- FindStat

Identifier

Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Mp00112: Set partitions —complement⟶ Set partitions

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 468 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[] => [1] => {{1}} => {{1}}

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

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

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

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

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

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

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

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

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

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

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

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

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

Map

Ringel

Description

The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.

Map

weak exceedance partition

Description

The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.

Map

complement

Description

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