Identifier
Mp00028: Dyck paths —reverse⟶ Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
Mp00082: Standard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0007;cc-rep-2Cc0018;cc-rep-3
[1,0]=>[1,0]=>[[1],[2]]=>[[1,1],[1]] [1,0,1,0]=>[1,0,1,0]=>[[1,3],[2,4]]=>[[2,2,0,0],[2,1,0],[1,1],[1]] [1,1,0,0]=>[1,1,0,0]=>[[1,2],[3,4]]=>[[2,2,0,0],[2,1,0],[2,0],[1]] [1,0,1,0,1,0]=>[1,0,1,0,1,0]=>[[1,3,5],[2,4,6]]=>[[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[[1,2,5],[3,4,6]]=>[[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[[1,3,4],[2,5,6]]=>[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,0,1,0,0]=>[1,1,0,1,0,0]=>[[1,2,4],[3,5,6]]=>[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[[1,2,3],[4,5,6]]=>[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>[[1,3,5,7],[2,4,6,8]]=>[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0]=>[[1,2,5,7],[3,4,6,8]]=>[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[[1,3,4,7],[2,5,6,8]]=>[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>[[1,2,4,7],[3,5,6,8]]=>[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0]=>[[1,2,3,7],[4,5,6,8]]=>[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0]=>[[1,3,5,6],[2,4,7,8]]=>[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[[1,2,5,6],[3,4,7,8]]=>[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0]=>[[1,3,4,6],[2,5,7,8]]=>[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0]=>[[1,2,4,6],[3,5,7,8]]=>[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0]=>[[1,2,3,6],[4,5,7,8]]=>[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0]=>[[1,3,4,5],[2,6,7,8]]=>[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0]=>[[1,2,4,5],[3,6,7,8]]=>[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0]=>[[1,2,3,5],[4,6,7,8]]=>[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>[[1,2,3,4],[5,6,7,8]]=>[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [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],[2,4,6,8,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[[1,2,5,7,9],[3,4,6,8,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[[1,3,4,7,9],[2,5,6,8,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[[1,2,4,7,9],[3,5,6,8,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[[1,2,3,7,9],[4,5,6,8,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[[1,3,5,6,9],[2,4,7,8,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [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]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]=>[[1,3,4,6,9],[2,5,7,8,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[[1,2,4,6,9],[3,5,7,8,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[[1,2,3,6,9],[4,5,7,8,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[[1,3,4,5,9],[2,6,7,8,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[[1,2,4,5,9],[3,6,7,8,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[[1,2,3,5,9],[4,6,7,8,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[[1,2,3,4,9],[5,6,7,8,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>[[1,3,5,7,8],[2,4,6,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[[1,2,5,7,8],[3,4,6,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[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]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[[1,2,4,7,8],[3,5,6,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[[1,2,3,7,8],[4,5,6,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0]=>[[1,3,5,6,8],[2,4,7,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>[[1,2,5,6,8],[3,4,7,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0]=>[[1,3,4,6,8],[2,5,7,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>[[1,2,4,6,8],[3,5,7,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>[[1,2,3,6,8],[4,5,7,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]=>[[1,3,4,5,8],[2,6,7,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>[[1,2,4,5,8],[3,6,7,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>[[1,2,3,5,8],[4,6,7,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[[1,2,3,4,8],[5,6,7,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0]=>[[1,3,5,6,7],[2,4,8,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[[1,2,5,6,7],[3,4,8,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0]=>[[1,3,4,6,7],[2,5,8,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[[1,2,4,6,7],[3,5,8,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[[1,2,3,6,7],[4,5,8,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0]=>[[1,3,4,5,7],[2,6,8,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[[1,2,4,5,7],[3,6,8,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[[1,2,3,5,7],[4,6,8,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[[1,2,3,4,7],[5,6,8,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>[[1,3,4,5,6],[2,7,8,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[[1,2,4,5,6],[3,7,8,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[[1,2,3,5,6],[4,7,8,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[[1,2,3,4,6],[5,7,8,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [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]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[[1,2,5,7,9,11],[3,4,6,8,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[1,3,4,7,9,11],[2,5,6,8,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[[1,2,4,7,9,11],[3,5,6,8,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[[1,2,3,7,9,11],[4,5,6,8,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[1,3,5,6,9,11],[2,4,7,8,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[[1,2,5,6,9,11],[3,4,7,8,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[[1,3,4,6,9,11],[2,5,7,8,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[[1,2,4,6,9,11],[3,5,7,8,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[[1,2,3,6,9,11],[4,5,7,8,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[[1,3,4,5,9,11],[2,6,7,8,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[[1,2,4,5,9,11],[3,6,7,8,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[[1,2,3,5,9,11],[4,6,7,8,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[[1,2,3,4,9,11],[5,6,7,8,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[1,3,5,7,8,11],[2,4,6,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[[1,2,5,7,8,11],[3,4,6,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[[1,3,4,7,8,11],[2,5,6,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[[1,2,4,7,8,11],[3,5,6,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[[1,2,3,7,8,11],[4,5,6,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[[1,3,5,6,8,11],[2,4,7,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[[1,2,5,6,8,11],[3,4,7,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[[1,3,4,6,8,11],[2,5,7,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[[1,2,4,6,8,11],[3,5,7,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[[1,2,3,6,8,11],[4,5,7,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[[1,3,4,5,8,11],[2,6,7,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[[1,2,4,5,8,11],[3,6,7,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[[1,2,3,5,8,11],[4,6,7,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[[1,2,3,4,8,11],[5,6,7,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[[1,3,5,6,7,11],[2,4,8,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[[1,2,5,6,7,11],[3,4,8,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[[1,3,4,6,7,11],[2,5,8,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[[1,2,4,6,7,11],[3,5,8,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[[1,2,3,6,7,11],[4,5,8,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[[1,3,4,5,7,11],[2,6,8,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[[1,2,4,5,7,11],[3,6,8,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[[1,2,3,5,7,11],[4,6,8,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[[1,2,3,4,7,11],[5,6,8,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[[1,3,4,5,6,11],[2,7,8,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[[1,2,4,5,6,11],[3,7,8,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[[1,2,3,5,6,11],[4,7,8,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[[1,2,3,4,6,11],[5,7,8,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[[1,2,3,4,5,11],[6,7,8,9,10,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[[1,3,5,7,9,10],[2,4,6,8,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[[1,2,5,7,9,10],[3,4,6,8,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[[1,3,4,7,9,10],[2,5,6,8,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[[1,2,4,7,9,10],[3,5,6,8,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[[1,2,3,7,9,10],[4,5,6,8,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[[1,3,5,6,9,10],[2,4,7,8,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[[1,2,5,6,9,10],[3,4,7,8,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[[1,3,4,6,9,10],[2,5,7,8,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[[1,2,4,6,9,10],[3,5,7,8,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[[1,2,3,6,9,10],[4,5,7,8,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[[1,3,4,5,9,10],[2,6,7,8,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[[1,2,4,5,9,10],[3,6,7,8,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[[1,2,3,5,9,10],[4,6,7,8,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[[1,2,3,4,9,10],[5,6,7,8,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[[1,3,5,7,8,10],[2,4,6,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[[1,2,5,7,8,10],[3,4,6,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[[1,3,4,7,8,10],[2,5,6,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[[1,2,4,7,8,10],[3,5,6,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[[1,2,3,7,8,10],[4,5,6,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[[1,3,5,6,8,10],[2,4,7,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[[1,2,5,6,8,10],[3,4,7,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[[1,3,4,6,8,10],[2,5,7,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[[1,2,4,6,8,10],[3,5,7,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[[1,2,3,6,8,10],[4,5,7,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[[1,3,4,5,8,10],[2,6,7,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[[1,2,4,5,8,10],[3,6,7,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[[1,2,3,5,8,10],[4,6,7,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[[1,2,3,4,8,10],[5,6,7,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[[1,3,5,6,7,10],[2,4,8,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[[1,2,5,6,7,10],[3,4,8,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[[1,3,4,6,7,10],[2,5,8,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[[1,2,4,6,7,10],[3,5,8,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[[1,2,3,6,7,10],[4,5,8,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[[1,3,4,5,7,10],[2,6,8,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[[1,2,4,5,7,10],[3,6,8,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[[1,2,3,5,7,10],[4,6,8,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[[1,2,3,4,7,10],[5,6,8,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[[1,3,4,5,6,10],[2,7,8,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[[1,2,4,5,6,10],[3,7,8,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[[1,2,3,5,6,10],[4,7,8,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[[1,2,3,4,6,10],[5,7,8,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[[1,2,3,4,5,10],[6,7,8,9,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[[1,3,5,7,8,9],[2,4,6,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[[1,2,5,7,8,9],[3,4,6,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[[1,3,4,7,8,9],[2,5,6,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[[1,2,4,7,8,9],[3,5,6,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[[1,2,3,7,8,9],[4,5,6,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[[1,3,5,6,8,9],[2,4,7,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[[1,2,5,6,8,9],[3,4,7,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[[1,3,4,6,8,9],[2,5,7,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[[1,2,4,6,8,9],[3,5,7,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[[1,2,3,6,8,9],[4,5,7,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[[1,3,4,5,8,9],[2,6,7,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[[1,2,4,5,8,9],[3,6,7,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[[1,2,3,5,8,9],[4,6,7,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[[1,2,3,4,8,9],[5,6,7,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[[1,3,5,6,7,9],[2,4,8,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[[1,2,5,6,7,9],[3,4,8,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[[1,3,4,6,7,9],[2,5,8,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[[1,2,4,6,7,9],[3,5,8,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[[1,2,3,6,7,9],[4,5,8,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[[1,3,4,5,7,9],[2,6,8,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[[1,2,4,5,7,9],[3,6,8,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[[1,2,3,5,7,9],[4,6,8,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[[1,2,3,4,7,9],[5,6,8,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[[1,3,4,5,6,9],[2,7,8,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[[1,2,4,5,6,9],[3,7,8,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[[1,2,3,5,6,9],[4,7,8,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[[1,2,3,4,6,9],[5,7,8,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[[1,2,3,4,5,9],[6,7,8,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[[1,3,5,6,7,8],[2,4,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] [1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[[1,2,5,6,7,8],[3,4,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[[1,3,4,6,7,8],[2,5,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[[1,2,4,6,7,8],[3,5,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[[1,2,3,6,7,8],[4,5,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[[1,3,4,5,7,8],[2,6,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[[1,2,4,5,7,8],[3,6,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[[1,2,3,5,7,8],[4,6,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[[1,2,3,4,7,8],[5,6,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[[1,3,4,5,6,8],[2,7,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[[1,2,4,5,6,8],[3,7,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[[1,2,3,5,6,8],[4,7,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[[1,2,3,4,6,8],[5,7,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[[1,2,3,4,5,8],[6,7,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[[1,3,4,5,6,7],[2,8,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] [1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[[1,2,4,5,6,7],[3,8,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] [1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[[1,2,3,5,6,7],[4,8,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[[1,2,3,4,6,7],[5,8,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[[1,2,3,4,5,7],[6,8,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
Map
reverse
Description
The reversal of a Dyck path.
This is the Dyck path obtained by reading the path backwards.
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.
Map
to Gelfand-Tsetlin pattern
Description
Sends a tableau to its corresponding Gelfand-Tsetlin pattern.
To obtain this Gelfand-Tsetlin pattern, fill in the first row of the pattern with the shape of the tableau.
Then remove the maximal entry from the tableau to obtain a smaller tableau, and repeat the process until the tableau is empty.