{5},{6},{7,8},{9}}=>{{1,2,8},{3},{4},{5},{6},{7},{9}} [2,1,2,1,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4,5},{6},{7},{8},{9}}=>{{1,2,5},{3},{4},{6},{7},{8},{9}} [2,2,1,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7},{8},{9}}=>{{1,2,4},{3},{5},{6},{7},{8},{9}} [2,2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5,6},{7},{8},{9}}=>{{1,2,4,6},{3},{5},{7},{8},{9}} [2,2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5,6},{7,8},{9}}=>{{1,2,4,6,8},{3},{5},{7},{9}} [2,2,2,3]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6},{7,8,9}}=>{{1,2,4,6,8,9},{3},{5},{7}} [2,2,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4},{5,6,7,8,9}}=>{{1,2,4,6,7,8,9},{3},{5}} [2,3,4]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5},{6,7,8,9}}=>{{1,2,4,5,7,8,9},{3},{6}} [2,6,1]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2},{3,4,5,6,7,8},{9}}=>{{1,2,4,5,6,7,8},{3},{9}} [2,7]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8,9}}=>{{1,2,4,5,6,7,8,9},{3}} [3,1,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6},{7},{8},{9}}=>{{1,2,3},{4},{5},{6},{7},{8},{9}} [3,2,1,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2,3},{4,5},{6},{7},{8},{9}}=>{{1,2,3,5},{4},{6},{7},{8},{9}} [3,2,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7},{8,9}}=>{{1,2,3,5,7,9},{4},{6},{8}} [3,3,1,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>{{1,2,3},{4,5,6},{7},{8},{9}}=>{{1,2,3,5,6},{4},{7},{8},{9}} [3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5,6},{7,8,9}}=>{{1,2,3,5,6,8,9},{4},{7}} [3,4,2]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2,3},{4,5,6,7},{8,9}}=>{{1,2,3,5,6,7,9},{4},{8}} [3,6]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8,9}}=>{{1,2,3,5,6,7,8,9},{4}} [4,1,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2,3,4},{5},{6},{7},{8},{9}}=>{{1,2,3,4},{5},{6},{7},{8},{9}} [4,2,1,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2,3,4},{5,6},{7},{8},{9}}=>{{1,2,3,4,6},{5},{7},{8},{9}} [4,2,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2,3,4},{5,6},{7,8},{9}}=>{{1,2,3,4,6,8},{5},{7},{9}} [4,3,1,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2,3,4},{5,6,7},{8},{9}}=>{{1,2,3,4,6,7},{5},{8},{9}} [4,3,2]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2,3,4},{5,6,7},{8,9}}=>{{1,2,3,4,6,7,9},{5},{8}} [4,4,1]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3,4},{5,6,7,8},{9}}=>{{1,2,3,4,6,7,8},{5},{9}} [4,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3,4},{5,6,7,8,9}}=>{{1,2,3,4,6,7,8,9},{5}} [5,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>{{1,2,3,4,5},{6},{7},{8},{9}}=>{{1,2,3,4,5},{6},{7},{8},{9}} [5,2,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>{{1,2,3,4,5},{6,7},{8},{9}}=>{{1,2,3,4,5,7},{6},{8},{9}} [5,3,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3,4,5},{6,7,8},{9}}=>{{1,2,3,4,5,7,8},{6},{9}} [5,4]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4,5},{6,7,8,9}}=>{{1,2,3,4,5,7,8,9},{6}} [6,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>{{1,2,3,4,5,6},{7},{8},{9}}=>{{1,2,3,4,5,6},{7},{8},{9}} [6,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4,5,6},{7,8},{9}}=>{{1,2,3,4,5,6,8},{7},{9}} [6,3]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5,6},{7,8,9}}=>{{1,2,3,4,5,6,8,9},{7}} [7,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,5,6,7},{8},{9}}=>{{1,2,3,4,5,6,7},{8},{9}} [7,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7},{8,9}}=>{{1,2,3,4,5,6,7,9},{8}} [8,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6,7,8},{9}}=>{{1,2,3,4,5,6,7,8},{9}} [9]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7,8,9}}=>{{1,2,3,4,5,6,7,8,9}} [1,1,1,1,1,1,1,1,1,1]=>[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}}=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} [1,1,1,1,1,1,1,1,2]=>[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}}=>{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} [1,1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7},{8,9},{10}}=>{{1,9},{2},{3},{4},{5},{6},{7},{8},{10}} [1,1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5},{6},{7},{8,9,10}}=>{{1,9,10},{2},{3},{4},{5},{6},{7},{8}} [1,1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6},{7,8},{9,10}}=>{{1,8,10},{2},{3},{4},{5},{6},{7},{9}} [1,1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}}=>{{1,8,9,10},{2},{3},{4},{5},{6},{7}} [1,1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6,7},{8},{9},{10}}=>{{1,7},{2},{3},{4},{5},{6},{8},{9},{10}} [1,1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3},{4},{5},{6,7,8,9,10}}=>{{1,7,8,9,10},{2},{3},{4},{5},{6}} [1,1,1,1,2,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6},{7,8},{9,10}}=>{{1,6,8,10},{2},{3},{4},{5},{7},{9}} [1,1,1,1,6]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2},{3},{4},{5,6,7,8,9,10}}=>{{1,6,7,8,9,10},{2},{3},{4},{5}} [1,1,1,7]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2},{3},{4,5,6,7,8,9,10}}=>{{1,5,6,7,8,9,10},{2},{3},{4}} [1,1,2,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6},{7,8},{9,10}}=>{{1,4,6,8,10},{2},{3},{5},{7},{9}} [1,1,4,4]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3,4,5,6},{7,8,9,10}}=>{{1,4,5,6,8,9,10},{2},{3},{7}} [1,1,8]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8,9,10}}=>{{1,4,5,6,7,8,9,10},{2},{3}} [1,2,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}=>{{1,3,5,7,9},{2},{4},{6},{8},{10}} [1,2,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5},{6,7},{8,9,10}}=>{{1,3,5,7,9,10},{2},{4},{6},{8}} [1,2,3,4]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6},{7,8,9,10}}=>{{1,3,5,6,8,9,10},{2},{4},{7}} [1,2,7]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2,3},{4,5,6,7,8,9,10}}=>{{1,3,5,6,7,8,9,10},{2},{4}} [1,3,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7},{8,9,10}}=>{{1,3,4,6,7,9,10},{2},{5},{8}} [1,3,6]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4},{5,6,7,8,9,10}}=>{{1,3,4,6,7,8,9,10},{2},{5}} [1,4,5]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3,4,5},{6,7,8,9,10}}=>{{1,3,4,5,7,8,9,10},{2},{6}} [1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7,8,9},{10}}=>{{1,3,4,5,6,7,8,9},{2},{10}} [1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8,9,10}}=>{{1,3,4,5,6,7,8,9,10},{2}} [2,1,1,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} [2,1,1,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5},{6},{7},{8},{9,10}}=>{{1,2,10},{3},{4},{5},{6},{7},{8},{9}} [2,2,1,1,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7},{8},{9},{10}}=>{{1,2,4},{3},{5},{6},{7},{8},{9},{10}} [2,2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5,6},{7},{8},{9},{10}}=>{{1,2,4,6},{3},{5},{7},{8},{9},{10}} [2,2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1,2},{3,4},{5,6},{7,8},{9},{10}}=>{{1,2,4,6,8},{3},{5},{7},{9},{10}} [2,2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,6,8,10},{3},{5},{7},{9}} [2,2,2,4]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4},{5,6},{7,8,9,10}}=>{{1,2,4,6,8,9,10},{3},{5},{7}} [2,2,3,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7},{8,9,10}}=>{{1,2,4,6,7,9,10},{3},{5},{8}} [2,4,4]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6},{7,8,9,10}}=>{{1,2,4,5,6,8,9,10},{3},{7}} [2,6,2]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1,2},{3,4,5,6,7,8},{9,10}}=>{{1,2,4,5,6,7,8,10},{3},{9}} [2,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8,9,10}}=>{{1,2,4,5,6,7,8,9,10},{3}} [3,1,1,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6},{7},{8},{9},{10}}=>{{1,2,3},{4},{5},{6},{7},{8},{9},{10}} [3,2,1,1,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2,3},{4,5},{6},{7},{8},{9},{10}}=>{{1,2,3,5},{4},{6},{7},{8},{9},{10}} [3,2,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6,7},{8,9},{10}}=>{{1,2,3,5,7,9},{4},{6},{8},{10}} [3,3,2,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5,6},{7,8},{9,10}}=>{{1,2,3,5,6,8,10},{4},{7},{9}} [3,3,4]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6},{7,8,9,10}}=>{{1,2,3,5,6,8,9,10},{4},{7}} [3,7]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3},{4,5,6,7,8,9,10}}=>{{1,2,3,5,6,7,8,9,10},{4}} [4,1,1,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2,3,4},{5},{6},{7},{8},{9},{10}}=>{{1,2,3,4},{5},{6},{7},{8},{9},{10}} [4,2,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3,4},{5,6},{7,8},{9,10}}=>{{1,2,3,4,6,8,10},{5},{7},{9}} [4,2,4]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4},{5,6},{7,8,9,10}}=>{{1,2,3,4,6,8,9,10},{5},{7}} [4,3,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7},{8,9,10}}=>{{1,2,3,4,6,7,9,10},{5},{8}} [4,4,1,1]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>{{1,2,3,4},{5,6,7,8},{9},{10}}=>{{1,2,3,4,6,7,8},{5},{9},{10}} [4,4,2]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2,3,4},{5,6,7,8},{9,10}}=>{{1,2,3,4,6,7,8,10},{5},{9}} [4,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4},{5,6,7,8,9,10}}=>{{1,2,3,4,6,7,8,9,10},{5}} [5,1,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2,3,4,5},{6},{7},{8},{9},{10}}=>{{1,2,3,4,5},{6},{7},{8},{9},{10}} [5,2,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2,3,4,5},{6,7},{8,9},{10}}=>{{1,2,3,4,5,7,9},{6},{8},{10}} [5,4,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2,3,4,5},{6,7,8,9},{10}}=>{{1,2,3,4,5,7,8,9},{6},{10}} [5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2,3,4,5},{6,7,8,9,10}}=>{{1,2,3,4,5,7,8,9,10},{6}} [6,1,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>{{1,2,3,4,5,6},{7},{8},{9},{10}}=>{{1,2,3,4,5,6},{7},{8},{9},{10}} [6,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3,4,5,6},{7,8,9},{10}}=>{{1,2,3,4,5,6,8,9},{7},{10}} [6,4]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3,4,5,6},{7,8,9,10}}=>{{1,2,3,4,5,6,8,9,10},{7}} [7,1,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>{{1,2,3,4,5,6,7},{8},{9},{10}}=>{{1,2,3,4,5,6,7},{8},{9},{10}} [7,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4,5,6,7},{8,9},{10}}=>{{1,2,3,4,5,6,7,9},{8},{10}} [7,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4,5,6,7},{8,9,10}}=>{{1,2,3,4,5,6,7,9,10},{8}} [8,1,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,5,6,7,8},{9},{10}}=>{{1,2,3,4,5,6,7,8},{9},{10}} [8,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6,7,8},{9,10}}=>{{1,2,3,4,5,6,7,8,10},{9}} [9,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6,7,8,9},{10}}=>{{1,2,3,4,5,6,7,8,9},{10}} [10]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7,8,9,10}}=>{{1,2,3,4,5,6,7,8,9,10}} [1,10]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8,9,10,11}}=>{{1,3,4,5,6,7,8,9,10,11},{2}} [10,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6,7,8,9,10},{11}}=>{{1,2,3,4,5,6,7,8,9,10},{11}} [2,2,2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}} [1,1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}}=>{{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.
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 $\psi$.