Identifier
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Images
=>
Cc0005;cc-rep-1Cc0009;cc-rep-3
[1]=>[1,0]=>[1]=>{{1}} [1,1]=>[1,0,1,0]=>[1,2]=>{{1},{2}} [2]=>[1,1,0,0]=>[2,1]=>{{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]=>[1,3,2]=>{{1},{2,3}} [2,1]=>[1,1,0,0,1,0]=>[2,1,3]=>{{1,2},{3}} [3]=>[1,1,1,0,0,0]=>[3,1,2]=>{{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]=>[1,2,4,3]=>{{1},{2},{3,4}} [1,2,1]=>[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>{{1},{2,3},{4}} [1,3]=>[1,0,1,1,1,0,0,0]=>[1,4,2,3]=>{{1},{2,3,4}} [2,1,1]=>[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>{{1,2},{3},{4}} [2,2]=>[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>{{1,2},{3,4}} [3,1]=>[1,1,1,0,0,0,1,0]=>[3,1,2,4]=>{{1,2,3},{4}} [4]=>[1,1,1,1,0,0,0,0]=>[4,1,2,3]=>{{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]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}} [1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}} [1,1,3]=>[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,3,4]=>{{1},{2},{3,4,5}} [1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}} [1,2,2]=>[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>{{1},{2,3},{4,5}} [1,3,1]=>[1,0,1,1,1,0,0,0,1,0]=>[1,4,2,3,5]=>{{1},{2,3,4},{5}} [1,4]=>[1,0,1,1,1,1,0,0,0,0]=>[1,5,2,3,4]=>{{1},{2,3,4,5}} [2,1,1,1]=>[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>{{1,2},{3},{4},{5}} [2,1,2]=>[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>{{1,2},{3},{4,5}} [2,2,1]=>[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>{{1,2},{3,4},{5}} [2,3]=>[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,3,4]=>{{1,2},{3,4,5}} [3,1,1]=>[1,1,1,0,0,0,1,0,1,0]=>[3,1,2,4,5]=>{{1,2,3},{4},{5}} [3,2]=>[1,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4]=>{{1,2,3},{4,5}} [4,1]=>[1,1,1,1,0,0,0,0,1,0]=>[4,1,2,3,5]=>{{1,2,3,4},{5}} [5]=>[1,1,1,1,1,0,0,0,0,0]=>[5,1,2,3,4]=>{{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]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}} [1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}} [1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,4,5]=>{{1},{2},{3},{4,5,6}} [1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}} [1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}} [1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,3,4,6]=>{{1},{2},{3,4,5},{6}} [1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,3,4,5]=>{{1},{2},{3,4,5,6}} [1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}} [1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}} [1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}} [1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,4,5]=>{{1},{2,3},{4,5,6}} [1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,2,3,5,6]=>{{1},{2,3,4},{5},{6}} [1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,2,3,6,5]=>{{1},{2,3,4},{5,6}} [1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,2,3,4,6]=>{{1},{2,3,4,5},{6}} [1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,2,3,4,5]=>{{1},{2,3,4,5,6}} [2,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>{{1,2},{3},{4},{5},{6}} [2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>{{1,2},{3},{4},{5,6}} [2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>{{1,2},{3},{4,5},{6}} [2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,4,5]=>{{1,2},{3},{4,5,6}} [2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>{{1,2},{3,4},{5},{6}} [2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>{{1,2},{3,4},{5,6}} [2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,3,4,6]=>{{1,2},{3,4,5},{6}} [2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,3,4,5]=>{{1,2},{3,4,5,6}} [3,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,2,4,5,6]=>{{1,2,3},{4},{5},{6}} [3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2,4,6,5]=>{{1,2,3},{4},{5,6}} [3,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,6]=>{{1,2,3},{4,5},{6}} [3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,2,6,4,5]=>{{1,2,3},{4,5,6}} [4,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,3,5,6]=>{{1,2,3,4},{5},{6}} [4,2]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,6,5]=>{{1,2,3,4},{5,6}} [5,1]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>{{1,2,3,4,5},{6}} [6]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,5]=>{{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]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}} [1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}} [1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,5,6]=>{{1},{2},{3},{4},{5,6,7}} [1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}} [1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}} [1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,4,5,7]=>{{1},{2},{3},{4,5,6},{7}} [1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>{{1},{2},{3},{4,5,6,7}} [1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}} [1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}} [1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}} [1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,5,6]=>{{1},{2},{3,4},{5,6,7}} [1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,3,4,6,7]=>{{1},{2},{3,4,5},{6},{7}} [1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,3,4,7,6]=>{{1},{2},{3,4,5},{6,7}} [1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,3,4,5,7]=>{{1},{2},{3,4,5,6},{7}} [1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,3,4,5,6]=>{{1},{2},{3,4,5,6,7}} [1,2,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}} [1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}} [1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}} [1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,5,6]=>{{1},{2,3},{4},{5,6,7}} [1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}} [1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>{{1},{2,3},{4,5},{6,7}} [1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,4,5,7]=>{{1},{2,3},{4,5,6},{7}} [1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,4,5,6]=>{{1},{2,3},{4,5,6,7}} [1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,2,3,5,6,7]=>{{1},{2,3,4},{5},{6},{7}} [1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,2,3,5,7,6]=>{{1},{2,3,4},{5},{6,7}} [1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,7]=>{{1},{2,3,4},{5,6},{7}} [1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,2,3,7,5,6]=>{{1},{2,3,4},{5,6,7}} [1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,2,3,4,6,7]=>{{1},{2,3,4,5},{6},{7}} [1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,2,3,4,7,6]=>{{1},{2,3,4,5},{6,7}} [1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,2,3,4,5,7]=>{{1},{2,3,4,5,6},{7}} [1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,2,3,4,5,6]=>{{1},{2,3,4,5,6,7}} [2,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>{{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]=>[2,1,3,4,5,7,6]=>{{1,2},{3},{4},{5},{6,7}} [2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>{{1,2},{3},{4},{5,6},{7}} [2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,5,6]=>{{1,2},{3},{4},{5,6,7}} [2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>{{1,2},{3},{4,5},{6},{7}} [2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>{{1,2},{3},{4,5},{6,7}} [2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,4,5,7]=>{{1,2},{3},{4,5,6},{7}} [2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,4,5,6]=>{{1,2},{3},{4,5,6,7}} [2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>{{1,2},{3,4},{5},{6},{7}} [2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>{{1,2},{3,4},{5},{6,7}} [2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>{{1,2},{3,4},{5,6},{7}} [2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,5,6]=>{{1,2},{3,4},{5,6,7}} [2,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7]=>{{1,2},{3,4,5},{6},{7}} [2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,3,4,7,6]=>{{1,2},{3,4,5},{6,7}} [2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,3,4,5,7]=>{{1,2},{3,4,5,6},{7}} [2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,3,4,5,6]=>{{1,2},{3,4,5,6,7}} [3,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,2,4,5,6,7]=>{{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]=>[3,1,2,4,5,7,6]=>{{1,2,3},{4},{5},{6,7}} [3,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,4,6,5,7]=>{{1,2,3},{4},{5,6},{7}} [3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,2,4,7,5,6]=>{{1,2,3},{4},{5,6,7}} [3,2,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,5,4,6,7]=>{{1,2,3},{4,5},{6},{7}} [3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,5,4,7,6]=>{{1,2,3},{4,5},{6,7}} [3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,2,6,4,5,7]=>{{1,2,3},{4,5,6},{7}} [3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,2,7,4,5,6]=>{{1,2,3},{4,5,6,7}} [4,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,2,3,5,6,7]=>{{1,2,3,4},{5},{6},{7}} [4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2,3,5,7,6]=>{{1,2,3,4},{5},{6,7}} [4,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,3,6,5,7]=>{{1,2,3,4},{5,6},{7}} [4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,2,3,7,5,6]=>{{1,2,3,4},{5,6,7}} [5,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,2,3,4,6,7]=>{{1,2,3,4,5},{6},{7}} [5,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,1,2,3,4,7,6]=>{{1,2,3,4,5},{6,7}} [6,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7]=>{{1,2,3,4,5,6},{7}} [7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6]=>{{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]=>[1,2,3,4,5,6,8,7]=>{{1},{2},{3},{4},{5},{6},{7,8}} [1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>{{1},{2},{3},{4},{5},{6,7},{8}} [1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,6,7]=>{{1},{2},{3},{4},{5},{6,7,8}} [1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,6,5,7,8]=>{{1},{2},{3},{4},{5,6},{7},{8}} [1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,6,5,8,7]=>{{1},{2},{3},{4},{5,6},{7,8}} [1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,4,7,5,6,8]=>{{1},{2},{3},{4},{5,6,7},{8}} [1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,5,6,7]=>{{1},{2},{3},{4},{5,6,7,8}} [1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>{{1},{2},{3},{4,5},{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]=>[1,2,3,5,4,6,8,7]=>{{1},{2},{3},{4,5},{6},{7,8}} [1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>{{1},{2},{3},{4,5},{6,7},{8}} [1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,6,7]=>{{1},{2},{3},{4,5},{6,7,8}} [1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,6,4,5,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}} [1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,4,5,8,7]=>{{1},{2},{3},{4,5,6},{7,8}} [1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,4,5,6,8]=>{{1},{2},{3},{4,5,6,7},{8}} [1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,4,5,6,7]=>{{1},{2},{3},{4,5,6,7,8}} [1,1,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8]=>{{1},{2},{3,4},{5},{6},{7},{8}} [1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,3,5,6,8,7]=>{{1},{2},{3,4},{5},{6},{7,8}} [1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5,7,6,8]=>{{1},{2},{3,4},{5},{6,7},{8}} [1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,3,5,8,6,7]=>{{1},{2},{3,4},{5},{6,7,8}} [1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>{{1},{2},{3,4},{5,6},{7},{8}} [1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7]=>{{1},{2},{3,4},{5,6},{7,8}} [1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,7,5,6,8]=>{{1},{2},{3,4},{5,6,7},{8}} [1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,5,6,7]=>{{1},{2},{3,4},{5,6,7,8}} [1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,5,3,4,6,7,8]=>{{1},{2},{3,4,5},{6},{7},{8}} [1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,5,3,4,6,8,7]=>{{1},{2},{3,4,5},{6},{7,8}} [1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,5,3,4,7,6,8]=>{{1},{2},{3,4,5},{6,7},{8}} [1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,5,3,4,8,6,7]=>{{1},{2},{3,4,5},{6,7,8}} [1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,3,4,5,7,8]=>{{1},{2},{3,4,5,6},{7},{8}} [1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,6,3,4,5,8,7]=>{{1},{2},{3,4,5,6},{7,8}} [1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,7,3,4,5,6,8]=>{{1},{2},{3,4,5,6,7},{8}} [1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,3,4,5,6,7]=>{{1},{2},{3,4,5,6,7,8}} [1,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{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]=>[1,3,2,4,5,6,8,7]=>{{1},{2,3},{4},{5},{6},{7,8}} [1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>{{1},{2,3},{4},{5},{6,7},{8}} [1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,8,6,7]=>{{1},{2,3},{4},{5},{6,7,8}} [1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,6,5,7,8]=>{{1},{2,3},{4},{5,6},{7},{8}} [1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,2,4,6,5,8,7]=>{{1},{2,3},{4},{5,6},{7,8}} [1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,5,6,7]=>{{1},{2,3},{4},{5,6,7,8}} [1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>{{1},{2,3},{4,5},{6},{7},{8}} [1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>{{1},{2,3},{4,5},{6,7},{8}} [1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,6,7]=>{{1},{2,3},{4,5},{6,7,8}} [1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,6,4,5,7,8]=>{{1},{2,3},{4,5,6},{7},{8}} [1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,7,4,5,6,8]=>{{1},{2,3},{4,5,6,7},{8}} [1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,4,5,6,7]=>{{1},{2,3},{4,5,6,7,8}} [1,3,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,2,3,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}} [1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,4,2,3,5,6,8,7]=>{{1},{2,3,4},{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]=>[1,4,2,3,5,7,6,8]=>{{1},{2,3,4},{5},{6,7},{8}} [1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,2,3,5,8,6,7]=>{{1},{2,3,4},{5},{6,7,8}} [1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,4,2,3,6,5,7,8]=>{{1},{2,3,4},{5,6},{7},{8}} [1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,3,6,5,8,7]=>{{1},{2,3,4},{5,6},{7,8}} [1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,2,3,7,5,6,8]=>{{1},{2,3,4},{5,6,7},{8}} [1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,2,3,8,5,6,7]=>{{1},{2,3,4},{5,6,7,8}} [1,4,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,5,2,3,4,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}} [1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,5,2,3,4,6,8,7]=>{{1},{2,3,4,5},{6},{7,8}} [1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,5,2,3,4,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}} [1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,5,2,3,4,8,6,7]=>{{1},{2,3,4,5},{6,7,8}} [1,5,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,6,2,3,4,5,7,8]=>{{1},{2,3,4,5,6},{7},{8}} [1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,6,2,3,4,5,8,7]=>{{1},{2,3,4,5,6},{7,8}} [1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,7,2,3,4,5,6,8]=>{{1},{2,3,4,5,6,7},{8}} [1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7]=>{{1},{2,3,4,5,6,7,8}} [2,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>{{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]=>[2,1,3,4,5,6,8,7]=>{{1,2},{3},{4},{5},{6},{7,8}} [2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,5,7,6,8]=>{{1,2},{3},{4},{5},{6,7},{8}} [2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,5,8,6,7]=>{{1,2},{3},{4},{5},{6,7,8}} [2,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,4,6,5,7,8]=>{{1,2},{3},{4},{5,6},{7},{8}} [2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,4,6,5,8,7]=>{{1,2},{3},{4},{5,6},{7,8}} [2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,7,5,6,8]=>{{1,2},{3},{4},{5,6,7},{8}} [2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,5,6,7]=>{{1,2},{3},{4},{5,6,7,8}} [2,1,2,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,3,5,4,6,7,8]=>{{1,2},{3},{4,5},{6},{7},{8}} [2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4,6,8,7]=>{{1,2},{3},{4,5},{6},{7,8}} [2,1,3,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,6,4,5,7,8]=>{{1,2},{3},{4,5,6},{7},{8}} [2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,6,4,5,8,7]=>{{1,2},{3},{4,5,6},{7,8}} [2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,4,5,6,7]=>{{1,2},{3},{4,5,6,7,8}} [2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>{{1,2},{3,4},{5},{6},{7},{8}} [2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,3,5,6,8,7]=>{{1,2},{3,4},{5},{6},{7,8}} [2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,3,5,8,6,7]=>{{1,2},{3,4},{5},{6,7,8}} [2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>{{1,2},{3,4},{5,6},{7},{8}} [2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>{{1,2},{3,4},{5,6},{7,8}} [2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,5,6,7]=>{{1,2},{3,4},{5,6,7,8}} [2,3,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,5,3,4,6,7,8]=>{{1,2},{3,4,5},{6},{7},{8}} [2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,3,4,6,8,7]=>{{1,2},{3,4,5},{6},{7,8}} [2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,3,4,5,8,7]=>{{1,2},{3,4,5,6},{7,8}} [2,5,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,7,3,4,5,6,8]=>{{1,2},{3,4,5,6,7},{8}} [2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,3,4,5,6,7]=>{{1,2},{3,4,5,6,7,8}} [3,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,2,4,5,6,7,8]=>{{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]=>[3,1,2,4,5,6,8,7]=>{{1,2,3},{4},{5},{6},{7,8}} [3,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,2,4,5,7,6,8]=>{{1,2,3},{4},{5},{6,7},{8}} [3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,2,4,5,8,6,7]=>{{1,2,3},{4},{5},{6,7,8}} [3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,4,6,5,8,7]=>{{1,2,3},{4},{5,6},{7,8}} [3,1,3,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,2,4,7,5,6,8]=>{{1,2,3},{4},{5,6,7},{8}} [3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,2,4,8,5,6,7]=>{{1,2,3},{4},{5,6,7,8}} [3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,2,5,4,6,8,7]=>{{1,2,3},{4,5},{6},{7,8}} [3,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6,8]=>{{1,2,3},{4,5},{6,7},{8}} [3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,2,6,4,5,8,7]=>{{1,2,3},{4,5,6},{7,8}} [3,4,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,2,7,4,5,6,8]=>{{1,2,3},{4,5,6,7},{8}} [3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,2,8,4,5,6,7]=>{{1,2,3},{4,5,6,7,8}} [4,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,2,3,5,6,7,8]=>{{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]=>[4,1,2,3,5,6,8,7]=>{{1,2,3,4},{5},{6},{7,8}} [4,1,2,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,3,5,7,6,8]=>{{1,2,3,4},{5},{6,7},{8}} [4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,2,3,5,8,6,7]=>{{1,2,3,4},{5},{6,7,8}} [4,2,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,2,3,6,5,7,8]=>{{1,2,3,4},{5,6},{7},{8}} [4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,3,6,5,8,7]=>{{1,2,3,4},{5,6},{7,8}} [4,3,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,2,3,7,5,6,8]=>{{1,2,3,4},{5,6,7},{8}} [4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,1,2,3,8,5,6,7]=>{{1,2,3,4},{5,6,7,8}} [5,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,2,3,4,6,7,8]=>{{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]=>[5,1,2,3,4,6,8,7]=>{{1,2,3,4,5},{6},{7,8}} [5,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,1,2,3,4,8,6,7]=>{{1,2,3,4,5},{6,7,8}} [6,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,2,3,4,5,7,8]=>{{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]=>[6,1,2,3,4,5,8,7]=>{{1,2,3,4,5,6},{7,8}} [7,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8]=>{{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]=>[8,1,2,3,4,5,6,7]=>{{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]=>[1,2,3,4,5,6,7,9,8]=>{{1},{2},{3},{4},{5},{6},{7},{8,9}} [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]=>[1,2,3,4,5,6,8,7,9]=>{{1},{2},{3},{4},{5},{6},{7,8},{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]=>[1,2,3,4,5,6,9,7,8]=>{{1},{2},{3},{4},{5},{6},{7,8,9}} [1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,5,7,6,8,9]=>{{1},{2},{3},{4},{5},{6,7},{8},{9}} [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]=>[1,2,3,4,5,7,6,9,8]=>{{1},{2},{3},{4},{5},{6,7},{8,9}} [1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,9,6,7,8]=>{{1},{2},{3},{4},{5},{6,7,8,9}} [1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,4,6,5,7,8,9]=>{{1},{2},{3},{4},{5,6},{7},{8},{9}} [1,1,1,1,2,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7,9]=>{{1},{2},{3},{4},{5,6},{7,8},{9}} [1,1,1,1,3,2]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,4,7,5,6,9,8]=>{{1},{2},{3},{4},{5,6,7},{8,9}} [1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,9,5,6,7,8]=>{{1},{2},{3},{4},{5,6,7,8,9}} [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]=>[1,2,3,5,4,6,7,8,9]=>{{1},{2},{3},{4,5},{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]=>[1,2,3,5,4,7,6,9,8]=>{{1},{2},{3},{4,5},{6,7},{8,9}} [1,1,1,6]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,9,4,5,6,7,8]=>{{1},{2},{3},{4,5,6,7,8,9}} [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]=>[1,2,4,3,5,6,7,8,9]=>{{1},{2},{3,4},{5},{6},{7},{8},{9}} [1,1,2,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7,9]=>{{1},{2},{3,4},{5,6},{7,8},{9}} [1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,9,3,4,5,6,7,8]=>{{1},{2},{3,4,5,6,7,8,9}} [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]=>[1,3,2,4,5,6,7,8,9]=>{{1},{2,3},{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]=>[1,3,2,4,5,6,7,9,8]=>{{1},{2,3},{4},{5},{6},{7},{8,9}} [1,2,1,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,6,9,7,8]=>{{1},{2,3},{4},{5},{6},{7,8,9}} [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]=>[1,3,2,5,4,6,7,8,9]=>{{1},{2,3},{4,5},{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]=>[1,3,2,5,4,7,6,9,8]=>{{1},{2,3},{4,5},{6,7},{8,9}} [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]=>[1,4,2,3,5,6,7,8,9]=>{{1},{2,3,4},{5},{6},{7},{8},{9}} [1,3,2,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,8,7,9]=>{{1},{2,3,4},{5,6},{7,8},{9}} [1,6,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,7,2,3,4,5,6,8,9]=>{{1},{2,3,4,5,6,7},{8},{9}} [1,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,7,2,3,4,5,6,9,8]=>{{1},{2,3,4,5,6,7},{8,9}} [1,7,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,8,2,3,4,5,6,7,9]=>{{1},{2,3,4,5,6,7,8},{9}} [1,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9,2,3,4,5,6,7,8]=>{{1},{2,3,4,5,6,7,8,9}} [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]=>[2,1,3,4,5,6,7,8,9]=>{{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]=>[2,1,3,4,5,6,7,9,8]=>{{1,2},{3},{4},{5},{6},{7},{8,9}} [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]=>[2,1,3,4,5,6,8,7,9]=>{{1,2},{3},{4},{5},{6},{7,8},{9}} [2,1,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,5,6,9,7,8]=>{{1,2},{3},{4},{5},{6},{7,8,9}} [2,1,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,5,8,6,7,9]=>{{1,2},{3},{4},{5},{6,7,8},{9}} [2,1,1,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,5,9,6,7,8]=>{{1,2},{3},{4},{5},{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]=>[2,1,4,3,5,6,7,8,9]=>{{1,2},{3,4},{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]=>[2,1,4,3,6,5,7,8,9]=>{{1,2},{3,4},{5,6},{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]=>[2,1,4,3,6,5,8,7,9]=>{{1,2},{3,4},{5,6},{7,8},{9}} [2,6,1]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,8,3,4,5,6,7,9]=>{{1,2},{3,4,5,6,7,8},{9}} [2,7]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,9,3,4,5,6,7,8]=>{{1,2},{3,4,5,6,7,8,9}} [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]=>[3,1,2,4,5,6,7,8,9]=>{{1,2,3},{4},{5},{6},{7},{8},{9}} [3,1,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,2,4,5,6,7,9,8]=>{{1,2,3},{4},{5},{6},{7},{8,9}} [3,1,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,2,4,5,6,9,7,8]=>{{1,2,3},{4},{5},{6},{7,8,9}} [3,1,2,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,4,6,5,8,7,9]=>{{1,2,3},{4},{5,6},{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]=>[3,1,2,5,4,7,6,9,8]=>{{1,2,3},{4,5},{6,7},{8,9}} [3,6]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,2,9,4,5,6,7,8]=>{{1,2,3},{4,5,6,7,8,9}} [4,1,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,2,3,5,6,7,8,9]=>{{1,2,3,4},{5},{6},{7},{8},{9}} [4,1,4]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,3,5,9,6,7,8]=>{{1,2,3,4},{5},{6,7,8,9}} [4,2,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,3,6,5,8,7,9]=>{{1,2,3,4},{5,6},{7,8},{9}} [4,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,1,2,3,9,5,6,7,8]=>{{1,2,3,4},{5,6,7,8,9}} [5,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,2,3,4,6,7,8,9]=>{{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]=>[5,1,2,3,4,7,6,8,9]=>{{1,2,3,4,5},{6,7},{8},{9}} [5,4]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,4,9,6,7,8]=>{{1,2,3,4,5},{6,7,8,9}} [6,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,2,3,4,5,7,8,9]=>{{1,2,3,4,5,6},{7},{8},{9}} [6,3]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,1,2,3,4,5,9,7,8]=>{{1,2,3,4,5,6},{7,8,9}} [7,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,1,2,3,4,5,6,8,9]=>{{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]=>[7,1,2,3,4,5,6,9,8]=>{{1,2,3,4,5,6,7},{8,9}} [8,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7,9]=>{{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]=>[9,1,2,3,4,5,6,7,8]=>{{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]=>[1,2,3,4,5,6,7,8,10,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} [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]=>[1,2,3,4,5,6,7,9,8,10]=>{{1},{2},{3},{4},{5},{6},{7},{8,9},{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]=>[1,2,3,4,5,6,7,10,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8,9,10}} [1,1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,5,6,8,7,9,10]=>{{1},{2},{3},{4},{5},{6},{7,8},{9},{10}} [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]=>[1,2,3,4,5,6,8,7,10,9]=>{{1},{2},{3},{4},{5},{6},{7,8},{9,10}} [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]=>[1,2,3,4,5,6,10,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}} [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]=>[1,2,3,4,5,7,6,8,9,10]=>{{1},{2},{3},{4},{5},{6,7},{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]=>[1,2,3,4,5,10,6,7,8,9]=>{{1},{2},{3},{4},{5},{6,7,8,9,10}} [1,1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,6,5,7,8,9,10]=>{{1},{2},{3},{4},{5,6},{7},{8},{9},{10}} [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]=>[1,2,3,4,6,5,8,7,10,9]=>{{1},{2},{3},{4},{5,6},{7,8},{9,10}} [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]=>[1,2,3,4,10,5,6,7,8,9]=>{{1},{2},{3},{4},{5,6,7,8,9,10}} [1,1,1,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8,9,10]=>{{1},{2},{3},{4,5},{6},{7},{8},{9},{10}} [1,1,1,2,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,9,8,10]=>{{1},{2},{3},{4,5},{6,7},{8,9},{10}} [1,1,1,7]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,10,4,5,6,7,8,9]=>{{1},{2},{3},{4,5,6,7,8,9,10}} [1,1,2,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8,9,10]=>{{1},{2},{3,4},{5},{6},{7},{8},{9},{10}} [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]=>[1,2,4,3,6,5,8,7,10,9]=>{{1},{2},{3,4},{5,6},{7,8},{9,10}} [1,1,8]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,10,3,4,5,6,7,8,9]=>{{1},{2},{3,4,5,6,7,8,9,10}} [1,2,1,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8,9,10]=>{{1},{2,3},{4},{5},{6},{7},{8},{9},{10}} [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]=>[1,3,2,5,4,7,6,9,8,10]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}} [1,3,2,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,3,6,5,8,7,10,9]=>{{1},{2,3,4},{5,6},{7,8},{9,10}} [1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,9,2,3,4,5,6,7,8,10]=>{{1},{2,3,4,5,6,7,8,9},{10}} [1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10,2,3,4,5,6,7,8,9]=>{{1},{2,3,4,5,6,7,8,9,10}} [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]=>[2,1,3,4,5,6,7,8,9,10]=>{{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]=>[2,1,3,4,5,6,7,8,10,9]=>{{1,2},{3},{4},{5},{6},{7},{8},{9,10}} [2,1,1,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,5,6,7,10,8,9]=>{{1,2},{3},{4},{5},{6},{7},{8,9,10}} [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]=>[2,1,4,3,5,6,7,8,9,10]=>{{1,2},{3,4},{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]=>[2,1,4,3,6,5,7,8,9,10]=>{{1,2},{3,4},{5,6},{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]=>[2,1,4,3,6,5,8,7,9,10]=>{{1,2},{3,4},{5,6},{7,8},{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]=>[2,1,4,3,6,5,8,7,10,9]=>{{1,2},{3,4},{5,6},{7,8},{9,10}} [2,2,2,4]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,10,7,8,9]=>{{1,2},{3,4},{5,6},{7,8,9,10}} [2,4,4]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,3,4,5,10,7,8,9]=>{{1,2},{3,4,5,6},{7,8,9,10}} [2,6,2]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,8,3,4,5,6,7,10,9]=>{{1,2},{3,4,5,6,7,8},{9,10}} [2,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,10,3,4,5,6,7,8,9]=>{{1,2},{3,4,5,6,7,8,9,10}} [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]=>[3,1,2,4,5,6,7,8,9,10]=>{{1,2,3},{4},{5},{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]=>[3,1,2,5,4,7,6,9,8,10]=>{{1,2,3},{4,5},{6,7},{8,9},{10}} [3,7]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,2,10,4,5,6,7,8,9]=>{{1,2,3},{4,5,6,7,8,9,10}} [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]=>[4,1,2,3,5,6,7,8,9,10]=>{{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]=>[4,1,2,3,6,5,8,7,10,9]=>{{1,2,3,4},{5,6},{7,8},{9,10}} [4,2,4]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,1,2,3,6,5,10,7,8,9]=>{{1,2,3,4},{5,6},{7,8,9,10}} [4,4,2]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,8,5,6,7,10,9]=>{{1,2,3,4},{5,6,7,8},{9,10}} [4,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,1,2,3,10,5,6,7,8,9]=>{{1,2,3,4},{5,6,7,8,9,10}} [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]=>[5,1,2,3,4,6,7,8,9,10]=>{{1,2,3,4,5},{6},{7},{8},{9},{10}} [5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,1,2,3,4,10,6,7,8,9]=>{{1,2,3,4,5},{6,7,8,9,10}} [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]=>[6,1,2,3,4,5,7,8,9,10]=>{{1,2,3,4,5,6},{7},{8},{9},{10}} [6,4]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,1,2,3,4,5,10,7,8,9]=>{{1,2,3,4,5,6},{7,8,9,10}} [7,1,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,6,8,9,10]=>{{1,2,3,4,5,6,7},{8},{9},{10}} [7,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,1,2,3,4,5,6,10,8,9]=>{{1,2,3,4,5,6,7},{8,9,10}} [8,1,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,2,3,4,5,6,7,9,10]=>{{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]=>[8,1,2,3,4,5,6,7,10,9]=>{{1,2,3,4,5,6,7,8},{9,10}} [9,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8,10]=>{{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]=>[10,1,2,3,4,5,6,7,8,9]=>{{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]=>[1,11,2,3,4,5,6,7,8,9,10]=>{{1},{2,3,4,5,6,7,8,9,10,11}} [10,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,9,11]=>{{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]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} [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]=>[1,2,3,4,5,6,7,8,9,11,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}} [1,2,2,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,11,10]=>{{1},{2,3},{4,5},{6,7},{8,9},{10,11}}
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Map
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].