Identifier
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00229: Dyck paths —Delest-Viennot⟶ Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
Images
=>
Cc0005;cc-rep-1Cc0005;cc-rep-2Cc0007;cc-rep-3
[1]=>[1,0]=>[1,0]=>[[1],[2]] [1,1]=>[1,0,1,0]=>[1,1,0,0]=>[[1,2],[3,4]] [2]=>[1,1,0,0]=>[1,0,1,0]=>[[1,3],[2,4]] [1,1,1]=>[1,0,1,0,1,0]=>[1,1,0,1,0,0]=>[[1,2,4],[3,5,6]] [1,2]=>[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[[1,2,5],[3,4,6]] [2,1]=>[1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[[1,3,4],[2,5,6]] [3]=>[1,1,1,0,0,0]=>[1,0,1,0,1,0]=>[[1,3,5],[2,4,6]] [1,1,1,1]=>[1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0]=>[[1,2,4,6],[3,5,7,8]] [1,1,2]=>[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0]=>[[1,2,4,7],[3,5,6,8]] [1,2,1]=>[1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0]=>[[1,2,5,6],[3,4,7,8]] [1,3]=>[1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0]=>[[1,2,5,7],[3,4,6,8]] [2,1,1]=>[1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0]=>[[1,3,4,6],[2,5,7,8]] [2,2]=>[1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0]=>[[1,3,4,7],[2,5,6,8]] [3,1]=>[1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0]=>[[1,3,5,6],[2,4,7,8]] [4]=>[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>[[1,3,5,7],[2,4,6,8]] [1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]=>[[1,2,4,6,8],[3,5,7,9,10]] [1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[[1,2,4,6,9],[3,5,7,8,10]] [1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0]=>[[1,2,4,7,8],[3,5,6,9,10]] [1,1,3]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[[1,2,4,7,9],[3,5,6,8,10]] [1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,0]=>[[1,2,5,6,8],[3,4,7,9,10]] [1,2,2]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[[1,2,5,6,9],[3,4,7,8,10]] [1,3,1]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]=>[[1,2,5,7,8],[3,4,6,9,10]] [1,4]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[[1,2,5,7,9],[3,4,6,8,10]] [2,1,1,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0]=>[[1,3,4,6,8],[2,5,7,9,10]] [2,1,2]=>[1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>[[1,3,4,6,9],[2,5,7,8,10]] [2,2,1]=>[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[[1,3,4,7,8],[2,5,6,9,10]] [2,3]=>[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>[[1,3,4,7,9],[2,5,6,8,10]] [3,1,1]=>[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0]=>[[1,3,5,6,8],[2,4,7,9,10]] [3,2]=>[1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>[[1,3,5,6,9],[2,4,7,8,10]] [4,1]=>[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>[[1,3,5,7,8],[2,4,6,9,10]] [5]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[1,3,5,7,9],[2,4,6,8,10]] [1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[[1,2,4,6,8,10],[3,5,7,9,11,12]] [1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[[1,2,4,6,8,11],[3,5,7,9,10,12]] [1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[[1,2,4,6,9,10],[3,5,7,8,11,12]] [1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[[1,2,4,6,9,11],[3,5,7,8,10,12]] [1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[[1,2,4,7,8,10],[3,5,6,9,11,12]] [1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[[1,2,4,7,8,11],[3,5,6,9,10,12]] [1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[[1,2,4,7,9,10],[3,5,6,8,11,12]] [1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[[1,2,4,7,9,11],[3,5,6,8,10,12]] [1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[[1,2,5,6,8,10],[3,4,7,9,11,12]] [1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[[1,2,5,6,8,11],[3,4,7,9,10,12]] [1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[[1,2,5,6,9,10],[3,4,7,8,11,12]] [1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[[1,2,5,6,9,11],[3,4,7,8,10,12]] [1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[[1,2,5,7,8,10],[3,4,6,9,11,12]] [1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[[1,2,5,7,8,11],[3,4,6,9,10,12]] [1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[[1,2,5,7,9,10],[3,4,6,8,11,12]] [1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[[1,2,5,7,9,11],[3,4,6,8,10,12]] [2,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[[1,3,4,6,8,10],[2,5,7,9,11,12]] [2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[[1,3,4,6,8,11],[2,5,7,9,10,12]] [2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[[1,3,4,6,9,10],[2,5,7,8,11,12]] [2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[[1,3,4,6,9,11],[2,5,7,8,10,12]] [2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[[1,3,4,7,8,10],[2,5,6,9,11,12]] [2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[[1,3,4,7,8,11],[2,5,6,9,10,12]] [2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[[1,3,4,7,9,10],[2,5,6,8,11,12]] [2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[1,3,4,7,9,11],[2,5,6,8,10,12]] [3,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[[1,3,5,6,8,10],[2,4,7,9,11,12]] [3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[[1,3,5,6,8,11],[2,4,7,9,10,12]] [3,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[[1,3,5,6,9,10],[2,4,7,8,11,12]] [3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[1,3,5,6,9,11],[2,4,7,8,10,12]] [4,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[[1,3,5,7,8,10],[2,4,6,9,11,12]] [4,2]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[1,3,5,7,8,11],[2,4,6,9,10,12]] [5,1]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[[1,3,5,7,9,10],[2,4,6,8,11,12]] [6]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]] [1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[1,2,4,6,8,10,12],[3,5,7,9,11,13,14]] [1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[1,2,4,6,8,10,13],[3,5,7,9,11,12,14]] [1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[1,2,4,6,8,11,12],[3,5,7,9,10,13,14]] [1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[1,2,4,6,8,11,13],[3,5,7,9,10,12,14]] [1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[1,2,4,6,9,10,12],[3,5,7,8,11,13,14]] [1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[1,2,4,6,9,10,13],[3,5,7,8,11,12,14]] [1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[1,2,4,6,9,11,12],[3,5,7,8,10,13,14]] [1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[1,2,4,6,9,11,13],[3,5,7,8,10,12,14]] [1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[1,2,4,7,8,10,12],[3,5,6,9,11,13,14]] [1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[1,2,4,7,8,10,13],[3,5,6,9,11,12,14]] [1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[1,2,4,7,8,11,12],[3,5,6,9,10,13,14]] [1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[1,2,4,7,8,11,13],[3,5,6,9,10,12,14]] [1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[1,2,4,7,9,10,12],[3,5,6,8,11,13,14]] [1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[1,2,4,7,9,10,13],[3,5,6,8,11,12,14]] [1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[1,2,4,7,9,11,12],[3,5,6,8,10,13,14]] [1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[1,2,4,7,9,11,13],[3,5,6,8,10,12,14]] [1,2,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[1,2,5,6,8,10,12],[3,4,7,9,11,13,14]] [1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[1,2,5,6,8,10,13],[3,4,7,9,11,12,14]] [1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[1,2,5,6,8,11,12],[3,4,7,9,10,13,14]] [1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[1,2,5,6,8,11,13],[3,4,7,9,10,12,14]] [1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[1,2,5,6,9,10,12],[3,4,7,8,11,13,14]] [1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[1,2,5,6,9,10,13],[3,4,7,8,11,12,14]] [1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[1,2,5,6,9,11,12],[3,4,7,8,10,13,14]] [1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[1,2,5,6,9,11,13],[3,4,7,8,10,12,14]] [1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[1,2,5,7,8,10,12],[3,4,6,9,11,13,14]] [1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[1,2,5,7,8,10,13],[3,4,6,9,11,12,14]] [1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[1,2,5,7,8,11,12],[3,4,6,9,10,13,14]] [1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[1,2,5,7,8,11,13],[3,4,6,9,10,12,14]] [1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[1,2,5,7,9,10,12],[3,4,6,8,11,13,14]] [1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[1,2,5,7,9,10,13],[3,4,6,8,11,12,14]] [1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[1,2,5,7,9,11,12],[3,4,6,8,10,13,14]] [1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[1,2,5,7,9,11,13],[3,4,6,8,10,12,14]] [2,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[1,3,4,6,8,10,12],[2,5,7,9,11,13,14]] [2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[1,3,4,6,8,10,13],[2,5,7,9,11,12,14]] [2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[1,3,4,6,8,11,12],[2,5,7,9,10,13,14]] [2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[1,3,4,6,8,11,13],[2,5,7,9,10,12,14]] [2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[1,3,4,6,9,10,12],[2,5,7,8,11,13,14]] [2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[1,3,4,6,9,10,13],[2,5,7,8,11,12,14]] [2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[1,3,4,6,9,11,12],[2,5,7,8,10,13,14]] [2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[1,3,4,6,9,11,13],[2,5,7,8,10,12,14]] [2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[1,3,4,7,8,10,12],[2,5,6,9,11,13,14]] [2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[1,3,4,7,8,10,13],[2,5,6,9,11,12,14]] [2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[1,3,4,7,8,11,12],[2,5,6,9,10,13,14]] [2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[1,3,4,7,8,11,13],[2,5,6,9,10,12,14]] [2,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[1,3,4,7,9,10,12],[2,5,6,8,11,13,14]] [2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[1,3,4,7,9,10,13],[2,5,6,8,11,12,14]] [2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[1,3,4,7,9,11,12],[2,5,6,8,10,13,14]] [2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[1,3,4,7,9,11,13],[2,5,6,8,10,12,14]] [3,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[1,3,5,6,8,10,12],[2,4,7,9,11,13,14]] [3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[1,3,5,6,8,10,13],[2,4,7,9,11,12,14]] [3,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[1,3,5,6,8,11,12],[2,4,7,9,10,13,14]] [3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[1,3,5,6,8,11,13],[2,4,7,9,10,12,14]] [3,2,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[1,3,5,6,9,10,12],[2,4,7,8,11,13,14]] [3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[1,3,5,6,9,10,13],[2,4,7,8,11,12,14]] [3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[1,3,5,6,9,11,12],[2,4,7,8,10,13,14]] [3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[1,3,5,6,9,11,13],[2,4,7,8,10,12,14]] [4,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[1,3,5,7,8,10,12],[2,4,6,9,11,13,14]] [4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[1,3,5,7,8,10,13],[2,4,6,9,11,12,14]] [4,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[1,3,5,7,8,11,12],[2,4,6,9,10,13,14]] [4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[1,3,5,7,8,11,13],[2,4,6,9,10,12,14]] [5,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[1,3,5,7,9,10,12],[2,4,6,8,11,13,14]] [5,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[1,3,5,7,9,10,13],[2,4,6,8,11,12,14]] [6,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[1,3,5,7,9,11,12],[2,4,6,8,10,13,14]] [7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,3,5,7,9,11,13],[2,4,6,8,10,12,14]] [1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[1,2,4,6,8,10,12,14],[3,5,7,9,11,13,15,16]] [1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[1,2,4,6,8,10,12,15],[3,5,7,9,11,13,14,16]] [1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[1,2,4,6,8,10,13,14],[3,5,7,9,11,12,15,16]] [1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[1,2,4,6,8,10,13,15],[3,5,7,9,11,12,14,16]] [1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[1,2,4,6,8,11,12,14],[3,5,7,9,10,13,15,16]] [1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[1,2,4,6,8,11,12,15],[3,5,7,9,10,13,14,16]] [1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[1,2,4,6,8,11,13,14],[3,5,7,9,10,12,15,16]] [1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[1,2,4,6,8,11,13,15],[3,5,7,9,10,12,14,16]] [1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[1,2,4,6,9,10,12,14],[3,5,7,8,11,13,15,16]] [1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[1,2,4,6,9,10,12,15],[3,5,7,8,11,13,14,16]] [1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[1,2,4,6,9,10,13,14],[3,5,7,8,11,12,15,16]] [1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[1,2,4,6,9,10,13,15],[3,5,7,8,11,12,14,16]] [1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[1,2,4,6,9,11,12,14],[3,5,7,8,10,13,15,16]] [1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[1,2,4,6,9,11,12,15],[3,5,7,8,10,13,14,16]] [1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[1,2,4,6,9,11,13,14],[3,5,7,8,10,12,15,16]] [1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[1,2,4,6,9,11,13,15],[3,5,7,8,10,12,14,16]] [1,1,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[1,2,4,7,8,10,12,14],[3,5,6,9,11,13,15,16]] [1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[1,2,4,7,8,10,12,15],[3,5,6,9,11,13,14,16]] [1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[1,2,4,7,8,10,13,14],[3,5,6,9,11,12,15,16]] [1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[1,2,4,7,8,10,13,15],[3,5,6,9,11,12,14,16]] [1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[1,2,4,7,8,11,12,14],[3,5,6,9,10,13,15,16]] [1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[1,2,4,7,8,11,12,15],[3,5,6,9,10,13,14,16]] [1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[1,2,4,7,8,11,13,14],[3,5,6,9,10,12,15,16]] [1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[1,2,4,7,8,11,13,15],[3,5,6,9,10,12,14,16]] [1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[1,2,4,7,9,10,12,14],[3,5,6,8,11,13,15,16]] [1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[1,2,4,7,9,10,12,15],[3,5,6,8,11,13,14,16]] [1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[1,2,4,7,9,10,13,14],[3,5,6,8,11,12,15,16]] [1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[1,2,4,7,9,10,13,15],[3,5,6,8,11,12,14,16]] [1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[1,2,4,7,9,11,12,14],[3,5,6,8,10,13,15,16]] [1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[1,2,4,7,9,11,12,15],[3,5,6,8,10,13,14,16]] [1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[1,2,4,7,9,11,13,14],[3,5,6,8,10,12,15,16]] [1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[1,2,4,7,9,11,13,15],[3,5,6,8,10,12,14,16]] [1,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[1,2,5,6,8,10,12,14],[3,4,7,9,11,13,15,16]] [1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[1,2,5,6,8,10,12,15],[3,4,7,9,11,13,14,16]] [1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[1,2,5,6,8,10,13,14],[3,4,7,9,11,12,15,16]] [1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[1,2,5,6,8,10,13,15],[3,4,7,9,11,12,14,16]] [1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[1,2,5,6,8,11,12,14],[3,4,7,9,10,13,15,16]] [1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[1,2,5,6,8,11,12,15],[3,4,7,9,10,13,14,16]] [1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[1,2,5,6,8,11,13,14],[3,4,7,9,10,12,15,16]] [1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[1,2,5,6,8,11,13,15],[3,4,7,9,10,12,14,16]] [1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[1,2,5,6,9,10,12,14],[3,4,7,8,11,13,15,16]] [1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[1,2,5,6,9,10,12,15],[3,4,7,8,11,13,14,16]] [1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[1,2,5,6,9,10,13,14],[3,4,7,8,11,12,15,16]] [1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[1,2,5,6,9,10,13,15],[3,4,7,8,11,12,14,16]] [1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[1,2,5,6,9,11,12,14],[3,4,7,8,10,13,15,16]] [1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[1,2,5,6,9,11,12,15],[3,4,7,8,10,13,14,16]] [1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[1,2,5,6,9,11,13,14],[3,4,7,8,10,12,15,16]] [1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[1,2,5,6,9,11,13,15],[3,4,7,8,10,12,14,16]] [1,3,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[1,2,5,7,8,10,12,14],[3,4,6,9,11,13,15,16]] [1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[1,2,5,7,8,10,12,15],[3,4,6,9,11,13,14,16]] [1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[1,2,5,7,8,10,13,14],[3,4,6,9,11,12,15,16]] [1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[1,2,5,7,8,10,13,15],[3,4,6,9,11,12,14,16]] [1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[1,2,5,7,8,11,12,14],[3,4,6,9,10,13,15,16]] [1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[1,2,5,7,8,11,12,15],[3,4,6,9,10,13,14,16]] [1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[1,2,5,7,8,11,13,14],[3,4,6,9,10,12,15,16]] [1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[1,2,5,7,8,11,13,15],[3,4,6,9,10,12,14,16]] [1,4,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[1,2,5,7,9,10,12,14],[3,4,6,8,11,13,15,16]] [1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[1,2,5,7,9,10,12,15],[3,4,6,8,11,13,14,16]] [1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[1,2,5,7,9,10,13,14],[3,4,6,8,11,12,15,16]] [1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[1,2,5,7,9,10,13,15],[3,4,6,8,11,12,14,16]] [1,5,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[1,2,5,7,9,11,12,14],[3,4,6,8,10,13,15,16]] [1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[1,2,5,7,9,11,12,15],[3,4,6,8,10,13,14,16]] [1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[1,2,5,7,9,11,13,14],[3,4,6,8,10,12,15,16]] [1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,2,5,7,9,11,13,15],[3,4,6,8,10,12,14,16]] [2,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[1,3,4,6,8,10,12,14],[2,5,7,9,11,13,15,16]] [2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[1,3,4,6,8,10,12,15],[2,5,7,9,11,13,14,16]] [2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[1,3,4,6,8,10,13,14],[2,5,7,9,11,12,15,16]] [2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[1,3,4,6,8,10,13,15],[2,5,7,9,11,12,14,16]] [2,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[1,3,4,6,8,11,12,14],[2,5,7,9,10,13,15,16]] [2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[1,3,4,6,8,11,12,15],[2,5,7,9,10,13,14,16]] [2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[1,3,4,6,8,11,13,14],[2,5,7,9,10,12,15,16]] [2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[1,3,4,6,8,11,13,15],[2,5,7,9,10,12,14,16]] [2,1,2,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[1,3,4,6,9,10,12,14],[2,5,7,8,11,13,15,16]] [2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[1,3,4,6,9,10,12,15],[2,5,7,8,11,13,14,16]] [2,1,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[1,3,4,6,9,10,13,14],[2,5,7,8,11,12,15,16]] [2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[1,3,4,6,9,10,13,15],[2,5,7,8,11,12,14,16]] [2,1,3,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[1,3,4,6,9,11,12,14],[2,5,7,8,10,13,15,16]] [2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[1,3,4,6,9,11,12,15],[2,5,7,8,10,13,14,16]] [2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[1,3,4,6,9,11,13,14],[2,5,7,8,10,12,15,16]] [2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[1,3,4,6,9,11,13,15],[2,5,7,8,10,12,14,16]] [2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[1,3,4,7,8,10,12,14],[2,5,6,9,11,13,15,16]] [2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[1,3,4,7,8,10,12,15],[2,5,6,9,11,13,14,16]] [2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[1,3,4,7,8,10,13,14],[2,5,6,9,11,12,15,16]] [2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[1,3,4,7,8,10,13,15],[2,5,6,9,11,12,14,16]] [2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[1,3,4,7,8,11,12,14],[2,5,6,9,10,13,15,16]] [2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[1,3,4,7,8,11,12,15],[2,5,6,9,10,13,14,16]] [2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[1,3,4,7,8,11,13,14],[2,5,6,9,10,12,15,16]] [2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[1,3,4,7,8,11,13,15],[2,5,6,9,10,12,14,16]] [2,3,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[1,3,4,7,9,10,12,14],[2,5,6,8,11,13,15,16]] [2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[1,3,4,7,9,10,12,15],[2,5,6,8,11,13,14,16]] [2,3,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[1,3,4,7,9,10,13,14],[2,5,6,8,11,12,15,16]] [2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[1,3,4,7,9,10,13,15],[2,5,6,8,11,12,14,16]] [2,4,1,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[1,3,4,7,9,11,12,14],[2,5,6,8,10,13,15,16]] [2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[1,3,4,7,9,11,12,15],[2,5,6,8,10,13,14,16]] [2,5,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[1,3,4,7,9,11,13,14],[2,5,6,8,10,12,15,16]] [2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[1,3,4,7,9,11,13,15],[2,5,6,8,10,12,14,16]] [3,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[1,3,5,6,8,10,12,14],[2,4,7,9,11,13,15,16]] [3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[1,3,5,6,8,10,12,15],[2,4,7,9,11,13,14,16]] [3,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[1,3,5,6,8,10,13,14],[2,4,7,9,11,12,15,16]] [3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[1,3,5,6,8,10,13,15],[2,4,7,9,11,12,14,16]] [3,1,2,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[1,3,5,6,8,11,12,14],[2,4,7,9,10,13,15,16]] [3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[1,3,5,6,8,11,12,15],[2,4,7,9,10,13,14,16]] [3,1,3,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[1,3,5,6,8,11,13,14],[2,4,7,9,10,12,15,16]] [3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[1,3,5,6,8,11,13,15],[2,4,7,9,10,12,14,16]] [3,2,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[1,3,5,6,9,10,12,14],[2,4,7,8,11,13,15,16]] [3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[1,3,5,6,9,10,12,15],[2,4,7,8,11,13,14,16]] [3,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[1,3,5,6,9,10,13,14],[2,4,7,8,11,12,15,16]] [3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[1,3,5,6,9,10,13,15],[2,4,7,8,11,12,14,16]] [3,3,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[1,3,5,6,9,11,12,14],[2,4,7,8,10,13,15,16]] [3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[1,3,5,6,9,11,12,15],[2,4,7,8,10,13,14,16]] [3,4,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[1,3,5,6,9,11,13,14],[2,4,7,8,10,12,15,16]] [3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[1,3,5,6,9,11,13,15],[2,4,7,8,10,12,14,16]] [4,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[1,3,5,7,8,10,12,14],[2,4,6,9,11,13,15,16]] [4,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[1,3,5,7,8,10,12,15],[2,4,6,9,11,13,14,16]] [4,1,2,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[1,3,5,7,8,10,13,14],[2,4,6,9,11,12,15,16]] [4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[1,3,5,7,8,10,13,15],[2,4,6,9,11,12,14,16]] [4,2,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[1,3,5,7,8,11,12,14],[2,4,6,9,10,13,15,16]] [4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[1,3,5,7,8,11,12,15],[2,4,6,9,10,13,14,16]] [4,3,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[1,3,5,7,8,11,13,14],[2,4,6,9,10,12,15,16]] [4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[1,3,5,7,8,11,13,15],[2,4,6,9,10,12,14,16]] [5,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[1,3,5,7,9,10,12,14],[2,4,6,8,11,13,15,16]] [5,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[1,3,5,7,9,10,12,15],[2,4,6,8,11,13,14,16]] [5,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[1,3,5,7,9,10,13,14],[2,4,6,8,11,12,15,16]] [5,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[1,3,5,7,9,10,13,15],[2,4,6,8,11,12,14,16]] [6,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[1,3,5,7,9,11,12,14],[2,4,6,8,10,13,15,16]] [6,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[1,3,5,7,9,11,12,15],[2,4,6,8,10,13,14,16]] [7,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[1,3,5,7,9,11,13,14],[2,4,6,8,10,12,15,16]] [8]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,3,5,7,9,11,13,15],[2,4,6,8,10,12,14,16]] [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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[1,2,4,6,8,10,12,14,16],[3,5,7,9,11,13,15,17,18]] [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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[1,2,4,6,8,10,12,14,17],[3,5,7,9,11,13,15,16,18]] [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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[1,2,4,6,8,10,12,15,16],[3,5,7,9,11,13,14,17,18]] [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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[1,2,4,6,8,10,12,15,17],[3,5,7,9,11,13,14,16,18]] [1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[1,2,4,6,8,10,13,15,17],[3,5,7,9,11,12,14,16,18]] [1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[1,2,4,6,8,11,13,15,17],[3,5,7,9,10,12,14,16,18]] [1,1,1,6]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[1,2,4,6,9,11,13,15,17],[3,5,7,8,10,12,14,16,18]] [1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,2,4,7,9,11,13,15,17],[3,5,6,8,10,12,14,16,18]] [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]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[1,2,5,6,8,10,12,14,16],[3,4,7,9,11,13,15,17,18]] [1,2,6]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[1,2,5,6,9,11,13,15,17],[3,4,7,8,10,12,14,16,18]] [1,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[1,2,5,7,9,11,13,14,17],[3,4,6,8,10,12,15,16,18]] [1,7,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[1,2,5,7,9,11,13,15,16],[3,4,6,8,10,12,14,17,18]] [1,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,2,5,7,9,11,13,15,17],[3,4,6,8,10,12,14,16,18]] [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]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[1,3,4,6,8,10,12,14,16],[2,5,7,9,11,13,15,17,18]] [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]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[1,3,4,7,8,10,12,14,16],[2,5,6,9,11,13,15,17,18]] [2,7]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,3,4,7,9,11,13,15,17],[2,5,6,8,10,12,14,16,18]] [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]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[1,3,5,6,8,10,12,14,16],[2,4,7,9,11,13,15,17,18]] [3,6]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[1,3,5,6,9,11,13,15,17],[2,4,7,8,10,12,14,16,18]] [4,1,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[1,3,5,7,8,10,12,14,16],[2,4,6,9,11,13,15,17,18]] [4,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[1,3,5,7,8,11,13,15,17],[2,4,6,9,10,12,14,16,18]] [5,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[1,3,5,7,9,10,12,14,16],[2,4,6,8,11,13,15,17,18]] [5,4]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[1,3,5,7,9,10,13,15,17],[2,4,6,8,11,12,14,16,18]] [6,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[1,3,5,7,9,11,12,14,16],[2,4,6,8,10,13,15,17,18]] [6,3]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[1,3,5,7,9,11,12,15,17],[2,4,6,8,10,13,14,16,18]] [7,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[1,3,5,7,9,11,13,14,16],[2,4,6,8,10,12,15,17,18]] [7,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[1,3,5,7,9,11,13,14,17],[2,4,6,8,10,12,15,16,18]] [8,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[1,3,5,7,9,11,13,15,16],[2,4,6,8,10,12,14,17,18]] [9]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,3,5,7,9,11,13,15,17],[2,4,6,8,10,12,14,16,18]] [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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[1,2,4,6,8,10,12,14,16,18],[3,5,7,9,11,13,15,17,19,20]] [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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[1,2,4,6,8,10,12,14,16,19],[3,5,7,9,11,13,15,17,18,20]] [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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[1,2,4,6,8,10,12,14,17,19],[3,5,7,9,11,13,15,16,18,20]] [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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[1,2,4,6,8,10,12,15,17,19],[3,5,7,9,11,13,14,16,18,20]] [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]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[1,2,4,6,8,10,13,15,17,19],[3,5,7,9,11,12,14,16,18,20]] [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]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[1,2,4,6,8,11,13,15,17,19],[3,5,7,9,10,12,14,16,18,20]] [1,1,1,7]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,2,4,6,9,11,13,15,17,19],[3,5,7,8,10,12,14,16,18,20]] [1,1,8]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,2,4,7,9,11,13,15,17,19],[3,5,6,8,10,12,14,16,18,20]] [1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[1,2,5,7,9,11,13,15,17,18],[3,4,6,8,10,12,14,16,19,20]] [1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,2,5,7,9,11,13,15,17,19],[3,4,6,8,10,12,14,16,18,20]] [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]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[1,3,4,6,8,10,12,14,16,18],[2,5,7,9,11,13,15,17,19,20]] [2,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,3,4,7,9,11,13,15,17,19],[2,5,6,8,10,12,14,16,18,20]] [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]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[1,3,5,6,8,10,12,14,16,18],[2,4,7,9,11,13,15,17,19,20]] [3,7]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,3,5,6,9,11,13,15,17,19],[2,4,7,8,10,12,14,16,18,20]] [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]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[1,3,5,7,8,10,12,14,16,18],[2,4,6,9,11,13,15,17,19,20]] [4,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[1,3,5,7,8,11,13,15,17,19],[2,4,6,9,10,12,14,16,18,20]] [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]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[1,3,5,7,9,10,12,14,16,18],[2,4,6,8,11,13,15,17,19,20]] [5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[1,3,5,7,9,10,13,15,17,19],[2,4,6,8,11,12,14,16,18,20]] [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]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[1,3,5,7,9,11,12,14,16,18],[2,4,6,8,10,13,15,17,19,20]] [6,4]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[1,3,5,7,9,11,12,15,17,19],[2,4,6,8,10,13,14,16,18,20]] [7,1,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[1,3,5,7,9,11,13,14,16,18],[2,4,6,8,10,12,15,17,19,20]] [7,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[1,3,5,7,9,11,13,14,17,19],[2,4,6,8,10,12,15,16,18,20]] [8,1,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[1,3,5,7,9,11,13,15,16,18],[2,4,6,8,10,12,14,17,19,20]] [8,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[1,3,5,7,9,11,13,15,16,19],[2,4,6,8,10,12,14,17,18,20]] [9,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[1,3,5,7,9,11,13,15,17,18],[2,4,6,8,10,12,14,16,19,20]] [10]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,3,5,7,9,11,13,15,17,19],[2,4,6,8,10,12,14,16,18,20]]
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
Delest-Viennot
Description
Return the Dyck path corresponding to the parallelogram polyomino obtained by applying Delest-Viennot's bijection.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
The Delest-Viennot bijection $\beta$ returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path $(\gamma^{(-1)}\circ\beta)(D)$.
Map
to two-row standard tableau
Description
Return a standard tableau of shape $(n,n)$ where $n$ is the semilength of the Dyck path.
Given a Dyck path $D$, its image is given by recording the positions of the up-steps in the first row and the positions of the down-steps in the second row.