- FindStat

Identifier

Mp00028: Dyck paths —reverse⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 1212 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [7,1,2,8,3,4,5,9,6] => {{1,2,3,5,7},{4,6,8,9}}

[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,1,7,2,3,4,5,9,6] => {{1,2,4,6,8,9},{3,5,7}}

[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,7,1,2,3,4,5,9,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [7,3,4,8,1,2,5,9,6] => {{1,5,7},{2,3,4,6,8,9}}

[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [8,7,5,1,2,3,4,9,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,3,1,5,8,7,2,9,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [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] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,9,1,4,7,8,5,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [2,3,4,9,1,7,8,5,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [9,7,1,2,3,4,8,5,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [2,3,4,9,7,1,8,5,6] => {{1,2,3,4,6,9},{5,7,8}}

[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,9,1,3,8,7,4,5,6] => {{1,2,3,4,6,7,9},{5,8}}

[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,9,1,8,7,4,5,6] => {{1,2,3,4,6,7,9},{5,8}}

[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9,8,1,2,3,7,4,5,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,8,1,9,7,3,4,5,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [2,9,8,1,7,3,4,5,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,1,8,9,2,3,4,5,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,1,9,2,3,4,5,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,7,8,1,2,3,4,5,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [2,7,8,9,1,3,4,5,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [3,1,8,9,7,2,4,5,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [7,3,8,9,1,2,4,5,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [8,1,4,9,7,2,3,5,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [3,1,4,9,8,7,2,5,6] => {{1,2,3,4,6,7,9},{5,8}}

[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [9,3,4,1,8,7,2,5,6] => {{1,2,3,4,6,7,9},{5,8}}

[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [9,8,5,1,7,2,3,4,6] => {{1,2,4,6,8,9},{3,5,7}}

[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [2,8,9,5,7,1,3,4,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [9,5,4,1,8,7,2,3,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [2,9,4,5,8,7,1,3,6] => {{1,2,6,7,9},{3,4,5,8}}

[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,3,4,1,9,7,8,2,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,3,4,5,9,7,8,1,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,7,8,9,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [6,3,1,2,4,7,8,9,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [6,1,4,2,3,7,8,9,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [6,4,1,2,3,7,8,9,5] => {{1,3,5,6,7,8,9},{2,4}}

[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [2,6,4,1,3,7,8,9,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [6,3,4,1,2,7,8,9,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,6,1,7,8,9,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,7,1,6,3,4,8,9,5] => {{1,2,3,5,7,8,9},{4,6}}

[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7,6,1,2,3,4,8,9,5] => {{1,3,5,7,8,9},{2,4,6}}

[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [2,6,7,1,3,4,8,9,5] => {{1,2,4,6},{3,5,7,8,9}}

[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,8,1,6,7,4,9,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [8,6,1,2,3,7,4,9,5] => {{1,3,5,8,9},{2,4,6,7}}

[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [8,7,1,6,2,3,4,9,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,8,1,2,3,4,9,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [7,8,4,6,1,2,3,9,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,3,4,1,6,7,2,9,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,3,4,7,6,1,2,9,5] => {{1,5,6,8,9},{2,3,4,7}}

[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,9,1,3,6,7,8,4,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [9,3,1,2,6,7,8,4,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,9,1,6,7,8,4,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [9,6,1,2,3,7,8,4,5] => {{1,3,5,9},{2,4,6,7,8}}

[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [2,3,9,6,1,7,8,4,5] => {{1,2,3,5,9},{4,6,7,8}}

[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [9,7,1,2,6,3,8,4,5] => {{1,3,5,6,9},{2,4,7,8}}

[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [9,1,2,8,6,7,3,4,5] => {{1,2,3,5,6,7,9},{4,8}}

[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,9,1,8,6,7,3,4,5] => {{1,2,3,5,6,7,9},{4,8}}

[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [9,8,1,2,6,7,3,4,5] => {{1,3,5,6,7,9},{2,4,8}}

[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [9,8,1,6,2,7,3,4,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [2,8,9,6,1,7,3,4,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [8,1,9,7,6,2,3,4,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [9,8,1,7,6,2,3,4,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [7,8,9,1,6,2,3,4,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,8,9,6,1,2,3,4,5] => {{1,3,5,7,9},{2,4,6,8}}

[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [2,8,9,7,6,1,3,4,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,1,9,8,6,7,2,4,5] => {{1,2,3,5,6,7,9},{4,8}}

[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8,3,9,6,1,7,2,4,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8,3,9,7,6,1,2,4,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,1,2,9,6,7,8,3,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [9,1,4,8,6,7,2,3,5] => {{1,2,5,6,7,9},{3,4,8}}

[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [2,9,4,8,6,7,1,3,5] => {{1,2,5,6,7,9},{3,4,8}}

[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3,1,4,9,6,7,8,2,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [9,3,4,6,1,7,8,2,5] => {{1,5,9},{2,3,4,6,7,8}}

[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [2,3,4,9,6,7,8,1,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,6,7,8,9,4] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,5,1,3,6,7,8,9,4] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [5,3,1,2,6,7,8,9,4] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,1,5,3,7,8,9,4] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [5,6,1,2,3,7,8,9,4] => {{1,3,5},{2,4,6,7,8,9}}

[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [7,8,5,1,6,2,3,9,4] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [7,8,6,5,1,2,3,9,4] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,6,5,1,7,2,9,4] => {{1,4,5,8,9},{2,3,6,7}}

[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8,3,7,5,6,1,2,9,4] => {{1,4,5,6,8,9},{2,3,7}}

[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [9,1,2,5,6,7,8,3,4] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,9,1,5,6,7,8,3,4] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [2,9,5,1,6,7,8,3,4] => {{1,2,4,9},{3,5,6,7,8}}

[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [2,9,6,5,1,7,8,3,4] => {{1,2,4,5,9},{3,6,7,8}}

[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [2,9,7,5,6,1,8,3,4] => {{1,2,4,5,6,9},{3,7,8}}

[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [9,1,8,5,6,7,2,3,4] => {{1,2,4,5,6,7,9},{3,8}}

[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8,9,1,5,6,7,2,3,4] => {{1,3,8},{2,4,5,6,7,9}}

[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,9,7,5,6,1,2,3,4] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [2,9,8,5,6,7,1,3,4] => {{1,2,4,5,6,7,9},{3,8}}

[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,9,5,6,7,8,2,4] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [9,3,1,5,6,7,8,2,4] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [9,3,5,1,6,7,8,2,4] => {{1,4,9},{2,3,5,6,7,8}}

[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [9,3,7,5,6,1,8,2,4] => {{1,4,5,6,9},{2,3,7,8}}

[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [2,3,9,5,6,7,8,1,4] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,5,6,7,8,9,3] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [5,4,1,2,6,7,8,9,3] => {{1,3,5,6,7,8,9},{2,4}}

[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [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] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [8,1,4,5,6,7,2,9,3] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,5,4,1,6,7,2,9,3] => {{1,3,4,8,9},{2,5,6,7}}

[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,6,4,5,1,7,2,9,3] => {{1,3,4,5,8,9},{2,6,7}}

[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,4,5,6,1,2,9,3] => {{1,3,4,5,6,8,9},{2,7}}

[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,8,4,5,6,7,1,9,3] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [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] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [9,4,1,5,6,7,8,2,3] => {{1,3,9},{2,4,5,6,7,8}}

[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [9,5,4,1,6,7,8,2,3] => {{1,3,4,9},{2,5,6,7,8}}

[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [9,8,4,5,6,7,1,2,3] => {{1,3,4,5,6,7,9},{2,8}}

[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,9,4,5,6,7,8,1,3] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [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] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,3,1,5,6,7,8,9,2] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [5,3,4,1,6,7,8,9,2] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [6,3,4,5,1,7,8,9,2] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [7,3,4,5,6,1,8,9,2] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,3,4,5,6,7,1,9,2] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [9,3,4,5,6,7,8,1,2] => {{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] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [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] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [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] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [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] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [10,1,4,5,6,7,8,9,2,3] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,1,2,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [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] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,12,2] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [11,1,4,5,6,7,8,9,10,2,3] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [9,1,4,5,6,7,8,2,10,3] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,10,5,6,7,8,9,2,4] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,10,2,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [2,10,4,5,6,7,8,1,3,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [11,3,4,5,6,7,8,9,1,2,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,9,10,12,1,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,11,5,6,7,8,9,10,2,4] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [10,1,9,5,6,7,8,2,3,4] => {{1,2,4,5,6,7,8,10},{3,9}}

[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [11,1,10,5,6,7,8,9,2,3,4] => {{1,2,4,5,6,7,8,9,11},{3,10}}

[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [2,3,4,10,6,7,8,1,5,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,1,10,9,6,7,8,2,4,5] => {{1,2,3,5,6,7,8,10},{4,9}}

[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [2,3,4,5,10,7,8,1,6,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [9,1,10,8,6,7,2,3,4,5] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [4,3,1,5,6,7,8,10,2,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,7,9,1,10,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [2,3,4,5,6,10,8,1,7,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [10,1,11,9,6,7,8,2,3,4,5] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,5,6,7,8,9,10,3] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,10,2,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,10,1,5,6,7,8,9,3,4] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [9,3,4,5,6,7,1,2,10,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,7,10,1,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,7,8,10,1,11,9] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,9,11,2,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [3,1,9,10,8,7,2,4,5,6] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,7,8,11,1,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[] => [] => [1] => {{1}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,9,10,1,3,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [10,3,1,9,2,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9,3,10,1,2,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [10,6,1,2,3,4,9,5,7,8] => {{1,3,5,8,10},{2,4,6},{7,9}}

[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [10,7,1,2,3,4,5,9,6,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [10,3,1,5,2,7,4,9,6,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,10,5,1,7,4,9,6,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0] => [2,3,4,5,10,7,1,9,6,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [10,7,1,2,3,4,9,5,6,8] => {{1,3,5,8,10},{2,4,6,7,9}}

[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10,7,1,9,2,3,4,5,6,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10,7,9,1,2,3,4,5,6,8] => {{1,2,4,5,7,8,10},{3,6,9}}

[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,6,1,2,3,4,10,9,5,8] => {{1,3,5,7,8,9,10},{2,4,6}}

[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [2,10,4,5,6,7,9,1,3,8] => {{1,2,8,10},{3,4,5,6,7,9}}

[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [4,3,1,5,6,7,10,9,2,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [10,3,4,5,6,7,1,9,2,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [10,3,4,5,6,7,9,1,2,8] => {{1,8,10},{2,3,4,5,6,7,9}}

[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,3,4,5,6,7,10,9,1,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,1,2,3,4,5,6,10,7] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,10,1,2,3,4,5,9,6,7] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [9,10,1,2,3,4,8,5,6,7] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,8,1,9,2,3,4,5,6,7] => {{1,3,4,6,7,9,10},{2,5,8}}

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,9,8,1,2,3,4,5,6,7] => {{1,4,7,10},{2,3,5,6,8,9}}

[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [10,8,4,9,1,2,3,5,6,7] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => [8,9,4,5,10,1,2,3,6,7] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [2,8,9,10,6,1,3,4,5,7] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0] => [2,3,10,5,6,1,8,9,4,7] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5,3,4,1,6,10,8,9,2,7] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [2,3,4,5,6,10,8,9,1,7] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [8,7,1,2,3,4,5,9,10,6] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [9,7,1,2,3,4,8,5,10,6] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [2,7,8,9,1,3,4,5,10,6] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [7,8,9,5,1,2,3,4,10,6] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [10,7,1,2,3,4,8,9,5,6] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [10,9,1,2,3,7,8,4,5,6] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [10,9,1,2,8,7,3,4,5,6] => {{1,3,6,7,10},{2,4,5,8,9}}

[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [2,8,9,10,1,7,3,4,5,6] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9,8,1,10,7,2,3,4,5,6] => {{1,3,5,7,9},{2,4,6,8,10}}

[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [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] => {{1,3,5,7,9},{2,4,6,8,10}}

[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [2,8,9,10,7,1,3,4,5,6] => {{1,2,4,6,8,10},{3,5,7,9}}

[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [10,3,4,5,1,7,8,9,2,6] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [2,3,4,5,10,7,8,9,1,6] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [6,7,8,1,2,3,4,9,10,5] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [7,8,9,1,6,2,3,4,10,5] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [7,8,9,6,1,2,3,4,10,5] => {{1,3,5,7,9,10},{2,4,6,8}}

[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [2,9,10,8,6,7,1,3,4,5] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [2,10,4,9,6,7,8,1,3,5] => {{1,2,5,6,7,8,10},{3,4,9}}

[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [10,3,4,7,6,1,8,9,2,5] => {{1,5,6,10},{2,3,4,7,8,9}}

[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [2,3,4,10,6,7,8,9,1,5] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [5,6,1,2,3,7,8,9,10,4] => {{1,3,5},{2,4,6,7,8,9,10}}

[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [8,9,7,5,6,1,2,3,10,4] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [9,3,8,5,6,7,1,2,10,4] => {{1,4,5,6,7,9,10},{2,3,8}}

[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [2,10,8,5,6,7,1,9,3,4] => {{1,2,4,5,6,7,10},{3,8,9}}

[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [2,10,9,5,6,7,8,1,3,4] => {{1,2,4,5,6,7,8,10},{3,9}}

[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [10,3,1,5,6,7,8,9,2,4] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [10,3,8,5,6,7,1,9,2,4] => {{1,4,5,6,7,10},{2,3,8,9}}

[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [2,3,10,5,6,7,8,9,1,4] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [9,7,4,5,6,1,8,2,10,3] => {{1,3,4,5,6,9,10},{2,7,8}}

[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [9,8,4,5,6,7,1,2,10,3] => {{1,3,4,5,6,7,9,10},{2,8}}

[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,9,4,5,6,7,8,1,10,3] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [10,4,1,5,6,7,8,9,2,3] => {{1,3,10},{2,4,5,6,7,8,9}}

[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [10,9,4,5,6,7,8,1,2,3] => {{1,3,4,5,6,7,8,10},{2,9}}

[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,10,4,5,6,7,8,9,1,3] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,3,1,5,6,7,8,9,10,2] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [5,3,4,1,6,7,8,9,10,2] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [6,3,4,5,1,7,8,9,10,2] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [7,3,4,5,6,1,8,9,10,2] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [8,3,4,5,6,7,1,9,10,2] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [9,3,4,5,6,7,8,1,10,2] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [10,3,4,5,6,7,8,9,1,2] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [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}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [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] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,3,1,2,4,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,4,1,2,3,5,6,7,8,9] => {{1,3,5,6,7,8,9,10},{2,4}}

[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [5,10,1,2,3,4,6,7,8,9] => {{1,3,5},{2,4,6,7,8,9,10}}

[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [10,6,1,2,3,4,5,7,8,9] => {{1,3,5,7,8,9,10},{2,4,6}}

[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [10,7,1,2,3,4,5,6,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,10,1,2,3,4,5,6,7,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,11,1,3,4,5,6,7,8,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,10,1,4,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,3,1,2,4,5,6,7,8,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,3,1,10,2,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,4,1,2,3,5,6,7,8,9,10] => {{1,3,5,6,7,8,9,10,11},{2,4}}

[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [5,4,1,2,10,3,6,7,8,9] => {{1,3,5,6,7,8,9,10},{2,4}}

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [5,11,1,2,3,4,6,7,8,9,10] => {{1,3,5},{2,4,6,7,8,9,10,11}}

[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [5,6,1,2,3,10,4,7,8,9] => {{1,3,5},{2,4,6,7,8,9,10}}

[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [11,6,1,2,3,4,5,7,8,9,10] => {{1,3,5,7,8,9,10,11},{2,4,6}}

[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,1,2,3,4,10,5,8,9] => {{1,3,5,7,8,9,10},{2,4,6}}

[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [11,7,1,2,3,4,5,6,8,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,7,1,2,3,4,5,10,6,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,11,1,2,3,4,5,6,7,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [11,9,1,2,3,4,5,6,7,8,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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] => {{1,3,5,7,9,11},{2,4,6,8,10}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,12,1,3,4,5,6,7,8,9,10,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,11,1,4,5,6,7,8,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [10,3,4,1,2,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,10,1,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [10,9,1,2,3,4,5,6,7,11,8] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11,12,1,2,3,4,5,6,7,8,9,10] => {{1,3,5,7,9,11},{2,4,6,8,10,12}}

[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [10,5,4,1,2,3,6,7,8,9] => {{1,3,4,6,7,8,9,10},{2,5}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,11,1,5,6,7,8,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [8,9,1,2,3,4,5,6,10,11,7] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [6,10,5,1,2,3,4,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,10,1,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [8,11,1,2,3,4,5,9,10,6,7] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,7,10,1,2,3,4,5,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,11,1,6,7,8,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,7,1,10,2,3,4,5,6,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0] => [2,3,10,5,6,1,4,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [10,11,1,2,3,4,8,9,5,6,7] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [10,7,8,1,2,3,4,5,6,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [2,3,4,5,6,10,1,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [10,11,1,2,3,9,8,4,5,6,7] => {{1,3,5,6,9,10},{2,4,7,8,11}}

[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,11,1,7,8,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0] => [2,3,4,10,6,7,1,5,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [10,9,1,2,11,8,3,4,5,6,7] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,11,1,9,2,3,4,5,6,7,8] => {{1,3,4,6,7,9,10},{2,5,8,11}}

[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [9,8,1,10,11,2,3,4,5,6,7] => {{1,3,5,7,9,11},{2,4,6,8,10}}

[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,10,3,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,10,2,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [5,1,2,3,10,4,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,10,4,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,8,1,3,4,5,6,10,7,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,4,1,5,6,7,8,10,3,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,1,2,3,4,5,6,7,10,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,9,1,3,4,5,6,7,10,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,9,2,4,5,6,7,10,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,1,2,3,4,5,9,6,10,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,10,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [3,1,4,5,6,7,9,2,10,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,1,2,3,4,5,6,9,10,7] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,1,2,3,4,5,8,9,10,6] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,1,2,3,4,7,8,9,10,5] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,6,1,7,8,9,10,5] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,1,2,3,6,7,8,9,10,4] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,5,1,3,6,7,8,9,10,4] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,1,2,3,4,5,11,6,8,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,11,1,8,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [10,1,2,3,4,5,6,7,8,11,9] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,10,1,3,4,5,6,7,8,11,9] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,7,9,1,10,11,8] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,8,1,9,10,11,7] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,6,1,7,8,9,10,11,5] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [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}}

[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [10,1,2,3,4,5,6,9,7,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [10,1,2,3,4,5,9,6,7,8] => {{1,2,3,4,5,6,8,10},{7,9}}

[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,1,2,3,4,10,5,6,7,8] => {{1,2,3,4,5,7,9},{6,8,10}}

[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [10,1,2,3,9,4,5,6,7,8] => {{1,2,3,4,6,8,10},{5,7,9}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,1,2,9,3,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,1,10,2,3,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [11,1,2,3,4,5,6,7,10,8,9] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [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] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [11,1,2,3,4,5,6,10,7,8,9] => {{1,2,3,4,5,6,7,9,11},{8,10}}

[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,1,2,3,4,10,9,5,7,8] => {{1,2,3,4,5,6,8,10},{7,9}}

[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [10,1,2,3,4,5,11,6,7,8,9] => {{1,2,3,4,5,6,8,10},{7,9,11}}

[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,1,2,3,9,10,4,6,7,8] => {{1,2,3,4,5,7,9},{6,8,10}}

[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [11,1,2,3,4,10,5,6,7,8,9] => {{1,2,3,4,5,7,9,11},{6,8,10}}

[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [4,1,2,10,9,3,5,6,7,8] => {{1,2,3,4,6,8,10},{5,7,9}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11,1,2,3,10,4,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,10,9,2,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,1,2,11,3,4,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11,1,10,2,3,4,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [2,9,10,11,8,7,1,3,4,5,6] => {{1,2,4,6,7,9,11},{3,5,8,10}}

[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [8,9,10,7,6,1,2,3,4,11,5] => {{1,3,5,6,8,10,11},{2,4,7,9}}

[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [2,9,10,11,12,8,1,3,4,5,6,7] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,8,9,10,11,1,3,4,5,6,7] => {{1,2,4,6,8,10},{3,5,7,9,11}}

[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [7,8,9,10,1,2,3,4,5,11,6] => {{1,3,5,7,9},{2,4,6,8,10,11}}

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [11,1,2,3,4,5,6,7,8,9,12,10] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,3,1,2,4,5,6,7,10,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,11,10,1,3,4,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2,11,4,5,6,7,8,9,10,1,3] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [10,3,4,5,6,7,8,9,1,11,2] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2,12,4,5,6,7,8,9,10,11,1,3] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [2,11,10,5,6,7,8,9,1,3,4] => {{1,2,4,5,6,7,8,9,11},{3,10}}

[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [10,9,4,5,6,7,8,1,2,11,3] => {{1,3,4,5,6,7,8,10,11},{2,9}}

[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [11,3,4,5,6,7,8,9,10,1,12,2] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [10,3,1,2,4,5,6,9,7,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,10,1,3,4,5,6,9,7,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10,1,8,9,2,3,4,5,6,7] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [2,3,4,5,6,7,8,11,10,1,9] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [4,3,1,5,6,7,8,9,10,11,2] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [11,3,4,5,6,7,8,9,10,1,2] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [2,3,11,5,6,7,8,9,10,1,4] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [2,3,4,11,6,7,8,9,10,1,5] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [2,3,4,5,11,7,8,9,10,1,6] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [2,3,4,5,6,11,8,9,10,1,7] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [2,3,4,5,6,7,11,9,10,1,8] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,1,9,10,3,4,5,6,7] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,9,1,2,3,4,5,10,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,1,10,9,2,3,4,5,6,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10,11,8,1,2,3,4,5,6,7,9] => {{1,4,7,10},{2,3,5,6,8,9,11}}

[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [12,3,4,5,6,7,8,9,10,11,1,2] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [2,3,4,5,6,10,1,9,7,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [2,3,4,5,10,1,8,9,6,7] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,10,1,7,8,9,5,6] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,10,1,6,7,8,9,4,5] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [9,1,8,2,3,4,5,6,10,7] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,10,8,1,3,4,5,6,7,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,10,1,9,3,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [9,7,1,2,3,4,5,6,10,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [11,8,9,10,1,2,3,4,5,6,7] => {{1,3,5,7,9,11},{2,4,6,8,10}}

[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [7,3,4,5,1,2,8,9,10,6] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,3,1,2,6,7,8,9,10,4] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,3,4,1,6,7,8,9,10,11,2] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,3,4,1,2,7,8,9,10,5] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,3,4,5,1,7,8,9,10,11,2] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [7,3,4,5,6,1,8,9,10,11,2] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [8,3,4,5,6,1,2,9,10,7] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [8,3,4,5,6,7,1,9,10,11,2] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [9,3,4,5,6,7,8,1,10,11,2] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,6,1,5,3,7,8,9,10,4] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [5,3,4,1,6,7,9,2,10,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,8,1,6,7,4,9,10,5] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,3,4,5,1,8,2,9,10,7] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [10,1,5,2,3,4,6,7,8,9] => {{1,2,4,6,7,8,9,10},{3,5}}

[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [10,1,2,5,3,4,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [11,1,2,3,4,5,8,6,7,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [11,1,2,3,4,5,9,6,7,8,10] => {{1,2,3,4,5,6,8,10,11},{7,9}}

[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [5,9,1,2,3,4,6,7,10,8] => {{1,3,5},{2,4,6,7,8,9,10}}

[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,10,1,5,3,4,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,11,1,2,3,10,4,6,7,8,9] => {{1,3,5},{2,4,7,9,11},{6,8,10}}

[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,10,4,5,6,7,8,9,1,11,3] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,12,1] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [11,1,10,9,2,3,4,5,6,7,8] => {{1,2,5,8,11},{3,4,6,7,9,10}}

[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,1,9,10,7,2,3,4,5,6] => {{1,2,4,6,8,10},{3,5,7,9}}

[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [9,1,10,11,8,7,2,3,4,5,6] => {{1,2,4,6,7,9,11},{3,5,8,10}}

[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [3,1,8,9,10,2,4,5,6,7] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,1,9,10,11,2,3,4,5,6,7] => {{1,2,4,6,8,10},{3,5,7,9,11}}

[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [11,3,4,5,6,7,8,10,1,2,9] => {{1,9,11},{2,3,4,5,6,7,8,10}}

[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [2,3,4,5,6,7,8,9,12,11,1,10] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [12,1,2,3,4,5,6,7,8,11,9,10] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,11,1,3,4,5,6,7,10,8,9] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,1,10,2,4,5,6,9,7,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [2,3,4,5,10,7,1,6,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [2,3,4,10,6,1,5,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,10,5,1,4,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,10,4,1,3,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [8,6,1,2,3,4,5,9,10,7] => {{1,3,5,7,8,9,10},{2,4,6}}

[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,7,1,2,3,4,8,9,10,6] => {{1,3,5},{2,4,6,7,8,9,10}}

[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [10,4,1,2,3,7,8,9,5,6] => {{1,3,5,6,7,8,9,10},{2,4}}

[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [10,3,1,2,9,7,8,4,5,6] => {{1,2,3,4,6,7,8,10},{5,9}}

[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,9,1,10,8,7,3,4,5,6] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [10,1,2,9,6,3,4,5,7,8] => {{1,2,3,5,6,8,10},{4,7,9}}

[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [4,1,2,10,3,5,9,6,7,8] => {{1,2,3,4,5,6,8,10},{7,9}}

[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [8,9,10,11,12,1,2,3,4,5,6,7] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,1,10,2,3,4,5,9,7,8] => {{1,2,4,6},{3,5,7,8,9,10}}

[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,10,4,1,6,3,8,5,7,9] => {{1,2,3,4,5,6,7,8,9,10}}

Map

reverse

Description

The reversal of a Dyck path.
This is the Dyck path obtained by reading the path backwards.

Map

Ringel

Description

The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.

Map

to cycle type

Description

Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].