- FindStat

Identifier

Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
Mp00112: Set partitions —complement⟶ Set partitions

Images

[1] => [1,0] => {{1}} => {{1}}

[1,1] => [1,0,1,0] => {{1},{2}} => {{1},{2}}

[2] => [1,1,0,0] => {{1,2}} => {{1,2}}

[1,1,1] => [1,0,1,0,1,0] => {{1},{2},{3}} => {{1},{2},{3}}

[1,2] => [1,0,1,1,0,0] => {{1},{2,3}} => {{1,2},{3}}

[2,1] => [1,1,0,0,1,0] => {{1,2},{3}} => {{1},{2,3}}

[3] => [1,1,1,0,0,0] => {{1,2,3}} => {{1,2,3}}

[1,1,1,1] => [1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => {{1},{2},{3},{4}}

[1,1,2] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => {{1,2},{3},{4}}

[1,2,1] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => {{1},{2,3},{4}}

[1,3] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => {{1,2,3},{4}}

[2,1,1] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => {{1},{2},{3,4}}

[2,2] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => {{1,2},{3,4}}

[3,1] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => {{1},{2,3,4}}

[4] => [1,1,1,1,0,0,0,0] => {{1,2,3,4}} => {{1,2,3,4}}

[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5}}

[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => {{1,2},{3},{4},{5}}

[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => {{1},{2,3},{4},{5}}

[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => {{1,2,3},{4},{5}}

[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => {{1},{2},{3,4},{5}}

[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => {{1,2},{3,4},{5}}

[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => {{1},{2,3,4},{5}}

[1,4] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => {{1,2,3,4},{5}}

[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => {{1},{2},{3},{4,5}}

[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => {{1,2},{3},{4,5}}

[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => {{1},{2,3},{4,5}}

[2,3] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => {{1,2,3},{4,5}}

[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => {{1},{2},{3,4,5}}

[3,2] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => {{1,2},{3,4,5}}

[4,1] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => {{1},{2,3,4,5}}

[5] => [1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5}} => {{1,2,3,4,5}}

[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6}}

[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => {{1,2},{3},{4},{5},{6}}

[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{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},{4,5,6}} => {{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},{3,4},{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},{3,4},{5,6}} => {{1,2},{3,4},{5},{6}}

[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => {{1},{2,3,4},{5},{6}}

[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => {{1,2,3,4},{5},{6}}

[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{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},{2,3},{4},{5,6}} => {{1,2},{3},{4,5},{6}}

[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => {{1},{2,3},{4,5},{6}}

[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => {{1,2,3},{4,5},{6}}

[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => {{1},{2},{3,4,5},{6}}

[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => {{1,2},{3,4,5},{6}}

[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => {{1},{2,3,4,5},{6}}

[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => {{1,2,3,4,5},{6}}

[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5,6}}

[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => {{1,2},{3},{4},{5,6}}

[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => {{1},{2,3},{4},{5,6}}

[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => {{1,2,3},{4},{5,6}}

[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => {{1},{2},{3,4},{5,6}}

[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => {{1,2},{3,4},{5,6}}

[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => {{1},{2,3,4},{5,6}}

[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => {{1,2,3,4},{5,6}}

[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => {{1},{2},{3},{4,5,6}}

[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => {{1,2},{3},{4,5,6}}

[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => {{1},{2,3},{4,5,6}}

[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => {{1,2,3},{4,5,6}}

[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => {{1},{2},{3,4,5,6}}

[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => {{1,2},{3,4,5,6}}

[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}}

[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4,5,6}} => {{1,2,3,4,5,6}}

[1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7}}

[1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => {{1,2},{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},{5,6},{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},{5,6,7}} => {{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},{4,5},{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},{4,5},{6,7}} => {{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},{4,5,6},{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},{4,5,6,7}} => {{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},{3,4},{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},{3,4},{5},{6,7}} => {{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},{3,4},{5,6},{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},{3,4},{5,6,7}} => {{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},{3,4,5},{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},{3,4,5},{6,7}} => {{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},{3,4,5,6},{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},{3,4,5,6,7}} => {{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},{2,3},{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},{2,3},{4},{5},{6,7}} => {{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},{2,3},{4},{5,6},{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},{2,3},{4},{5,6,7}} => {{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},{2,3},{4,5},{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},{2,3},{4,5},{6,7}} => {{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},{2,3},{4,5,6},{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},{2,3},{4,5,6,7}} => {{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},{2,3,4},{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},{2,3,4},{5},{6,7}} => {{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},{2,3,4},{5,6},{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},{2,3,4},{5,6,7}} => {{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},{2,3,4,5},{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},{2,3,4,5},{6,7}} => {{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},{2,3,4,5,6},{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},{2,3,4,5,6,7}} => {{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] => {{1,2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6,7}}

[2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => {{1,2},{3},{4},{5},{6,7}}

[2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => {{1},{2,3},{4},{5},{6,7}}

[2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => {{1,2,3},{4},{5},{6,7}}

[2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => {{1},{2},{3,4},{5},{6,7}}

[2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => {{1,2},{3,4},{5},{6,7}}

>>> Load all 364 entries. <<<

[2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => {{1},{2,3,4},{5},{6,7}}

[2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => {{1,2,3,4},{5},{6,7}}

[2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => {{1},{2},{3},{4,5},{6,7}}

[2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => {{1,2},{3},{4,5},{6,7}}

[2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => {{1},{2,3},{4,5},{6,7}}

[2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => {{1,2,3},{4,5},{6,7}}

[2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => {{1},{2},{3,4,5},{6,7}}

[2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => {{1,2},{3,4,5},{6,7}}

[2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => {{1},{2,3,4,5},{6,7}}

[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => {{1,2,3,4,5},{6,7}}

[3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5,6,7}}

[3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => {{1,2},{3},{4},{5,6,7}}

[3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => {{1},{2,3},{4},{5,6,7}}

[3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => {{1,2,3},{4},{5,6,7}}

[3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => {{1},{2},{3,4},{5,6,7}}

[3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => {{1,2},{3,4},{5,6,7}}

[3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => {{1},{2,3,4},{5,6,7}}

[3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => {{1,2,3,4},{5,6,7}}

[4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => {{1},{2},{3},{4,5,6,7}}

[4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => {{1,2},{3},{4,5,6,7}}

[4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => {{1},{2,3},{4,5,6,7}}

[4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => {{1,2,3},{4,5,6,7}}

[5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}}

[5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => {{1,2},{3,4,5,6,7}}

[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}}

[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}}

[1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6},{7},{8}}

[1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7,8}} => {{1,2},{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},{6,7},{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},{6,7,8}} => {{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},{5,6},{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},{5,6},{7,8}} => {{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},{5,6,7},{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},{5,6,7,8}} => {{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},{4,5},{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},{4,5},{6},{7,8}} => {{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},{4,5},{6,7},{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},{4,5},{6,7,8}} => {{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},{4,5,6},{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},{4,5,6},{7,8}} => {{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},{4,5,6,7},{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},{4,5,6,7,8}} => {{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},{3,4},{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},{3,4},{5},{6},{7,8}} => {{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},{3,4},{5},{6,7},{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},{3,4},{5},{6,7,8}} => {{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},{3,4},{5,6},{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},{3,4},{5,6},{7,8}} => {{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},{3,4},{5,6,7,8}} => {{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},{3,4,5},{6},{7},{8}} => {{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},{3,4,5},{6,7},{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},{3,4,5},{6,7,8}} => {{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},{3,4,5,6},{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},{3,4,5,6},{7,8}} => {{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},{3,4,5,6,7},{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},{3,4,5,6,7,8}} => {{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},{2,3},{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},{2,3},{4},{5},{6},{7,8}} => {{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},{2,3},{4},{5},{6,7},{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},{2,3},{4},{5},{6,7,8}} => {{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},{2,3},{4},{5,6},{7,8}} => {{1,2},{3,4},{5},{6,7},{8}}

[1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4},{5,6,7},{8}} => {{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},{2,3},{4},{5,6,7,8}} => {{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},{2,3},{4,5},{6},{7},{8}} => {{1},{2},{3},{4,5},{6,7},{8}}

[1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4,5},{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},{2,3},{4,5},{6,7},{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},{2,3},{4,5},{6,7,8}} => {{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},{2,3},{4,5,6},{7},{8}} => {{1},{2},{3,4,5},{6,7},{8}}

[1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3},{4,5,6},{7,8}} => {{1,2},{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},{2,3},{4,5,6,7},{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},{2,3},{4,5,6,7,8}} => {{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},{2,3,4},{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},{2,3,4},{5},{6},{7,8}} => {{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},{2,3,4},{5},{6,7},{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},{2,3,4},{5},{6,7,8}} => {{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},{2,3,4},{5,6},{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},{2,3,4},{5,6},{7,8}} => {{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},{2,3,4},{5,6,7},{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},{2,3,4},{5,6,7,8}} => {{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},{2,3,4,5},{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},{2,3,4,5},{6},{7,8}} => {{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},{2,3,4,5},{6,7},{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},{2,3,4,5},{6,7,8}} => {{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},{2,3,4,5,6},{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},{2,3,4,5,6},{7,8}} => {{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},{2,3,4,5,6,7},{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},{2,3,4,5,6,7,8}} => {{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] => {{1,2},{3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6},{7,8}}

[2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7,8}} => {{1,2},{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] => {{1,2},{3},{4},{5},{6,7},{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] => {{1,2},{3},{4},{5},{6,7,8}} => {{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] => {{1,2},{3},{4},{5,6},{7},{8}} => {{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] => {{1,2},{3},{4},{5,6,7},{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] => {{1,2},{3},{4},{5,6,7,8}} => {{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] => {{1,2},{3},{4,5},{6},{7},{8}} => {{1},{2},{3},{4,5},{6},{7,8}}

[2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3},{4,5},{6,7,8}} => {{1,2,3},{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] => {{1,2},{3},{4,5,6},{7,8}} => {{1,2},{3,4,5},{6},{7,8}}

[2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3},{4,5,6,7},{8}} => {{1},{2,3,4,5},{6},{7,8}}

[2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3},{4,5,6,7,8}} => {{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] => {{1,2},{3,4},{5},{6},{7},{8}} => {{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] => {{1,2},{3,4},{5},{6,7,8}} => {{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] => {{1,2},{3,4},{5,6},{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] => {{1,2},{3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6},{7,8}}

[2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4},{5,6,7},{8}} => {{1},{2,3,4},{5,6},{7,8}}

[2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4},{5,6,7,8}} => {{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] => {{1,2},{3,4,5},{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] => {{1,2},{3,4,5},{6},{7,8}} => {{1,2},{3},{4,5,6},{7,8}}

[2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5},{6,7,8}} => {{1,2,3},{4,5,6},{7,8}}

[2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2},{3,4,5,6},{7,8}} => {{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] => {{1,2},{3,4,5,6,7},{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] => {{1,2},{3,4,5,6,7,8}} => {{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] => {{1,2,3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6,7,8}}

[3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6},{7,8}} => {{1,2},{3},{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] => {{1,2,3},{4},{5},{6,7,8}} => {{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] => {{1,2,3},{4},{5,6},{7,8}} => {{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] => {{1,2,3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6,7,8}}

[3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7},{8}} => {{1},{2},{3},{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] => {{1,2,3},{4,5},{6},{7,8}} => {{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] => {{1,2,3},{4,5},{6,7},{8}} => {{1},{2,3},{4,5},{6,7,8}}

[3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5},{6,7,8}} => {{1,2,3},{4,5},{6,7,8}}

[3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4,5,6},{7},{8}} => {{1},{2},{3,4,5},{6,7,8}}

[3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8}} => {{1,2},{3,4,5},{6,7,8}}

[3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3},{4,5,6,7},{8}} => {{1},{2,3,4,5},{6,7,8}}

[3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7,8}}

[4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6,7,8}}

[4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6},{7,8}} => {{1,2},{3},{4},{5,6,7,8}}

[4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3,4},{5},{6,7},{8}} => {{1},{2,3},{4},{5,6,7,8}}

[4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3,4},{5},{6,7,8}} => {{1,2,3},{4},{5,6,7,8}}

[4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3,4},{5,6},{7},{8}} => {{1},{2},{3,4},{5,6,7,8}}

[4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6,7,8}}

[4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4},{5,6,7},{8}} => {{1},{2,3,4},{5,6,7,8}}

[4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}}

[5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}}

[5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4,5},{6},{7,8}} => {{1,2},{3},{4,5,6,7,8}}

[5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5},{6,7},{8}} => {{1},{2,3},{4,5,6,7,8}}

[5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7,8}}

[6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}}

[6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}}

[7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}}

[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9}}

[1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8,9}} => {{1,2},{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},{7,8},{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},{7,8,9}} => {{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},{6,7},{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},{6,7},{8,9}} => {{1,2},{3,4},{5},{6},{7},{8},{9}}

[1,1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4},{5},{6,7,8},{9}} => {{1},{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},{6,7,8,9}} => {{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},{5,6},{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},{5,6},{7,8},{9}} => {{1},{2,3},{4,5},{6},{7},{8},{9}}

[1,1,1,1,3,1,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3},{4},{5,6,7},{8},{9}} => {{1},{2},{3,4,5},{6},{7},{8},{9}}

[1,1,1,1,5] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3},{4},{5,6,7,8,9}} => {{1,2,3,4,5},{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},{4,5},{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},{4,5},{6,7},{8,9}} => {{1,2},{3,4},{5,6},{7},{8},{9}}

[1,1,1,3,1,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2},{3},{4,5,6},{7},{8},{9}} => {{1},{2},{3},{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},{4,5,6,7,8,9}} => {{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},{3,4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,7},{8},{9}}

[1,1,3,1,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,6,7},{8},{9}}

[1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7},{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},{2,3},{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},{2,3},{4},{5},{6},{7},{8,9}} => {{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},{2,3},{4,5},{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},{2,3},{4,5},{6,7},{8,9}} => {{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},{2,3,4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,7,8},{9}}

[1,4,4] => [1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5},{6,7,8,9}} => {{1,2,3,4},{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},{2,3,4,5,6,7},{8,9}} => {{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},{2,3,4,5,6,7,8},{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},{2,3,4,5,6,7,8,9}} => {{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] => {{1,2},{3},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7},{8,9}}

[2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7},{8,9}} => {{1,2},{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] => {{1,2},{3},{4},{5},{6},{7,8},{9}} => {{1},{2,3},{4},{5},{6},{7},{8,9}}

[2,1,2,1,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,6},{7},{8,9}}

[2,1,6] => [1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3},{4,5,6,7,8,9}} => {{1,2,3,4,5,6},{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] => {{1,2},{3,4},{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] => {{1,2},{3,4},{5,6},{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] => {{1,2},{3,4},{5,6},{7,8},{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] => {{1,2},{3,4,5,6,7,8},{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] => {{1,2},{3,4,5,6,7,8,9}} => {{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] => {{1,2,3},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7,8,9}}

[3,1,5] => [1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3},{4},{5,6,7,8,9}} => {{1,2,3,4,5},{6},{7,8,9}}

[3,2,1,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7},{8},{9}} => {{1},{2},{3},{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] => {{1,2,3},{4,5},{6,7},{8,9}} => {{1,2},{3,4},{5,6},{7,8,9}}

[3,3,1,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4,5,6},{7},{8},{9}} => {{1},{2},{3},{4,5,6},{7,8,9}}

[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6},{7,8,9}} => {{1,2,3},{4,5,6},{7,8,9}}

[3,4,2] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3},{4,5,6,7},{8,9}} => {{1,2},{3,4,5,6},{7,8,9}}

[3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3},{4,5,6,7,8,9}} => {{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] => {{1,2,3,4},{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] => {{1,2,3,4},{5},{6,7,8,9}} => {{1,2,3,4},{5},{6,7,8,9}}

[4,2,1,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5,6},{7},{8},{9}} => {{1},{2},{3},{4,5},{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] => {{1,2,3,4},{5,6},{7,8},{9}} => {{1},{2,3},{4,5},{6,7,8,9}}

[4,3,1,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2,3,4},{5,6,7},{8},{9}} => {{1},{2},{3,4,5},{6,7,8,9}}

[4,3,2] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6,7},{8,9}} => {{1,2},{3,4,5},{6,7,8,9}}

[4,4,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5,6,7,8},{9}} => {{1},{2,3,4,5},{6,7,8,9}}

[4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4},{5,6,7,8,9}} => {{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] => {{1,2,3,4,5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,6,7,8,9}}

[5,1,3] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3,4,5},{6},{7,8,9}} => {{1,2,3},{4},{5,6,7,8,9}}

[5,2,1,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3,4,5},{6,7},{8},{9}} => {{1},{2},{3,4},{5,6,7,8,9}}

[5,3,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4,5},{6,7,8},{9}} => {{1},{2,3,4},{5,6,7,8,9}}

[5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5},{6,7,8,9}} => {{1,2,3,4},{5,6,7,8,9}}

[6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4,5,6},{7},{8},{9}} => {{1},{2},{3},{4,5,6,7,8,9}}

[6,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4,5,6},{7},{8,9}} => {{1,2},{3},{4,5,6,7,8,9}}

[6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5,6},{7,8},{9}} => {{1},{2,3},{4,5,6,7,8,9}}

[6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6},{7,8,9}} => {{1,2,3},{4,5,6,7,8,9}}

[7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5,6,7},{8},{9}} => {{1},{2},{3,4,5,6,7,8,9}}

[7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7},{8,9}} => {{1,2},{3,4,5,6,7,8,9}}

[8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}}

[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}

[1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => {{1,2},{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},{8,9},{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},{8,9,10}} => {{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},{7,8},{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},{7,8},{9,10}} => {{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},{7,8,9,10}} => {{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},{6,7},{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},{6,7,8,9,10}} => {{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},{5,6},{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},{5,6},{7,8},{9,10}} => {{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},{5,6,7,8,9,10}} => {{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},{4,5},{6},{7},{8},{9},{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},{4,5,6,7,8,9,10}} => {{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},{3,4},{5},{6},{7},{8},{9},{10}} => {{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},{3,4,5,6,7,8,9,10}} => {{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},{2,3},{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},{2,3},{4,5},{6,7},{8,9},{10}} => {{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},{2,3,4,5,6,7,8,9},{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},{2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9},{10}}

[2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}

[2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6},{7},{8},{9,10}} => {{1,2},{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] => {{1,2},{3,4},{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] => {{1,2},{3,4},{5,6},{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] => {{1,2},{3,4},{5,6},{7,8},{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] => {{1,2},{3,4},{5,6},{7,8},{9,10}} => {{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] => {{1,2},{3,4,5,6,7,8,9,10}} => {{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] => {{1,2,3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}}

[3,2,1,1,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{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] => {{1,2,3},{4,5},{6,7},{8,9},{10}} => {{1},{2,3},{4,5},{6,7},{8,9,10}}

[3,3,2,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5,6},{7,8},{9,10}} => {{1,2},{3,4},{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] => {{1,2,3},{4,5,6,7,8,9,10}} => {{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] => {{1,2,3,4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7,8,9,10}}

[4,2,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2,3,4},{5,6},{7,8},{9,10}} => {{1,2},{3,4},{5,6},{7,8,9,10}}

[4,3,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7},{8,9,10}} => {{1,2,3},{4,5,6},{7,8,9,10}}

[4,4,1,1] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5,6,7,8},{9},{10}} => {{1},{2},{3,4,5,6},{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] => {{1,2,3,4},{5,6,7,8},{9,10}} => {{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] => {{1,2,3,4},{5,6,7,8,9,10}} => {{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] => {{1,2,3,4,5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6,7,8,9,10}}

[5,2,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2,3,4,5},{6,7},{8,9},{10}} => {{1},{2,3},{4,5},{6,7,8,9,10}}

[5,4,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4,5},{6,7,8,9},{10}} => {{1},{2,3,4,5},{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] => {{1,2,3,4,5},{6,7,8,9,10}} => {{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] => {{1,2,3,4,5,6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5,6,7,8,9,10}}

[6,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3,4,5,6},{7,8,9},{10}} => {{1},{2,3,4},{5,6,7,8,9,10}}

[6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3,4,5,6},{7,8,9,10}} => {{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] => {{1,2,3,4,5,6,7},{8},{9},{10}} => {{1},{2},{3},{4,5,6,7,8,9,10}}

[7,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4,5,6,7},{8,9},{10}} => {{1},{2,3},{4,5,6,7,8,9,10}}

[7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4,5,6,7},{8,9,10}} => {{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] => {{1,2,3,4,5,6,7,8},{9},{10}} => {{1},{2},{3,4,5,6,7,8,9,10}}

[8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6,7,8},{9,10}} => {{1,2},{3,4,5,6,7,8,9,10}}

[9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9,10}}

[10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}}

[1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10},{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] => {{1,2,3,4,5,6,7,8,9,10},{11}} => {{1},{2,3,4,5,6,7,8,9,10,11}}

[2,2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => {{1,2},{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},{10,11}} => {{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 noncrossing partition

Description

Biane's map to noncrossing set partitions.

Map

complement

Description

The complement of a set partition obtained by replacing $i$ with $n+1-i$.