- FindStat

Identifier

Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 1758 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,8,6,5,7,4,2] => [1,4,3,7,6,8,5,2] => {{1},{2,4,5,6,7,8},{3}}

[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [1,4,3,5,6,7,8,2] => {{1},{2,4,5,6,7,8},{3}}

[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [1,3,4,2,5,6,7,8] => {{1},{2,3,4},{5},{6},{7},{8}}

[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => [1,3,4,2,5,6,8,7] => {{1},{2,3,4},{5},{6},{7,8}}

[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => [1,3,4,2,5,7,6,8] => {{1},{2,3,4},{5},{6,7},{8}}

[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [1,3,4,2,5,7,8,6] => {{1},{2,3,4},{5},{6,7,8}}

[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,3,2,6,5,8,7] => [1,3,4,2,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}

[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => [1,3,4,2,8,6,7,5] => {{1},{2,3,4},{5,8},{6},{7}}

[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [1,3,4,2,7,6,8,5] => {{1},{2,3,4},{5,7,8},{6}}

[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [1,3,4,2,6,7,5,8] => {{1},{2,3,4},{5,6,7},{8}}

[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => [1,3,4,2,8,7,6,5] => {{1},{2,3,4},{5,8},{6,7}}

[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,3,2,8,6,7,5] => [1,3,4,2,7,8,6,5] => {{1},{2,3,4},{5,6,7,8}}

[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [1,3,4,2,6,7,8,5] => {{1},{2,3,4},{5,6,7,8}}

[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,3,5,2,6,7,8] => [1,5,4,3,2,6,7,8] => {{1},{2,5},{3,4},{6},{7},{8}}

[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => [1,5,4,3,2,7,6,8] => {{1},{2,5},{3,4},{6,7},{8}}

[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,3,5,2,7,8,6] => [1,5,4,3,2,8,7,6] => {{1},{2,5},{3,4},{6,8},{7}}

[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3,5,2,8,7,6] => [1,5,4,3,2,7,8,6] => {{1},{2,5},{3,4},{6,7,8}}

[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [1,6,4,3,5,2,7,8] => {{1},{2,6},{3,4},{5},{7},{8}}

[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [1,8,4,3,5,6,7,2] => {{1},{2,8},{3,4},{5},{6},{7}}

[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,3,5,7,6,8,2] => [1,8,4,3,5,7,6,2] => {{1},{2,8},{3,4},{5},{6,7}}

[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [1,5,4,3,6,2,7,8] => {{1},{2,5,6},{3,4},{7},{8}}

[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [1,8,4,3,6,5,7,2] => {{1},{2,8},{3,4},{5,6},{7}}

[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [1,7,4,3,6,5,8,2] => {{1},{2,7,8},{3,4},{5,6}}

[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,4,3,7,5,6,2,8] => [1,6,4,3,7,5,2,8] => {{1},{2,5,6,7},{3,4},{8}}

[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,8,5,7,6,2] => [1,6,4,3,7,8,2,5] => {{1},{2,5,6,7,8},{3,4}}

[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,4,3,7,6,5,2,8] => [1,5,4,3,6,7,2,8] => {{1},{2,5,6,7},{3,4},{8}}

[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,8,6,5,7,2] => [1,7,4,3,6,8,5,2] => {{1},{2,5,6,7,8},{3,4}}

[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [1,5,4,3,6,7,8,2] => {{1},{2,5,6,7,8},{3,4}}

[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,5,3,4,2,6,7,8] => [1,4,5,3,2,6,7,8] => {{1},{2,3,4,5},{6},{7},{8}}

[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,5,3,4,2,7,6,8] => [1,4,5,3,2,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}

[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,5,3,4,2,7,8,6] => [1,4,5,3,2,8,7,6] => {{1},{2,3,4,5},{6,8},{7}}

[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3,4,2,8,7,6] => [1,4,5,3,2,7,8,6] => {{1},{2,3,4,5},{6,7,8}}

[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => [1,8,5,3,4,6,7,2] => {{1},{2,8},{3,4,5},{6},{7}}

[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,5,3,4,7,6,8,2] => [1,8,5,3,4,7,6,2] => {{1},{2,8},{3,4,5},{6,7}}

[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,5,3,4,8,6,7,2] => [1,7,5,3,4,8,6,2] => {{1},{2,6,7,8},{3,4,5}}

[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,3,4,5,2,7,8] => [1,5,6,3,4,2,7,8] => {{1},{2,3,4,5,6},{7},{8}}

[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,6,3,4,5,7,2,8] => [1,7,6,3,4,5,2,8] => {{1},{2,7},{3,4,5,6},{8}}

[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,6,3,4,5,8,7,2] => [1,7,6,3,4,5,8,2] => {{1},{2,7,8},{3,4,5,6}}

[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7,3,4,5,6,8,2] => [1,8,7,3,4,5,6,2] => {{1},{2,8},{3,4,5,6,7}}

[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => [1,7,8,3,4,5,6,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,8,3,4,5,7,6,2] => [1,6,7,2,4,8,5,3] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,8,3,4,6,5,7,2] => [1,7,8,3,6,4,5,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8,3,4,7,6,5,2] => [1,5,6,3,7,8,4,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,3,5,4,2,7,8] => [1,4,5,6,2,3,7,8] => {{1},{2,3,4,5,6},{7},{8}}

[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,8,3,5,4,6,7,2] => [1,7,8,5,3,4,6,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,7,3,5,6,4,8,2] => [1,8,7,6,3,5,4,2] => {{1},{2,8},{3,4,5,6,7}}

[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,8,3,5,6,4,7,2] => [1,7,8,6,3,5,4,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8,3,5,7,6,4,2] => [1,4,6,7,3,8,5,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,7,3,6,5,4,2,8] => [1,4,5,6,7,3,2,8] => {{1},{2,3,4,5,6,7},{8}}

[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7,3,6,5,4,8,2] => [1,8,7,5,6,3,4,2] => {{1},{2,8},{3,4,5,6,7}}

[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,8,3,6,5,4,7,2] => [1,7,8,5,6,3,4,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,8,3,6,5,7,4,2] => [1,4,7,8,6,2,5,3] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8,3,7,6,5,4,2] => [1,4,5,6,7,8,2,3] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [1,3,4,5,2,6,7,8] => {{1},{2,3,4,5},{6},{7},{8}}

[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => [1,3,4,5,2,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}

[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => [1,3,4,5,2,8,7,6] => {{1},{2,3,4,5},{6,8},{7}}

[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [1,3,4,5,2,7,8,6] => {{1},{2,3,4,5},{6,7,8}}

[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => [1,6,4,5,3,2,7,8] => {{1},{2,6},{3,4,5},{7},{8}}

[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [1,8,4,5,3,6,7,2] => {{1},{2,8},{3,4,5},{6},{7}}

[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [1,7,4,5,3,6,8,2] => {{1},{2,7,8},{3,4,5},{6}}

[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,6,4,3,5,2,7,8] => [1,5,4,6,3,2,7,8] => {{1},{2,3,4,5,6},{7},{8}}

[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => [1,7,4,8,3,5,6,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,7,4,3,6,5,2,8] => [1,5,4,6,7,2,3,8] => {{1},{2,3,4,5,6,7},{8}}

[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7,4,3,6,5,8,2] => [1,8,4,7,6,3,5,2] => {{1},{2,8},{3,4,5,6,7}}

[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8,4,3,6,5,7,2] => [1,7,4,8,6,3,5,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,8,4,3,7,6,5,2] => [1,5,4,6,7,8,3,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,6,4,5,3,2,7,8] => [1,3,5,6,4,2,7,8] => {{1},{2,3,4,5,6},{7},{8}}

[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7,4,5,3,6,8,2] => [1,8,5,7,4,3,6,2] => {{1},{2,8},{3,4,5,6,7}}

[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => [1,7,5,8,4,3,6,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7,4,5,6,3,8,2] => [1,8,6,7,4,5,3,2] => {{1},{2,8},{3,4,5,6,7}}

[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,8,4,5,6,3,7,2] => [1,7,6,8,4,5,3,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => [1,3,7,8,4,5,6,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,7,4,6,5,3,2,8] => [1,3,5,6,7,2,4,8] => {{1},{2,3,4,5,6,7},{8}}

[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,8,4,7,5,6,3,2] => [1,3,6,8,7,5,4,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => [1,3,5,6,7,8,4,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [1,3,4,5,6,2,7,8] => {{1},{2,3,4,5,6},{7},{8}}

[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => [1,3,4,5,6,2,8,7] => {{1},{2,3,4,5,6},{7,8}}

[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,5,4,3,7,8,2] => [1,8,4,5,6,3,7,2] => {{1},{2,8},{3,4,5,6},{7}}

[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [1,7,4,5,6,3,8,2] => {{1},{2,7,8},{3,4,5,6}}

[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,7,5,4,3,6,2,8] => [1,6,4,5,7,3,2,8] => {{1},{2,3,4,5,6,7},{8}}

[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8,5,4,3,6,7,2] => [1,7,4,5,8,3,6,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8,5,4,6,3,7,2] => [1,7,6,5,8,4,3,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => [1,3,7,5,8,4,6,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => [1,3,6,5,7,8,2,4] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,7,6,4,5,3,2,8] => [1,3,5,6,4,7,2,8] => {{1},{2,3,4,5,6,7},{8}}

[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,7,6,4,5,3,8,2] => [1,8,5,6,4,7,3,2] => {{1},{2,8},{3,4,5,6,7}}

[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,8,6,4,5,3,7,2] => [1,7,5,6,4,8,3,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,8,6,4,5,7,3,2] => [1,3,7,6,4,8,5,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => [1,3,6,7,4,5,8,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [1,3,4,5,6,7,2,8] => {{1},{2,3,4,5,6,7},{8}}

[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => [1,8,4,5,6,7,3,2] => {{1},{2,8},{3,4,5,6,7}}

[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8,6,5,4,3,7,2] => [1,7,4,5,6,8,3,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => [1,3,7,5,6,8,4,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => [1,3,4,6,7,5,8,2] => {{1},{2,3,4,5,6,7,8}}

[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,2] => {{1},{2,3,4,5,6,7,8}}

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => {{1,2},{3},{4},{5},{6},{7},{8}}

[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => {{1,2},{3},{4},{5},{6},{7,8}}

[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => [2,1,3,4,5,7,6,8] => {{1,2},{3},{4},{5},{6,7},{8}}

[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => [2,1,3,4,5,8,7,6] => {{1,2},{3},{4},{5},{6,8},{7}}

[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [2,1,3,4,5,7,8,6] => {{1,2},{3},{4},{5},{6,7,8}}

[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => [2,1,3,4,6,5,7,8] => {{1,2},{3},{4},{5,6},{7},{8}}

[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => [2,1,3,4,6,5,8,7] => {{1,2},{3},{4},{5,6},{7,8}}

[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => [2,1,3,4,8,6,7,5] => {{1,2},{3},{4},{5,8},{6},{7}}

[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,4,6,8,7,5] => [2,1,3,4,7,6,8,5] => {{1,2},{3},{4},{5,7,8},{6}}

[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => [2,1,3,4,8,7,6,5] => {{1,2},{3},{4},{5,8},{6,7}}

[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,8,6,7,5] => [2,1,3,4,7,8,6,5] => {{1,2},{3},{4},{5,6,7,8}}

[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [2,1,3,4,6,7,8,5] => {{1,2},{3},{4},{5,6,7,8}}

[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => [2,1,3,5,4,6,7,8] => {{1,2},{3},{4,5},{6},{7},{8}}

[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => [2,1,3,5,4,6,8,7] => {{1,2},{3},{4,5},{6},{7,8}}

[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [2,1,3,5,4,8,7,6] => {{1,2},{3},{4,5},{6,8},{7}}

[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [2,1,3,5,4,7,8,6] => {{1,2},{3},{4,5},{6,7,8}}

[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [2,1,3,6,5,4,8,7] => {{1,2},{3},{4,6},{5},{7,8}}

[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => [2,1,3,8,5,6,7,4] => {{1,2},{3},{4,8},{5},{6},{7}}

[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,3,5,7,6,8,4] => [2,1,3,8,5,7,6,4] => {{1,2},{3},{4,8},{5},{6,7}}

[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,5,4,8,7] => [2,1,3,5,6,4,8,7] => {{1,2},{3},{4,5,6},{7,8}}

[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,6,5,7,8,4] => [2,1,3,8,6,5,7,4] => {{1,2},{3},{4,8},{5,6},{7}}

[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,7,5,6,8,4] => [2,1,3,8,7,5,6,4] => {{1,2},{3},{4,8},{5,6,7}}

[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,8,5,6,7,4] => [2,1,3,7,8,5,6,4] => {{1,2},{3},{4,5,6,7,8}}

[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,8,5,7,6,4] => [2,1,3,6,7,8,4,5] => {{1,2},{3},{4,5,6,7,8}}

[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,7,6,5,8,4] => [2,1,3,8,6,7,5,4] => {{1,2},{3},{4,8},{5,6,7}}

[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [2,1,3,5,6,7,8,4] => {{1,2},{3},{4,5,6,7,8}}

[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => [2,1,4,3,5,6,7,8] => {{1,2},{3,4},{5},{6},{7},{8}}

[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => [2,1,4,3,5,6,8,7] => {{1,2},{3,4},{5},{6},{7,8}}

[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [2,1,4,3,5,8,7,6] => {{1,2},{3,4},{5},{6,8},{7}}

[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [2,1,4,3,5,7,8,6] => {{1,2},{3,4},{5},{6,7,8}}

[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => [2,1,4,3,6,5,7,8] => {{1,2},{3,4},{5,6},{7},{8}}

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}

[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => [2,1,4,3,8,6,7,5] => {{1,2},{3,4},{5,8},{6},{7}}

[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [2,1,4,3,7,6,8,5] => {{1,2},{3,4},{5,7,8},{6}}

[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,3,7,6,5,8] => [2,1,4,3,6,7,5,8] => {{1,2},{3,4},{5,6,7},{8}}

[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => [2,1,4,3,8,7,6,5] => {{1,2},{3,4},{5,8},{6,7}}

[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => [2,1,4,3,7,8,6,5] => {{1,2},{3,4},{5,6,7,8}}

[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [2,1,4,3,6,7,8,5] => {{1,2},{3,4},{5,6,7,8}}

[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => [2,1,5,4,3,6,7,8] => {{1,2},{3,5},{4},{6},{7},{8}}

[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [2,1,5,4,3,6,8,7] => {{1,2},{3,5},{4},{6},{7,8}}

[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3,7,8,6] => [2,1,5,4,3,8,7,6] => {{1,2},{3,5},{4},{6,8},{7}}

[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [2,1,6,4,5,3,8,7] => {{1,2},{3,6},{4},{5},{7,8}}

[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => [2,1,8,4,5,6,7,3] => {{1,2},{3,8},{4},{5},{6},{7}}

[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,4,5,7,6,8,3] => [2,1,8,4,5,7,6,3] => {{1,2},{3,8},{4},{5},{6,7}}

[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => [2,1,7,4,5,8,6,3] => {{1,2},{3,6,7,8},{4},{5}}

[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [2,1,6,4,5,7,8,3] => {{1,2},{3,6,7,8},{4},{5}}

[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [2,1,5,4,6,3,8,7] => {{1,2},{3,5,6},{4},{7,8}}

[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,1,4,6,5,7,8,3] => [2,1,8,4,6,5,7,3] => {{1,2},{3,8},{4},{5,6},{7}}

[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [2,1,7,4,6,5,8,3] => {{1,2},{3,7,8},{4},{5,6}}

[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,7,5,6,8,3] => [2,1,8,4,7,5,6,3] => {{1,2},{3,8},{4},{5,6,7}}

[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,8,5,6,7,3] => [2,1,7,4,8,5,6,3] => {{1,2},{3,5,6,7,8},{4}}

[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,8,5,7,6,3] => [2,1,6,4,7,8,3,5] => {{1,2},{3,5,6,7,8},{4}}

[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,4,7,6,5,3,8] => [2,1,5,4,6,7,3,8] => {{1,2},{3,5,6,7},{4},{8}}

[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [2,1,8,4,6,7,5,3] => {{1,2},{3,8},{4},{5,6,7}}

[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,8,6,7,5,3] => [2,1,5,4,7,8,6,3] => {{1,2},{3,5,6,7,8},{4}}

[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [2,1,5,4,6,7,8,3] => {{1,2},{3,5,6,7,8},{4}}

[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [2,1,4,5,3,6,7,8] => {{1,2},{3,4,5},{6},{7},{8}}

[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => [2,1,4,5,3,6,8,7] => {{1,2},{3,4,5},{6},{7,8}}

[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,1,5,4,3,7,8,6] => [2,1,4,5,3,8,7,6] => {{1,2},{3,4,5},{6,8},{7}}

[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [2,1,6,5,4,3,8,7] => {{1,2},{3,6},{4,5},{7,8}}

[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [2,1,8,5,4,6,7,3] => {{1,2},{3,8},{4,5},{6},{7}}

[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [2,1,8,5,4,7,6,3] => {{1,2},{3,8},{4,5},{6,7}}

[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,8,6,7,3] => [2,1,7,5,4,8,6,3] => {{1,2},{3,6,7,8},{4,5}}

[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,6,4,5,3,7,8] => [2,1,5,6,4,3,7,8] => {{1,2},{3,4,5,6},{7},{8}}

[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => [2,1,5,6,4,3,8,7] => {{1,2},{3,4,5,6},{7,8}}

[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,6,4,5,7,8,3] => [2,1,8,6,4,5,7,3] => {{1,2},{3,8},{4,5,6},{7}}

[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,6,4,5,8,7,3] => [2,1,7,6,4,5,8,3] => {{1,2},{3,7,8},{4,5,6}}

[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,8,4,5,6,7,3] => [2,1,7,8,4,5,6,3] => {{1,2},{3,4,5,6,7,8}}

[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,8,4,5,7,6,3] => [2,1,6,7,3,8,5,4] => {{1,2},{3,4,5,6,7,8}}

[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,7,4,6,5,8,3] => [2,1,8,7,6,4,5,3] => {{1,2},{3,8},{4,5,6,7}}

[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,8,4,6,5,7,3] => [2,1,7,8,6,4,5,3] => {{1,2},{3,4,5,6,7,8}}

[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,8,4,7,6,5,3] => [2,1,5,6,7,8,4,3] => {{1,2},{3,4,5,6,7,8}}

[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => [2,1,4,5,6,3,8,7] => {{1,2},{3,4,5,6},{7,8}}

[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,1,6,5,4,7,8,3] => [2,1,8,5,6,4,7,3] => {{1,2},{3,8},{4,5,6},{7}}

[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [2,1,7,5,6,4,8,3] => {{1,2},{3,7,8},{4,5,6}}

[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,7,5,4,6,8,3] => [2,1,8,5,7,4,6,3] => {{1,2},{3,8},{4,5,6,7}}

[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,8,5,4,6,7,3] => [2,1,7,5,8,4,6,3] => {{1,2},{3,4,5,6,7,8}}

[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => [2,1,6,5,7,8,3,4] => {{1,2},{3,4,5,6,7,8}}

[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,7,5,6,4,8,3] => [2,1,8,6,7,5,4,3] => {{1,2},{3,8},{4,5,6,7}}

[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,8,5,6,4,7,3] => [2,1,7,6,8,5,4,3] => {{1,2},{3,4,5,6,7,8}}

[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,8,5,6,7,4,3] => [2,1,4,7,8,5,6,3] => {{1,2},{3,4,5,6,7,8}}

[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,8,5,7,6,4,3] => [2,1,4,6,7,8,3,5] => {{1,2},{3,4,5,6,7,8}}

[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [2,1,4,5,6,7,3,8] => {{1,2},{3,4,5,6,7},{8}}

[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => [2,1,8,5,6,7,4,3] => {{1,2},{3,8},{4,5,6,7}}

[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,8,6,5,4,7,3] => [2,1,7,5,6,8,4,3] => {{1,2},{3,4,5,6,7,8}}

[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => [2,1,4,6,7,5,8,3] => {{1,2},{3,4,5,6,7,8}}

[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [2,1,4,5,6,7,8,3] => {{1,2},{3,4,5,6,7,8}}

[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => {{1,3},{2},{4},{5},{6},{7},{8}}

[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [3,2,1,4,5,6,8,7] => {{1,3},{2},{4},{5},{6},{7,8}}

[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [3,2,1,4,5,7,6,8] => {{1,3},{2},{4},{5},{6,7},{8}}

[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => {{1,3},{2},{4},{5},{6,8},{7}}

[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5,8,7,6] => [3,2,1,4,5,7,8,6] => {{1,3},{2},{4},{5},{6,7,8}}

[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [3,2,1,4,7,6,5,8] => {{1,3},{2},{4},{5,7},{6},{8}}

[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [3,2,1,4,8,6,7,5] => {{1,3},{2},{4},{5,8},{6},{7}}

[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,3,1,4,6,8,7,5] => [3,2,1,4,7,6,8,5] => {{1,3},{2},{4},{5,7,8},{6}}

[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [3,2,1,4,8,7,6,5] => {{1,3},{2},{4},{5,8},{6,7}}

[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,8,6,7,5] => [3,2,1,4,7,8,6,5] => {{1,3},{2},{4},{5,6,7,8}}

[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [3,2,1,4,6,7,8,5] => {{1,3},{2},{4},{5,6,7,8}}

[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [3,2,1,5,4,6,7,8] => {{1,3},{2},{4,5},{6},{7},{8}}

[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [3,2,1,5,4,7,6,8] => {{1,3},{2},{4,5},{6,7},{8}}

[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [3,2,1,6,5,4,7,8] => {{1,3},{2},{4,6},{5},{7},{8}}

[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,6,4,8,7] => [3,2,1,6,5,4,8,7] => {{1,3},{2},{4,6},{5},{7,8}}

[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [3,2,1,7,5,6,4,8] => {{1,3},{2},{4,7},{5},{6},{8}}

[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [3,2,1,8,5,6,7,4] => {{1,3},{2},{4,8},{5},{6},{7}}

[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,3,1,5,6,8,7,4] => [3,2,1,7,5,6,8,4] => {{1,3},{2},{4,7,8},{5},{6}}

[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [3,2,1,8,5,7,6,4] => {{1,3},{2},{4,8},{5},{6,7}}

[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,8,6,7,4] => [3,2,1,7,5,8,6,4] => {{1,3},{2},{4,6,7,8},{5}}

[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,3,1,5,8,7,6,4] => [3,2,1,6,5,7,8,4] => {{1,3},{2},{4,6,7,8},{5}}

[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [3,2,1,5,6,4,7,8] => {{1,3},{2},{4,5,6},{7},{8}}

[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [3,2,1,7,6,5,4,8] => {{1,3},{2},{4,7},{5,6},{8}}

[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,5,7,8,4] => [3,2,1,8,6,5,7,4] => {{1,3},{2},{4,8},{5,6},{7}}

[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [3,2,1,7,6,5,8,4] => {{1,3},{2},{4,7,8},{5,6}}

[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,7,5,6,8,4] => [3,2,1,8,7,5,6,4] => {{1,3},{2},{4,8},{5,6,7}}

[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => [3,2,1,7,8,5,6,4] => {{1,3},{2},{4,5,6,7,8}}

[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,1,8,5,7,6,4] => [3,2,1,6,7,8,4,5] => {{1,3},{2},{4,5,6,7,8}}

[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [3,2,1,8,6,7,5,4] => {{1,3},{2},{4,8},{5,6,7}}

[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,8,6,5,7,4] => [3,2,1,7,6,8,5,4] => {{1,3},{2},{4,5,6,7,8}}

[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,8,6,7,5,4] => [3,2,1,5,7,8,6,4] => {{1,3},{2},{4,5,6,7,8}}

[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [3,2,1,5,6,7,8,4] => {{1,3},{2},{4,5,6,7,8}}

[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [4,2,3,1,5,6,7,8] => {{1,4},{2},{3},{5},{6},{7},{8}}

[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [4,2,3,1,5,7,6,8] => {{1,4},{2},{3},{5},{6,7},{8}}

[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [4,2,3,1,5,8,7,6] => {{1,4},{2},{3},{5},{6,8},{7}}

[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [4,2,3,1,5,7,8,6] => {{1,4},{2},{3},{5},{6,7,8}}

[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [4,2,3,1,6,5,7,8] => {{1,4},{2},{3},{5,6},{7},{8}}

[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [4,2,3,1,6,5,8,7] => {{1,4},{2},{3},{5,6},{7,8}}

[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [4,2,3,1,7,6,5,8] => {{1,4},{2},{3},{5,7},{6},{8}}

[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [4,2,3,1,8,6,7,5] => {{1,4},{2},{3},{5,8},{6},{7}}

[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [4,2,3,1,7,6,8,5] => {{1,4},{2},{3},{5,7,8},{6}}

[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [4,2,3,1,8,7,6,5] => {{1,4},{2},{3},{5,8},{6,7}}

[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,8,6,7,5] => [4,2,3,1,7,8,6,5] => {{1,4},{2},{3},{5,6,7,8}}

[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [4,2,3,1,6,7,8,5] => {{1,4},{2},{3},{5,6,7,8}}

[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [5,2,3,4,1,6,7,8] => {{1,5},{2},{3},{4},{6},{7},{8}}

[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [5,2,3,4,1,6,8,7] => {{1,5},{2},{3},{4},{6},{7,8}}

[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [5,2,3,4,1,8,7,6] => {{1,5},{2},{3},{4},{6,8},{7}}

[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [5,2,3,4,1,7,8,6] => {{1,5},{2},{3},{4},{6,7,8}}

[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [6,2,3,4,5,1,7,8] => {{1,6},{2},{3},{4},{5},{7},{8}}

[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [6,2,3,4,5,1,8,7] => {{1,6},{2},{3},{4},{5},{7,8}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [7,2,3,4,5,6,1,8] => {{1,7},{2},{3},{4},{5},{6},{8}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [8,2,3,4,5,6,7,1] => {{1,8},{2},{3},{4},{5},{6},{7}}

[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [7,2,3,4,5,6,8,1] => {{1,7,8},{2},{3},{4},{5},{6}}

[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [6,2,3,4,5,7,1,8] => {{1,6,7},{2},{3},{4},{5},{8}}

[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [8,2,3,4,5,7,6,1] => {{1,8},{2},{3},{4},{5},{6,7}}

[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,8,6,7,1] => [7,2,3,4,5,8,6,1] => {{1,6,7,8},{2},{3},{4},{5}}

[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [6,2,3,4,5,7,8,1] => {{1,6,7,8},{2},{3},{4},{5}}

[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [5,2,3,4,6,1,7,8] => {{1,5,6},{2},{3},{4},{7},{8}}

[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,4,6,5,1,8,7] => [5,2,3,4,6,1,8,7] => {{1,5,6},{2},{3},{4},{7,8}}

[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [7,2,3,4,6,5,1,8] => {{1,7},{2},{3},{4},{5,6},{8}}

[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,8,5,6,7,1] => [7,2,3,4,8,5,6,1] => {{1,5,6,7,8},{2},{3},{4}}

[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,8,5,7,6,1] => [6,2,3,4,7,8,1,5] => {{1,5,6,7,8},{2},{3},{4}}

[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [5,2,3,4,6,7,1,8] => {{1,5,6,7},{2},{3},{4},{8}}

[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,8,6,5,7,1] => [7,2,3,4,6,8,5,1] => {{1,5,6,7,8},{2},{3},{4}}

[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [5,2,3,4,6,7,8,1] => {{1,5,6,7,8},{2},{3},{4}}

[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [4,2,3,5,1,6,7,8] => {{1,4,5},{2},{3},{6},{7},{8}}

[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [4,2,3,5,1,6,8,7] => {{1,4,5},{2},{3},{6},{7,8}}

[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,3,5,4,1,7,8,6] => [4,2,3,5,1,8,7,6] => {{1,4,5},{2},{3},{6,8},{7}}

[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [4,2,3,5,1,7,8,6] => {{1,4,5},{2},{3},{6,7,8}}

[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [6,2,3,5,4,1,7,8] => {{1,6},{2},{3},{4,5},{7},{8}}

[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [7,2,3,5,4,6,1,8] => {{1,7},{2},{3},{4,5},{6},{8}}

[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [8,2,3,5,4,6,7,1] => {{1,8},{2},{3},{4,5},{6},{7}}

[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,3,5,4,7,6,1,8] => [6,2,3,5,4,7,1,8] => {{1,6,7},{2},{3},{4,5},{8}}

[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [8,2,3,5,4,7,6,1] => {{1,8},{2},{3},{4,5},{6,7}}

[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,8,6,7,1] => [7,2,3,5,4,8,6,1] => {{1,6,7,8},{2},{3},{4,5}}

[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,4,5,1,8,7] => [5,2,3,6,4,1,8,7] => {{1,4,5,6},{2},{3},{7,8}}

[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,7,4,5,6,1,8] => [6,2,3,7,4,5,1,8] => {{1,4,5,6,7},{2},{3},{8}}

[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,7,4,5,6,8,1] => [8,2,3,7,4,5,6,1] => {{1,8},{2},{3},{4,5,6,7}}

[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => [7,2,3,8,4,5,6,1] => {{1,4,5,6,7,8},{2},{3}}

[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,7,4,6,5,8,1] => [8,2,3,7,6,4,5,1] => {{1,8},{2},{3},{4,5,6,7}}

[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,8,4,6,5,7,1] => [7,2,3,8,6,4,5,1] => {{1,4,5,6,7,8},{2},{3}}

[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,8,4,6,7,5,1] => [5,2,3,7,8,1,6,4] => {{1,4,5,6,7,8},{2},{3}}

[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,8,4,7,6,5,1] => [5,2,3,6,7,8,4,1] => {{1,4,5,6,7,8},{2},{3}}

[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [4,2,3,5,6,1,7,8] => {{1,4,5,6},{2},{3},{7},{8}}

[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [4,2,3,5,6,1,8,7] => {{1,4,5,6},{2},{3},{7,8}}

[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,7,5,4,6,1,8] => [6,2,3,5,7,4,1,8] => {{1,4,5,6,7},{2},{3},{8}}

[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,5,6,4,1,8] => [4,2,3,6,7,5,1,8] => {{1,4,5,6,7},{2},{3},{8}}

[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,8,5,6,4,7,1] => [7,2,3,6,8,5,4,1] => {{1,4,5,6,7,8},{2},{3}}

[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,8,5,7,6,4,1] => [4,2,3,6,7,8,1,5] => {{1,4,5,6,7,8},{2},{3}}

[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [4,2,3,5,6,7,1,8] => {{1,4,5,6,7},{2},{3},{8}}

[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [8,2,3,5,6,7,4,1] => {{1,8},{2},{3},{4,5,6,7}}

[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,8,6,5,4,7,1] => [7,2,3,5,6,8,4,1] => {{1,4,5,6,7,8},{2},{3}}

[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [4,2,3,5,6,7,8,1] => {{1,4,5,6,7,8},{2},{3}}

[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [3,2,4,1,5,6,7,8] => {{1,3,4},{2},{5},{6},{7},{8}}

[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,4,3,1,5,6,8,7] => [3,2,4,1,5,6,8,7] => {{1,3,4},{2},{5},{6},{7,8}}

[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,4,3,1,5,7,6,8] => [3,2,4,1,5,7,6,8] => {{1,3,4},{2},{5},{6,7},{8}}

[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,4,3,1,5,7,8,6] => [3,2,4,1,5,8,7,6] => {{1,3,4},{2},{5},{6,8},{7}}

[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => [3,2,4,1,5,7,8,6] => {{1,3,4},{2},{5},{6,7,8}}

[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => [3,2,4,1,6,5,7,8] => {{1,3,4},{2},{5,6},{7},{8}}

[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [3,2,4,1,6,5,8,7] => {{1,3,4},{2},{5,6},{7,8}}

[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [3,2,4,1,8,6,7,5] => {{1,3,4},{2},{5,8},{6},{7}}

[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [3,2,4,1,7,6,8,5] => {{1,3,4},{2},{5,7,8},{6}}

[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [3,2,4,1,8,7,6,5] => {{1,3,4},{2},{5,8},{6,7}}

[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,8,6,7,5] => [3,2,4,1,7,8,6,5] => {{1,3,4},{2},{5,6,7,8}}

[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [3,2,4,1,6,7,8,5] => {{1,3,4},{2},{5,6,7,8}}

[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [5,2,4,3,1,6,7,8] => {{1,5},{2},{3,4},{6},{7},{8}}

[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [5,2,4,3,1,6,8,7] => {{1,5},{2},{3,4},{6},{7,8}}

[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [5,2,4,3,1,7,6,8] => {{1,5},{2},{3,4},{6,7},{8}}

[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [5,2,4,3,1,8,7,6] => {{1,5},{2},{3,4},{6,8},{7}}

[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [6,2,4,3,5,1,8,7] => {{1,6},{2},{3,4},{5},{7,8}}

[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => [5,2,4,3,6,1,7,8] => {{1,5,6},{2},{3,4},{7},{8}}

[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [5,2,4,3,6,1,8,7] => {{1,5,6},{2},{3,4},{7,8}}

[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [7,2,4,3,6,5,1,8] => {{1,7},{2},{3,4},{5,6},{8}}

[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [8,2,4,3,6,5,7,1] => {{1,8},{2},{3,4},{5,6},{7}}

[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [7,2,4,3,6,5,8,1] => {{1,7,8},{2},{3,4},{5,6}}

[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,4,3,7,5,6,1,8] => [6,2,4,3,7,5,1,8] => {{1,5,6,7},{2},{3,4},{8}}

[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,7,5,6,8,1] => [8,2,4,3,7,5,6,1] => {{1,8},{2},{3,4},{5,6,7}}

[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,4,3,7,6,5,1,8] => [5,2,4,3,6,7,1,8] => {{1,5,6,7},{2},{3,4},{8}}

[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [8,2,4,3,6,7,5,1] => {{1,8},{2},{3,4},{5,6,7}}

[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,3,4,1,6,7,8] => [4,2,5,3,1,6,7,8] => {{1,3,4,5},{2},{6},{7},{8}}

[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,5,3,4,1,7,6,8] => [4,2,5,3,1,7,6,8] => {{1,3,4,5},{2},{6,7},{8}}

[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,5,3,4,1,7,8,6] => [4,2,5,3,1,8,7,6] => {{1,3,4,5},{2},{6,8},{7}}

[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,3,4,1,8,7,6] => [4,2,5,3,1,7,8,6] => {{1,3,4,5},{2},{6,7,8}}

[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,5,3,4,6,1,8,7] => [6,2,5,3,4,1,8,7] => {{1,6},{2},{3,4,5},{7,8}}

[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,3,4,6,7,1,8] => [7,2,5,3,4,6,1,8] => {{1,7},{2},{3,4,5},{6},{8}}

[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,5,3,4,7,6,1,8] => [6,2,5,3,4,7,1,8] => {{1,6,7},{2},{3,4,5},{8}}

[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,5,3,4,7,6,8,1] => [8,2,5,3,4,7,6,1] => {{1,8},{2},{3,4,5},{6,7}}

[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,6,3,4,5,1,7,8] => [5,2,6,3,4,1,7,8] => {{1,3,4,5,6},{2},{7},{8}}

[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,6,3,4,5,1,8,7] => [5,2,6,3,4,1,8,7] => {{1,3,4,5,6},{2},{7,8}}

[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,6,3,4,5,7,8,1] => [8,2,6,3,4,5,7,1] => {{1,8},{2},{3,4,5,6},{7}}

[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,6,3,4,5,8,7,1] => [7,2,6,3,4,5,8,1] => {{1,7,8},{2},{3,4,5,6}}

[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,7,3,4,5,6,1,8] => [6,2,7,3,4,5,1,8] => {{1,3,4,5,6,7},{2},{8}}

[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,7,3,4,5,6,8,1] => [8,2,7,3,4,5,6,1] => {{1,8},{2},{3,4,5,6,7}}

[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,3,4,5,6,7,1] => [7,2,8,3,4,5,6,1] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,8,3,4,5,7,6,1] => [6,2,7,1,4,8,5,3] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,8,3,4,6,7,5,1] => [5,2,7,1,8,4,6,3] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,3,5,4,1,8,7] => [4,2,5,6,1,3,8,7] => {{1,3,4,5,6},{2},{7,8}}

[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,8,3,5,4,6,7,1] => [7,2,8,5,3,4,6,1] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,7,3,5,6,4,8,1] => [8,2,7,6,3,5,4,1] => {{1,8},{2},{3,4,5,6,7}}

[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8,3,5,7,6,4,1] => [4,2,6,7,3,8,5,1] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,8,3,6,5,4,7,1] => [7,2,8,5,6,3,4,1] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,8,3,6,5,7,4,1] => [4,2,7,8,6,1,5,3] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,8,3,7,6,5,4,1] => [4,2,5,6,7,8,1,3] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [3,2,4,5,1,6,7,8] => {{1,3,4,5},{2},{6},{7},{8}}

[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [3,2,4,5,1,8,7,6] => {{1,3,4,5},{2},{6,8},{7}}

[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,5,4,3,6,1,7,8] => [6,2,4,5,3,1,7,8] => {{1,6},{2},{3,4,5},{7},{8}}

[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [7,2,4,5,3,6,1,8] => {{1,7},{2},{3,4,5},{6},{8}}

[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [7,2,4,5,3,6,8,1] => {{1,7,8},{2},{3,4,5},{6}}

[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => [8,2,4,5,3,7,6,1] => {{1,8},{2},{3,4,5},{6,7}}

[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,4,3,5,6,8,1] => [8,2,4,7,3,5,6,1] => {{1,8},{2},{3,4,5,6,7}}

[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,8,4,3,5,7,6,1] => [6,2,4,7,1,8,5,3] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,7,4,3,6,5,1,8] => [5,2,4,6,7,1,3,8] => {{1,3,4,5,6,7},{2},{8}}

[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,3,6,5,7,1] => [7,2,4,8,6,3,5,1] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,4,3,6,7,5,1] => [5,2,4,7,8,1,6,3] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,6,4,5,3,1,8,7] => [3,2,5,6,4,1,8,7] => {{1,3,4,5,6},{2},{7,8}}

[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,7,4,5,6,3,1,8] => [3,2,6,7,4,5,1,8] => {{1,3,4,5,6,7},{2},{8}}

[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,8,4,5,6,3,7,1] => [7,2,6,8,4,5,3,1] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,8,4,6,5,3,7,1] => [7,2,5,6,8,3,4,1] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,8,4,6,5,7,3,1] => [3,2,7,8,6,4,5,1] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,8,4,7,5,6,3,1] => [3,2,6,8,7,5,4,1] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,8,4,7,6,5,3,1] => [3,2,5,6,7,8,4,1] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,7,5,4,3,6,1,8] => [6,2,4,5,7,3,1,8] => {{1,3,4,5,6,7},{2},{8}}

[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,7,5,4,3,6,8,1] => [8,2,4,5,7,3,6,1] => {{1,8},{2},{3,4,5,6,7}}

[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,8,5,4,3,6,7,1] => [7,2,4,5,8,3,6,1] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,7,5,4,6,3,8,1] => [8,2,6,5,7,4,3,1] => {{1,8},{2},{3,4,5,6,7}}

[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,8,5,4,6,3,7,1] => [7,2,6,5,8,4,3,1] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,8,5,4,7,6,3,1] => [3,2,6,5,7,8,1,4] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,8,6,4,5,3,7,1] => [7,2,5,6,4,8,3,1] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [3,2,4,5,6,7,1,8] => {{1,3,4,5,6,7},{2},{8}}

[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [8,2,4,5,6,7,3,1] => {{1,8},{2},{3,4,5,6,7}}

[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,8,6,5,4,3,7,1] => [7,2,4,5,6,8,3,1] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,8,6,5,4,7,3,1] => [3,2,7,5,6,8,4,1] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,7,5,4,6,3,1] => [3,2,6,5,7,4,8,1] => {{1,3,4,5,6,7,8},{2}}

[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,1] => {{1,3,4,5,6,7,8},{2}}

[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => {{1,2,3},{4},{5},{6},{7},{8}}

[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => [2,3,1,4,5,6,8,7] => {{1,2,3},{4},{5},{6},{7,8}}

[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,2,1,4,5,7,6,8] => [2,3,1,4,5,7,6,8] => {{1,2,3},{4},{5},{6,7},{8}}

[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [2,3,1,4,5,7,8,6] => {{1,2,3},{4},{5},{6,7,8}}

[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,2,1,4,6,5,8,7] => [2,3,1,4,6,5,8,7] => {{1,2,3},{4},{5,6},{7,8}}

[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [2,3,1,4,7,6,8,5] => {{1,2,3},{4},{5,7,8},{6}}

[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [2,3,1,4,6,7,5,8] => {{1,2,3},{4},{5,6,7},{8}}

[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => [2,3,1,4,8,7,6,5] => {{1,2,3},{4},{5,8},{6,7}}

[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,8,6,7,5] => [2,3,1,4,7,8,6,5] => {{1,2,3},{4},{5,6,7,8}}

[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [2,3,1,4,6,7,8,5] => {{1,2,3},{4},{5,6,7,8}}

[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => [2,3,1,5,4,6,7,8] => {{1,2,3},{4,5},{6},{7},{8}}

[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => [2,3,1,5,4,7,6,8] => {{1,2,3},{4,5},{6,7},{8}}

[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [2,3,1,6,5,4,7,8] => {{1,2,3},{4,6},{5},{7},{8}}

[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,2,1,5,6,4,8,7] => [2,3,1,6,5,4,8,7] => {{1,2,3},{4,6},{5},{7,8}}

[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,2,1,5,6,7,4,8] => [2,3,1,7,5,6,4,8] => {{1,2,3},{4,7},{5},{6},{8}}

[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => [2,3,1,8,5,6,7,4] => {{1,2,3},{4,8},{5},{6},{7}}

[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [2,3,1,6,5,7,4,8] => {{1,2,3},{4,6,7},{5},{8}}

[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,8,6,7,4] => [2,3,1,7,5,8,6,4] => {{1,2,3},{4,6,7,8},{5}}

[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [2,3,1,5,6,4,7,8] => {{1,2,3},{4,5,6},{7},{8}}

[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [2,3,1,7,6,5,8,4] => {{1,2,3},{4,7,8},{5,6}}

[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,2,1,7,5,6,4,8] => [2,3,1,6,7,5,4,8] => {{1,2,3},{4,5,6,7},{8}}

[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,7,5,6,8,4] => [2,3,1,8,7,5,6,4] => {{1,2,3},{4,8},{5,6,7}}

[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,8,5,6,7,4] => [2,3,1,7,8,5,6,4] => {{1,2,3},{4,5,6,7,8}}

[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,8,5,7,6,4] => [2,3,1,6,7,8,4,5] => {{1,2,3},{4,5,6,7,8}}

[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [2,3,1,5,6,7,4,8] => {{1,2,3},{4,5,6,7},{8}}

[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => [2,3,1,8,6,7,5,4] => {{1,2,3},{4,8},{5,6,7}}

[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,8,6,5,7,4] => [2,3,1,7,6,8,5,4] => {{1,2,3},{4,5,6,7,8}}

[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,8,6,7,5,4] => [2,3,1,5,7,8,6,4] => {{1,2,3},{4,5,6,7,8}}

[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [2,3,1,5,6,7,8,4] => {{1,2,3},{4,5,6,7,8}}

[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => [4,3,2,1,5,6,7,8] => {{1,4},{2,3},{5},{6},{7},{8}}

[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [4,3,2,1,5,6,8,7] => {{1,4},{2,3},{5},{6},{7,8}}

[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => [4,3,2,1,5,7,6,8] => {{1,4},{2,3},{5},{6,7},{8}}

[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [4,3,2,1,5,8,7,6] => {{1,4},{2,3},{5},{6,8},{7}}

[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [4,3,2,1,5,7,8,6] => {{1,4},{2,3},{5},{6,7,8}}

[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [4,3,2,1,6,5,7,8] => {{1,4},{2,3},{5,6},{7},{8}}

[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [4,3,2,1,6,5,8,7] => {{1,4},{2,3},{5,6},{7,8}}

[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [4,3,2,1,7,6,5,8] => {{1,4},{2,3},{5,7},{6},{8}}

[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [4,3,2,1,8,6,7,5] => {{1,4},{2,3},{5,8},{6},{7}}

[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [4,3,2,1,7,6,8,5] => {{1,4},{2,3},{5,7,8},{6}}

[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [4,3,2,1,6,7,5,8] => {{1,4},{2,3},{5,6,7},{8}}

[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [4,3,2,1,8,7,6,5] => {{1,4},{2,3},{5,8},{6,7}}

[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => [4,3,2,1,7,8,6,5] => {{1,4},{2,3},{5,6,7,8}}

[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [4,3,2,1,6,7,8,5] => {{1,4},{2,3},{5,6,7,8}}

[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [5,3,2,4,1,6,7,8] => {{1,5},{2,3},{4},{6},{7},{8}}

[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [3,2,4,5,1,6,8,7] => [5,3,2,4,1,6,8,7] => {{1,5},{2,3},{4},{6},{7,8}}

[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [3,2,4,5,1,7,6,8] => [5,3,2,4,1,7,6,8] => {{1,5},{2,3},{4},{6,7},{8}}

[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,2,4,5,1,7,8,6] => [5,3,2,4,1,8,7,6] => {{1,5},{2,3},{4},{6,8},{7}}

[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [8,3,2,4,5,6,7,1] => {{1,8},{2,3},{4},{5},{6},{7}}

[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [7,3,2,4,5,6,8,1] => {{1,7,8},{2,3},{4},{5},{6}}

[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [3,2,4,5,7,6,1,8] => [6,3,2,4,5,7,1,8] => {{1,6,7},{2,3},{4},{5},{8}}

[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,2,4,6,5,1,8,7] => [5,3,2,4,6,1,8,7] => {{1,5,6},{2,3},{4},{7,8}}

[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,2,4,7,5,6,1,8] => [6,3,2,4,7,5,1,8] => {{1,5,6,7},{2,3},{4},{8}}

[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [8,3,2,4,6,7,5,1] => {{1,8},{2,3},{4},{5,6,7}}

[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [5,3,2,4,6,7,8,1] => {{1,5,6,7,8},{2,3},{4}}

[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [4,3,2,5,1,6,7,8] => {{1,4,5},{2,3},{6},{7},{8}}

[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [4,3,2,5,1,8,7,6] => {{1,4,5},{2,3},{6,8},{7}}

[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [4,3,2,5,1,7,8,6] => {{1,4,5},{2,3},{6,7,8}}

[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [3,2,5,4,6,1,7,8] => [6,3,2,5,4,1,7,8] => {{1,6},{2,3},{4,5},{7},{8}}

[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [6,3,2,5,4,1,8,7] => {{1,6},{2,3},{4,5},{7,8}}

[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [3,2,5,4,6,7,1,8] => [7,3,2,5,4,6,1,8] => {{1,7},{2,3},{4,5},{6},{8}}

[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [6,3,2,5,4,7,1,8] => {{1,6,7},{2,3},{4,5},{8}}

[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [8,3,2,5,4,7,6,1] => {{1,8},{2,3},{4,5},{6,7}}

[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,8,6,7,1] => [7,3,2,5,4,8,6,1] => {{1,6,7,8},{2,3},{4,5}}

[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [3,2,6,4,5,1,7,8] => [5,3,2,6,4,1,7,8] => {{1,4,5,6},{2,3},{7},{8}}

[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,6,4,5,1,8,7] => [5,3,2,6,4,1,8,7] => {{1,4,5,6},{2,3},{7,8}}

[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,7,4,5,6,1,8] => [6,3,2,7,4,5,1,8] => {{1,4,5,6,7},{2,3},{8}}

[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,7,4,6,5,1,8] => [5,3,2,6,7,1,4,8] => {{1,4,5,6,7},{2,3},{8}}

[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,7,4,6,5,8,1] => [8,3,2,7,6,4,5,1] => {{1,8},{2,3},{4,5,6,7}}

[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,8,4,6,5,7,1] => [7,3,2,8,6,4,5,1] => {{1,4,5,6,7,8},{2,3}}

[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [4,3,2,5,6,1,8,7] => {{1,4,5,6},{2,3},{7,8}}

[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [7,3,2,5,6,4,8,1] => {{1,7,8},{2,3},{4,5,6}}

[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,7,5,4,6,1,8] => [6,3,2,5,7,4,1,8] => {{1,4,5,6,7},{2,3},{8}}

[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,8,5,4,6,7,1] => [7,3,2,5,8,4,6,1] => {{1,4,5,6,7,8},{2,3}}

[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,8,5,4,7,6,1] => [6,3,2,5,7,8,1,4] => {{1,4,5,6,7,8},{2,3}}

[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => [4,3,2,6,7,5,1,8] => {{1,4,5,6,7},{2,3},{8}}

[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,7,5,6,4,8,1] => [8,3,2,6,7,5,4,1] => {{1,8},{2,3},{4,5,6,7}}

[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,8,5,6,4,7,1] => [7,3,2,6,8,5,4,1] => {{1,4,5,6,7,8},{2,3}}

[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,8,5,7,6,4,1] => [4,3,2,6,7,8,1,5] => {{1,4,5,6,7,8},{2,3}}

[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [4,3,2,5,6,7,1,8] => {{1,4,5,6,7},{2,3},{8}}

[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [8,3,2,5,6,7,4,1] => {{1,8},{2,3},{4,5,6,7}}

[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [3,2,8,6,5,4,7,1] => [7,3,2,5,6,8,4,1] => {{1,4,5,6,7,8},{2,3}}

[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,8,7,5,6,4,1] => [4,3,2,6,7,5,8,1] => {{1,4,5,6,7,8},{2,3}}

[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [4,3,2,5,6,7,8,1] => {{1,4,5,6,7,8},{2,3}}

[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8] => [3,4,2,1,5,6,7,8] => {{1,2,3,4},{5},{6},{7},{8}}

[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,3,1,6,5,8,7] => [3,4,2,1,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}

[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,2,3,1,6,7,8,5] => [3,4,2,1,8,6,7,5] => {{1,2,3,4},{5,8},{6},{7}}

[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,2,3,1,6,8,7,5] => [3,4,2,1,7,6,8,5] => {{1,2,3,4},{5,7,8},{6}}

[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,2,3,1,7,6,8,5] => [3,4,2,1,8,7,6,5] => {{1,2,3,4},{5,8},{6,7}}

[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => [3,4,2,1,7,8,6,5] => {{1,2,3,4},{5,6,7,8}}

[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => [3,4,2,1,6,7,8,5] => {{1,2,3,4},{5,6,7,8}}

[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,2,3,5,1,6,7,8] => [5,4,2,3,1,6,7,8] => {{1,5},{2,3,4},{6},{7},{8}}

[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,2,3,5,1,6,8,7] => [5,4,2,3,1,6,8,7] => {{1,5},{2,3,4},{6},{7,8}}

[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,2,3,5,1,7,8,6] => [5,4,2,3,1,8,7,6] => {{1,5},{2,3,4},{6,8},{7}}

[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,2,3,5,1,8,7,6] => [5,4,2,3,1,7,8,6] => {{1,5},{2,3,4},{6,7,8}}

[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,2,3,5,6,1,8,7] => [6,4,2,3,5,1,8,7] => {{1,6},{2,3,4},{5},{7,8}}

[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,2,3,5,6,7,1,8] => [7,4,2,3,5,6,1,8] => {{1,7},{2,3,4},{5},{6},{8}}

[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,1] => [8,4,2,3,5,6,7,1] => {{1,8},{2,3,4},{5},{6},{7}}

[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,2,3,5,7,6,1,8] => [6,4,2,3,5,7,1,8] => {{1,6,7},{2,3,4},{5},{8}}

[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [4,2,3,5,7,6,8,1] => [8,4,2,3,5,7,6,1] => {{1,8},{2,3,4},{5},{6,7}}

[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [4,2,3,6,5,1,8,7] => [5,4,2,3,6,1,8,7] => {{1,5,6},{2,3,4},{7,8}}

[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,3,7,5,6,8,1] => [8,4,2,3,7,5,6,1] => {{1,8},{2,3,4},{5,6,7}}

[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,2,3,8,5,7,6,1] => [6,4,2,3,7,8,1,5] => {{1,5,6,7,8},{2,3,4}}

[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [4,2,3,7,6,5,1,8] => [5,4,2,3,6,7,1,8] => {{1,5,6,7},{2,3,4},{8}}

[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,2,3,7,6,5,8,1] => [8,4,2,3,6,7,5,1] => {{1,8},{2,3,4},{5,6,7}}

[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,3,8,6,5,7,1] => [7,4,2,3,6,8,5,1] => {{1,5,6,7,8},{2,3,4}}

[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [4,2,3,8,6,7,5,1] => [5,4,2,3,7,8,6,1] => {{1,5,6,7,8},{2,3,4}}

[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,2,3,8,7,6,5,1] => [5,4,2,3,6,7,8,1] => {{1,5,6,7,8},{2,3,4}}

[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => [4,5,2,3,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}}

[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,2,3,4,1,6,8,7] => [4,5,2,3,1,6,8,7] => {{1,2,3,4,5},{6},{7,8}}

[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [5,2,3,4,1,7,6,8] => [4,5,2,3,1,7,6,8] => {{1,2,3,4,5},{6,7},{8}}

[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => [4,5,2,3,1,8,7,6] => {{1,2,3,4,5},{6,8},{7}}

[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,2,3,4,1,8,7,6] => [4,5,2,3,1,7,8,6] => {{1,2,3,4,5},{6,7,8}}

[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [5,2,3,4,6,1,7,8] => [6,5,2,3,4,1,7,8] => {{1,6},{2,3,4,5},{7},{8}}

[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [5,2,3,4,6,8,7,1] => [7,5,2,3,4,6,8,1] => {{1,7,8},{2,3,4,5},{6}}

[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,2,3,4,8,6,7,1] => [7,5,2,3,4,8,6,1] => {{1,6,7,8},{2,3,4,5}}

[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,2,3,4,8,7,6,1] => [6,5,2,3,4,7,8,1] => {{1,6,7,8},{2,3,4,5}}

[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,2,3,4,5,1,7,8] => [5,6,2,3,4,1,7,8] => {{1,2,3,4,5,6},{7},{8}}

[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [6,2,3,4,5,7,1,8] => [7,6,2,3,4,5,1,8] => {{1,7},{2,3,4,5,6},{8}}

[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,2,3,4,5,7,8,1] => [8,6,2,3,4,5,7,1] => {{1,8},{2,3,4,5,6},{7}}

[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,2,3,4,5,8,7,1] => [7,6,2,3,4,5,8,1] => {{1,7,8},{2,3,4,5,6}}

[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => [6,7,2,3,4,5,1,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [8,7,2,3,4,5,6,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => [7,8,2,3,4,5,6,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8,2,3,4,5,7,6,1] => [6,7,1,3,4,8,5,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [8,2,3,4,6,5,7,1] => [7,8,2,3,6,4,5,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [8,2,3,4,6,7,5,1] => [5,7,1,3,8,4,6,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,2,3,5,4,1,7,8] => [4,5,1,6,3,2,7,8] => {{1,2,3,4,5,6},{7},{8}}

[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [6,2,3,5,4,7,1,8] => [7,6,2,5,3,4,1,8] => {{1,7},{2,3,4,5,6},{8}}

[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,2,3,5,4,7,8,1] => [8,6,2,5,3,4,7,1] => {{1,8},{2,3,4,5,6},{7}}

[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,2,3,5,4,6,1,8] => [6,7,2,5,3,4,1,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,2,3,5,6,4,1,8] => [4,6,1,7,3,5,2,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [7,2,3,5,6,4,8,1] => [8,7,2,6,3,5,4,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [8,2,3,5,6,4,7,1] => [7,8,2,6,3,5,4,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,6,5,4,1,8] => [4,5,2,6,7,3,1,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [8,2,3,6,5,7,4,1] => [4,7,1,8,6,3,5,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8,2,3,7,5,6,4,1] => [4,6,1,8,7,5,3,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8,2,3,7,6,5,4,1] => [4,5,1,6,7,8,3,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,2,4,3,1,6,7,8] => [3,4,5,1,2,6,7,8] => {{1,2,3,4,5},{6},{7},{8}}

[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,2,4,3,1,6,8,7] => [3,4,5,1,2,6,8,7] => {{1,2,3,4,5},{6},{7,8}}

[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [5,2,4,3,1,7,8,6] => [3,4,5,1,2,8,7,6] => {{1,2,3,4,5},{6,8},{7}}

[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,2,4,3,1,8,7,6] => [3,4,5,1,2,7,8,6] => {{1,2,3,4,5},{6,7,8}}

[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => [6,5,4,2,3,1,8,7] => {{1,6},{2,3,4,5},{7,8}}

[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [5,2,4,3,6,7,8,1] => [8,5,4,2,3,6,7,1] => {{1,8},{2,3,4,5},{6},{7}}

[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [5,2,4,3,7,6,8,1] => [8,5,4,2,3,7,6,1] => {{1,8},{2,3,4,5},{6,7}}

[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,2,4,3,8,7,6,1] => [6,5,4,2,3,7,8,1] => {{1,6,7,8},{2,3,4,5}}

[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2,4,3,5,1,8,7] => [5,6,4,2,3,1,8,7] => {{1,2,3,4,5,6},{7,8}}

[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [6,2,4,3,5,8,7,1] => [7,6,4,2,3,5,8,1] => {{1,7,8},{2,3,4,5,6}}

[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [8,2,4,3,5,6,7,1] => [7,8,4,2,3,5,6,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => [8,7,4,2,6,3,5,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8,2,4,3,6,5,7,1] => [7,8,4,2,6,3,5,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [6,2,4,5,3,1,7,8] => [3,5,6,1,4,2,7,8] => {{1,2,3,4,5,6},{7},{8}}

[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [6,2,4,5,3,7,8,1] => [8,6,5,2,4,3,7,1] => {{1,8},{2,3,4,5,6},{7}}

[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,2,4,5,3,6,8,1] => [8,7,5,2,4,3,6,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [8,2,4,5,3,6,7,1] => [7,8,5,2,4,3,6,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => [6,7,5,1,4,8,3,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,4,6,5,3,1,8] => [3,5,6,2,7,4,1,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [7,2,4,6,5,3,8,1] => [8,7,5,2,6,4,3,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [8,2,4,6,5,3,7,1] => [7,8,5,2,6,4,3,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [8,2,4,7,5,6,3,1] => [3,6,8,1,7,5,4,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8,2,4,7,6,5,3,1] => [3,5,6,1,7,8,4,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,2,5,4,3,1,7,8] => [3,4,5,6,2,1,7,8] => {{1,2,3,4,5,6},{7},{8}}

[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2,5,4,3,1,8,7] => [3,4,5,6,2,1,8,7] => {{1,2,3,4,5,6},{7,8}}

[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [6,2,5,4,3,7,1,8] => [7,6,4,5,2,3,1,8] => {{1,7},{2,3,4,5,6},{8}}

[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [6,2,5,4,3,8,7,1] => [7,6,4,5,2,3,8,1] => {{1,7,8},{2,3,4,5,6}}

[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,2,5,4,3,6,1,8] => [6,7,4,5,2,3,1,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,2,5,4,3,7,6,1] => [6,7,4,5,1,8,3,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,2,5,4,6,3,8,1] => [8,7,6,5,2,4,3,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [8,2,5,4,6,3,7,1] => [7,8,6,5,2,4,3,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [8,2,5,4,6,7,3,1] => [3,7,8,5,1,4,6,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [8,2,5,4,7,6,3,1] => [3,6,7,5,2,8,4,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [7,2,6,4,5,3,8,1] => [8,7,5,6,4,2,3,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8,2,6,4,5,7,3,1] => [3,7,8,6,4,1,5,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,2,7,4,6,5,3,1] => [3,5,6,8,7,2,4,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,2,6,5,4,3,1,8] => [3,4,5,6,7,1,2,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,6,5,4,3,8,1] => [8,7,4,5,6,2,3,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8,2,6,5,4,3,7,1] => [7,8,4,5,6,2,3,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8,2,6,5,4,7,3,1] => [3,7,8,5,6,1,4,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8,2,7,5,4,6,3,1] => [3,6,8,5,7,4,1,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8,2,7,6,5,4,3,1] => [3,4,5,6,7,8,2,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => {{1,2,3,4},{5},{6},{7},{8}}

[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => [2,3,4,1,5,6,8,7] => {{1,2,3,4},{5},{6},{7,8}}

[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => [2,3,4,1,5,7,6,8] => {{1,2,3,4},{5},{6,7},{8}}

[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => [2,3,4,1,5,8,7,6] => {{1,2,3,4},{5},{6,8},{7}}

[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [2,3,4,1,5,7,8,6] => {{1,2,3,4},{5},{6,7,8}}

[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => [2,3,4,1,6,5,7,8] => {{1,2,3,4},{5,6},{7},{8}}

[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => [2,3,4,1,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}

[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => [2,3,4,1,7,6,5,8] => {{1,2,3,4},{5,7},{6},{8}}

[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => [2,3,4,1,8,6,7,5] => {{1,2,3,4},{5,8},{6},{7}}

[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [2,3,4,1,7,6,8,5] => {{1,2,3,4},{5,7,8},{6}}

[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [2,3,4,1,6,7,5,8] => {{1,2,3,4},{5,6,7},{8}}

[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => [2,3,4,1,8,7,6,5] => {{1,2,3,4},{5,8},{6,7}}

[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => [2,3,4,1,7,8,6,5] => {{1,2,3,4},{5,6,7,8}}

[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [2,3,4,1,6,7,8,5] => {{1,2,3,4},{5,6,7,8}}

[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => [5,3,4,2,1,6,7,8] => {{1,5},{2,3,4},{6},{7},{8}}

[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [4,3,2,5,1,6,8,7] => [5,3,4,2,1,6,8,7] => {{1,5},{2,3,4},{6},{7,8}}

[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [5,3,4,2,1,8,7,6] => {{1,5},{2,3,4},{6,8},{7}}

[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [5,3,4,2,1,7,8,6] => {{1,5},{2,3,4},{6,7,8}}

[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [6,3,4,2,5,1,8,7] => {{1,6},{2,3,4},{5},{7,8}}

[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [8,3,4,2,5,6,7,1] => {{1,8},{2,3,4},{5},{6},{7}}

[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [5,3,4,2,6,1,8,7] => {{1,5,6},{2,3,4},{7,8}}

[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => [7,3,4,2,6,5,1,8] => {{1,7},{2,3,4},{5,6},{8}}

[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => [8,3,4,2,6,5,7,1] => {{1,8},{2,3,4},{5,6},{7}}

[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [7,3,4,2,6,5,8,1] => {{1,7,8},{2,3,4},{5,6}}

[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,7,5,6,8,1] => [8,3,4,2,7,5,6,1] => {{1,8},{2,3,4},{5,6,7}}

[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,8,5,6,7,1] => [7,3,4,2,8,5,6,1] => {{1,5,6,7,8},{2,3,4}}

[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,8,5,7,6,1] => [6,3,4,2,7,8,1,5] => {{1,5,6,7,8},{2,3,4}}

[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [5,3,4,2,6,7,8,1] => {{1,5,6,7,8},{2,3,4}}

[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,3,2,4,1,6,7,8] => [4,3,5,2,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}}

[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,3,2,4,1,6,8,7] => [4,3,5,2,1,6,8,7] => {{1,2,3,4,5},{6},{7,8}}

[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [5,3,2,4,1,7,8,6] => [4,3,5,2,1,8,7,6] => {{1,2,3,4,5},{6,8},{7}}

[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,3,2,4,6,1,7,8] => [6,3,5,2,4,1,7,8] => {{1,6},{2,3,4,5},{7},{8}}

[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,3,2,4,6,1,8,7] => [6,3,5,2,4,1,8,7] => {{1,6},{2,3,4,5},{7,8}}

[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [5,3,2,4,6,7,1,8] => [7,3,5,2,4,6,1,8] => {{1,7},{2,3,4,5},{6},{8}}

[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,3,2,4,8,7,6,1] => [6,3,5,2,4,7,8,1] => {{1,6,7,8},{2,3,4,5}}

[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [6,3,2,4,5,1,7,8] => [5,3,6,2,4,1,7,8] => {{1,2,3,4,5,6},{7},{8}}

[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [6,3,2,4,5,1,8,7] => [5,3,6,2,4,1,8,7] => {{1,2,3,4,5,6},{7,8}}

[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [6,3,2,4,5,7,8,1] => [8,3,6,2,4,5,7,1] => {{1,8},{2,3,4,5,6},{7}}

[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [6,3,2,4,5,8,7,1] => [7,3,6,2,4,5,8,1] => {{1,7,8},{2,3,4,5,6}}

[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [7,3,2,4,5,6,1,8] => [6,3,7,2,4,5,1,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [8,3,7,2,4,5,6,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => [7,3,8,2,4,5,6,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [8,3,2,4,5,7,6,1] => [6,3,7,1,4,8,5,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [7,3,2,4,6,5,8,1] => [8,3,7,2,6,4,5,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8,3,2,4,6,7,5,1] => [5,3,7,1,8,4,6,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [6,3,2,5,4,1,7,8] => [4,3,5,6,1,2,7,8] => {{1,2,3,4,5,6},{7},{8}}

[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => [4,3,5,6,1,2,8,7] => {{1,2,3,4,5,6},{7,8}}

[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,3,2,5,4,6,1,8] => [6,3,7,5,2,4,1,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [7,3,2,5,4,6,8,1] => [8,3,7,5,2,4,6,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [8,3,2,5,4,6,7,1] => [7,3,8,5,2,4,6,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => [6,3,7,5,1,8,4,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [7,3,2,5,6,4,8,1] => [8,3,7,6,2,5,4,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8,3,2,5,7,6,4,1] => [4,3,6,7,2,8,5,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [7,3,2,6,5,4,8,1] => [8,3,7,5,6,2,4,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [8,3,2,6,5,4,7,1] => [7,3,8,5,6,2,4,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8,3,2,6,5,7,4,1] => [4,3,7,8,6,1,5,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8,3,2,7,5,6,4,1] => [4,3,6,8,7,5,1,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => [4,3,5,6,7,8,1,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,3,4,2,1,6,7,8] => [2,4,5,3,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}}

[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,3,4,2,1,6,8,7] => [2,4,5,3,1,6,8,7] => {{1,2,3,4,5},{6},{7,8}}

[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [5,3,4,2,1,7,6,8] => [2,4,5,3,1,7,6,8] => {{1,2,3,4,5},{6,7},{8}}

[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3,4,2,1,7,8,6] => [2,4,5,3,1,8,7,6] => {{1,2,3,4,5},{6,8},{7}}

[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3,4,2,1,8,7,6] => [2,4,5,3,1,7,8,6] => {{1,2,3,4,5},{6,7,8}}

[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,3,4,2,6,1,8,7] => [6,4,5,3,2,1,8,7] => {{1,6},{2,3,4,5},{7,8}}

[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [5,3,4,2,6,7,1,8] => [7,4,5,3,2,6,1,8] => {{1,7},{2,3,4,5},{6},{8}}

[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,3,4,2,6,7,8,1] => [8,4,5,3,2,6,7,1] => {{1,8},{2,3,4,5},{6},{7}}

[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,3,4,2,7,6,8,1] => [8,4,5,3,2,7,6,1] => {{1,8},{2,3,4,5},{6,7}}

[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,3,4,2,8,6,7,1] => [7,4,5,3,2,8,6,1] => {{1,6,7,8},{2,3,4,5}}

[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [6,3,4,2,5,1,7,8] => [5,4,6,3,2,1,7,8] => {{1,2,3,4,5,6},{7},{8}}

[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,3,4,2,5,1,8,7] => [5,4,6,3,2,1,8,7] => {{1,2,3,4,5,6},{7,8}}

[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [7,3,4,2,5,6,8,1] => [8,4,7,3,2,5,6,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => [7,4,8,3,2,5,6,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [8,3,4,2,5,7,6,1] => [6,4,7,1,2,8,5,3] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,3,4,2,6,5,8,1] => [8,4,7,3,6,2,5,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8,3,4,2,6,5,7,1] => [7,4,8,3,6,2,5,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,3,4,5,2,1,8,7] => [2,5,6,3,4,1,8,7] => {{1,2,3,4,5,6},{7,8}}

[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [6,3,4,5,2,7,1,8] => [7,5,6,3,4,2,1,8] => {{1,7},{2,3,4,5,6},{8}}

[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,3,4,5,2,7,8,1] => [8,5,6,3,4,2,7,1] => {{1,8},{2,3,4,5,6},{7}}

[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,3,4,5,2,8,7,1] => [7,5,6,3,4,2,8,1] => {{1,7,8},{2,3,4,5,6}}

[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [7,3,4,5,2,6,1,8] => [6,5,7,3,4,2,1,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,3,4,5,2,6,8,1] => [8,5,7,3,4,2,6,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8,3,4,5,2,6,7,1] => [7,5,8,3,4,2,6,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1,8] => [2,6,7,3,4,5,1,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [8,6,7,3,4,5,2,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,3,4,5,6,2,7,1] => [7,6,8,3,4,5,2,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => [2,7,8,3,4,5,6,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,3,4,6,5,2,1,8] => [2,5,6,1,7,4,3,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [7,3,4,6,5,2,8,1] => [8,5,6,2,7,4,3,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [8,3,4,6,5,2,7,1] => [7,5,6,2,8,4,3,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [8,3,4,6,5,7,2,1] => [2,7,8,3,6,4,5,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8,3,4,7,6,5,2,1] => [2,5,6,3,7,8,4,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [6,3,5,4,2,1,7,8] => [2,4,5,6,1,3,7,8] => {{1,2,3,4,5,6},{7},{8}}

[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,3,5,4,2,1,8,7] => [2,4,5,6,1,3,8,7] => {{1,2,3,4,5,6},{7,8}}

[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,3,5,4,2,8,7,1] => [7,4,5,6,2,3,8,1] => {{1,7,8},{2,3,4,5,6}}

[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,3,5,4,6,2,8,1] => [8,6,7,5,3,4,2,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [8,3,5,4,6,2,7,1] => [7,6,8,5,3,4,2,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,5,4,7,6,2,1] => [2,6,7,5,1,8,4,3] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,3,6,4,5,2,1,8] => [2,5,7,6,4,3,1,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,6,4,5,2,8,1] => [8,5,7,6,4,3,2,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8,3,6,4,5,2,7,1] => [7,5,8,6,4,3,2,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,3,7,4,6,5,2,1] => [2,5,6,8,7,1,4,3] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,3,6,5,4,2,1,8] => [2,4,5,6,7,3,1,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,3,6,5,4,2,8,1] => [8,4,5,6,7,3,2,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8,3,6,5,4,2,7,1] => [7,4,5,6,8,3,2,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8,3,6,5,4,7,2,1] => [2,7,8,5,6,3,4,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8,3,7,5,4,6,2,1] => [2,6,8,5,7,4,3,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8,3,7,5,6,4,2,1] => [2,4,6,8,7,5,1,3] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8,3,7,6,5,4,2,1] => [2,4,5,6,7,8,1,3] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [2,3,4,5,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}}

[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => [2,3,4,5,1,6,8,7] => {{1,2,3,4,5},{6},{7,8}}

[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => [2,3,4,5,1,7,6,8] => {{1,2,3,4,5},{6,7},{8}}

[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => [2,3,4,5,1,8,7,6] => {{1,2,3,4,5},{6,8},{7}}

[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [2,3,4,5,1,7,8,6] => {{1,2,3,4,5},{6,7,8}}

[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [6,3,4,5,2,1,8,7] => {{1,6},{2,3,4,5},{7,8}}

[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [8,3,4,5,2,6,7,1] => {{1,8},{2,3,4,5},{6},{7}}

[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [6,3,4,5,2,7,1,8] => {{1,6,7},{2,3,4,5},{8}}

[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [8,3,4,5,2,7,6,1] => {{1,8},{2,3,4,5},{6,7}}

[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [6,3,4,5,2,7,8,1] => {{1,6,7,8},{2,3,4,5}}

[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [8,3,4,7,2,5,6,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [8,4,3,2,5,7,6,1] => [6,3,4,7,1,8,5,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,3,2,6,5,8,1] => [8,3,4,7,6,2,5,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [8,4,3,2,6,5,7,1] => [7,3,4,8,6,2,5,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [8,4,3,2,6,7,5,1] => [5,3,4,7,8,1,6,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8,4,3,2,7,6,5,1] => [5,3,4,6,7,8,2,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [6,4,3,5,2,7,1,8] => [7,5,4,6,3,2,1,8] => {{1,7},{2,3,4,5,6},{8}}

[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [6,4,3,5,2,7,8,1] => [8,5,4,6,3,2,7,1] => {{1,8},{2,3,4,5,6},{7}}

[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1,8] => [6,5,4,7,3,2,1,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [8,4,3,5,2,6,7,1] => [7,5,4,8,3,2,6,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [8,4,3,5,2,7,6,1] => [6,5,4,7,1,8,2,3] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,4,3,5,6,2,1,8] => [2,6,4,7,3,5,1,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8,4,3,5,6,2,7,1] => [7,6,4,8,3,5,2,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8,4,3,5,6,7,2,1] => [2,7,4,8,3,5,6,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8,4,3,5,7,6,2,1] => [2,6,4,7,1,8,5,3] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,4,3,6,5,2,1,8] => [2,5,4,6,7,1,3,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8,4,3,7,5,6,2,1] => [2,6,4,8,7,5,3,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [8,4,3,7,6,5,2,1] => [2,5,4,6,7,8,3,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,5,3,4,2,1,8,7] => [2,4,5,3,6,1,8,7] => {{1,2,3,4,5,6},{7,8}}

[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,3,4,2,7,8,1] => [8,4,5,3,6,2,7,1] => {{1,8},{2,3,4,5,6},{7}}

[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [6,5,3,4,2,8,7,1] => [7,4,5,3,6,2,8,1] => {{1,7,8},{2,3,4,5,6}}

[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,8,1] => [8,4,5,3,7,2,6,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8,5,3,4,2,6,7,1] => [7,4,5,3,8,2,6,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,5,3,4,2,7,6,1] => [6,4,5,1,7,8,2,3] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8,5,3,4,7,6,2,1] => [2,6,5,1,7,8,4,3] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,3,4,6,5,2,1] => [2,5,6,1,7,4,8,3] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,6,3,5,4,2,1,8] => [2,4,5,6,1,7,3,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8,7,3,5,4,6,2,1] => [2,6,7,5,3,4,8,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => [2,4,6,7,1,5,8,3] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8,7,3,6,5,4,2,1] => [2,4,5,6,7,3,8,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [2,3,4,5,6,1,7,8] => {{1,2,3,4,5,6},{7},{8}}

[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => [2,3,4,5,6,1,8,7] => {{1,2,3,4,5,6},{7,8}}

[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => [7,3,4,5,6,2,1,8] => {{1,7},{2,3,4,5,6},{8}}

[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [8,3,4,5,6,2,7,1] => {{1,8},{2,3,4,5,6},{7}}

[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [7,3,4,5,6,2,8,1] => {{1,7,8},{2,3,4,5,6}}

[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8,5,4,3,2,6,7,1] => [7,3,4,5,8,2,6,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => [6,3,4,5,7,8,1,2] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => [2,6,4,5,7,3,1,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [8,6,4,5,7,3,2,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8,5,4,3,6,2,7,1] => [7,6,4,5,8,3,2,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8,5,4,3,6,7,2,1] => [2,7,4,5,8,3,6,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8,5,4,3,7,6,2,1] => [2,6,4,5,7,8,1,3] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,6,4,3,5,2,1,8] => [2,5,4,6,3,7,1,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8,6,4,3,5,2,7,1] => [7,5,4,6,3,8,2,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8,6,4,3,5,7,2,1] => [2,7,4,6,3,8,5,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8,7,4,3,5,6,2,1] => [2,6,4,7,3,5,8,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => [2,5,4,6,7,1,8,3] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,6,4,5,3,2,8,1] => [8,3,5,6,4,7,2,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8,7,4,5,3,6,2,1] => [2,6,5,7,4,3,8,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => [2,3,6,7,4,5,8,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,7,4,6,5,3,2,1] => [2,3,5,6,7,1,8,4] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [2,3,4,5,6,7,1,8] => {{1,2,3,4,5,6,7},{8}}

[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => [8,3,4,5,6,7,2,1] => {{1,8},{2,3,4,5,6,7}}

[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8,6,5,4,3,2,7,1] => [7,3,4,5,6,8,2,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8,6,5,4,3,7,2,1] => [2,7,4,5,6,8,3,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8,7,5,4,3,6,2,1] => [2,6,4,5,7,3,8,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => [2,3,5,6,4,7,8,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,7,6,5,4,3,2,1,9] => [2,3,4,5,6,7,8,1,9] => {{1,2,3,4,5,6,7,8},{9}}

[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,2] => {{1},{2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,8,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,8,9,1,10] => {{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] => [1,10,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,10,2] => {{1},{2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,9,8,7,6,5,4,3,2,1,11] => [2,3,4,5,6,7,8,9,10,1,11] => {{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] => [1,11,10,9,8,7,6,5,4,3,2] => [1,3,4,5,6,7,8,9,10,11,2] => {{1},{2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,3,7,6,5,4,2,1,9] => [2,4,5,6,7,8,1,3,9] => {{1,2,3,4,5,6,7,8},{9}}

[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,7,6,5,4,3,1,9] => [3,2,4,5,6,7,8,1,9] => {{1,3,4,5,6,7,8},{2},{9}}

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => [2,3,4,5,6,7,1,9,8] => {{1,2,3,4,5,6,7},{8,9}}

[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,3] => {{1,2},{3,4,5,6,7,8,9}}

[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,9,8,7,6,5,4,2] => [1,4,3,5,6,7,8,9,2] => {{1},{2,4,5,6,7,8,9},{3}}

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [2,3,4,5,6,7,1,8,9] => {{1,2,3,4,5,6,7},{8},{9}}

[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [1,3,4,5,6,7,8,2,9] => {{1},{2,3,4,5,6,7,8},{9}}

[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [1,2,4,5,6,7,8,9,3] => {{1},{2},{3,4,5,6,7,8,9}}

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [2,3,4,5,6,7,8,1,10,9] => {{1,2,3,4,5,6,7,8},{9,10}}

[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,3] => {{1,2},{3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [2,3,4,5,6,7,8,1,9,10] => {{1,2,3,4,5,6,7,8},{9},{10}}

[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,9,8,7,6,5,4,3,2,10] => [1,3,4,5,6,7,8,9,2,10] => {{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] => [1,2,10,9,8,7,6,5,4,3] => [1,2,4,5,6,7,8,9,10,3] => {{1},{2},{3,4,5,6,7,8,9,10}}

[] => [] => [] => {}

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,1] => [9,2,3,4,5,6,7,8,1] => {{1,9},{2},{3},{4},{5},{6},{7},{8}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [8,2,3,4,5,6,7,9,1] => {{1,8,9},{2},{3},{4},{5},{6},{7}}

[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,9,8,7,6,5,4,1] => [4,2,3,5,6,7,8,9,1] => {{1,4,5,6,7,8,9},{2},{3}}

[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,9,1] => {{1,3,4,5,6,7,8,9},{2}}

[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [9,3,2,4,5,6,7,8,1] => {{1,9},{2,3},{4},{5},{6},{7},{8}}

[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,9,8,7,6,5,4,1] => [4,3,2,5,6,7,8,9,1] => {{1,4,5,6,7,8,9},{2,3}}

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => [9,8,2,3,4,5,6,7,1] => {{1,9},{2,3,4,5,6,7,8}}

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,2,3,4,5,6,7,8,1] => [8,9,2,3,4,5,6,7,1] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [9,2,7,4,5,6,3,8,1] => [8,9,6,7,4,5,2,3,1] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9,2,8,7,6,5,4,3,1] => [3,4,5,6,7,8,9,1,2] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,1] => [9,3,4,2,5,6,7,8,1] => {{1,9},{2,3,4},{5},{6},{7},{8}}

[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [9,3,8,7,6,5,4,2,1] => [2,4,5,6,7,8,9,3,1] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,1] => [9,3,4,5,2,6,7,8,1] => {{1,9},{2,3,4,5},{6},{7},{8}}

[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [9,8,3,7,6,5,4,2,1] => [2,4,5,6,7,8,1,9,3] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [9,3,4,5,6,7,8,2,1] => {{1,9},{2,3,4,5,6,7,8}}

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [9,7,6,5,4,3,2,8,1] => [8,3,4,5,6,7,9,2,1] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [9,7,6,5,4,3,8,2,1] => [2,8,4,5,6,7,9,3,1] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [9,8,7,5,6,4,3,2,1] => [2,3,4,6,7,5,8,9,1] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,1] => {{1,2,3,4,5,6,7,8,9}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => {{1},{2},{3},{4},{5},{6},{7},{8,9}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,8,7] => {{1},{2},{3},{4},{5},{6},{7,9},{8}}

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,9,7,8,6] => {{1},{2},{3},{4},{5},{6,9},{7},{8}}

[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,9,6,7,8,5] => {{1},{2},{3},{4},{5,9},{6},{7},{8}}

[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [1,2,3,9,5,6,7,8,4] => {{1},{2},{3},{4,9},{5},{6},{7},{8}}

[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [1,2,9,4,5,6,7,8,3] => {{1},{2},{3,9},{4},{5},{6},{7},{8}}

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [1,9,3,4,5,6,7,8,2] => {{1},{2,9},{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] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,9,8,7] => [1,2,3,4,5,6,8,9,7] => {{1},{2},{3},{4},{5},{6},{7,8,9}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,10,9,8] => {{1},{2},{3},{4},{5},{6},{7},{8,10},{9}}

[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,7,9,6] => [1,2,3,4,5,9,8,7,6] => {{1},{2},{3},{4},{5},{6,9},{7,8}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,10,8,9,7] => {{1},{2},{3},{4},{5},{6},{7,10},{8},{9}}

[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,4,7,6,8,9,5] => [1,2,3,4,9,7,6,8,5] => {{1},{2},{3},{4},{5,9},{6,7},{8}}

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,10,7,8,9,6] => {{1},{2},{3},{4},{5},{6,10},{7},{8},{9}}

[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,3,6,5,7,8,9,4] => [1,2,3,9,6,5,7,8,4] => {{1},{2},{3},{4,9},{5,6},{7},{8}}

[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,10,6,7,8,9,5] => {{1},{2},{3},{4},{5,10},{6},{7},{8},{9}}

[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,9,3] => [1,2,9,5,4,6,7,8,3] => {{1},{2},{3,9},{4,5},{6},{7},{8}}

[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,10,5,6,7,8,9,4] => {{1},{2},{3},{4,10},{5},{6},{7},{8},{9}}

[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,2] => [1,9,4,3,5,6,7,8,2] => {{1},{2,9},{3,4},{5},{6},{7},{8}}

[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [1,2,10,4,5,6,7,8,9,3] => {{1},{2},{3,10},{4},{5},{6},{7},{8},{9}}

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [1,10,3,4,5,6,7,8,9,2] => {{1},{2,10},{3},{4},{5},{6},{7},{8},{9}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [10,2,3,4,5,6,7,8,9,1] => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,10,9,8] => [1,2,3,4,5,6,7,9,10,8] => {{1},{2},{3},{4},{5},{6},{7},{8,9,10}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,6,7,8,10,11,9] => [1,2,3,4,5,6,7,8,11,10,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,11},{10}}

[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,9,7,8,6] => [1,2,3,4,5,8,9,7,6] => {{1},{2},{3},{4},{5},{6,7,8,9}}

[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [1,2,3,4,5,7,8,9,6] => {{1},{2},{3},{4},{5},{6,7,8,9}}

[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,10,1] => [10,3,2,4,5,6,7,8,9,1] => {{1,10},{2,3},{4},{5},{6},{7},{8},{9}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [11,2,3,4,5,6,7,8,9,10,1] => {{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,10,9] => [1,2,3,4,5,6,7,8,10,11,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10,11}}

[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,4,9,6,7,8,5] => [1,2,3,4,8,9,6,7,5] => {{1},{2},{3},{4},{5,6,7,8,9}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => [1,2,3,4,5,6,8,9,10,7] => {{1},{2},{3},{4},{5},{6},{7,8,9,10}}

[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,3,9,5,6,7,8,4] => [1,2,3,8,9,5,6,7,4] => {{1},{2},{3},{4,5,6,7,8,9}}

[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => [1,2,3,4,6,7,8,9,5] => {{1},{2},{3},{4},{5,6,7,8,9}}

[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,9,4,5,6,7,8,3] => [1,2,8,9,4,5,6,7,3] => {{1},{2},{3,4,5,6,7,8,9}}

[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5,10,9,8,7,6] => [1,2,3,4,5,7,8,9,10,6] => {{1},{2},{3},{4},{5},{6,7,8,9,10}}

[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,9,3,4,5,6,7,8,2] => [1,8,9,3,4,5,6,7,2] => {{1},{2,3,4,5,6,7,8,9}}

[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [1,2,3,5,6,7,8,9,4] => {{1},{2},{3},{4,5,6,7,8,9}}

[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => [1,2,3,4,6,7,8,9,10,5] => {{1},{2},{3},{4},{5,6,7,8,9,10}}

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9,2,3,4,5,6,7,8,10,1] => [10,9,2,3,4,5,6,7,8,1] => {{1,10},{2,3,4,5,6,7,8,9}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,8,7,9] => {{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] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,7,6,8,9] => {{1},{2},{3},{4},{5},{6,7},{8},{9}}

[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,7,6,9,8] => [1,2,3,4,5,7,6,9,8] => {{1},{2},{3},{4},{5},{6,7},{8,9}}

[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,6,5,7,8,9] => {{1},{2},{3},{4},{5,6},{7},{8},{9}}

[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,4,6,5,8,7,9] => [1,2,3,4,6,5,8,7,9] => {{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] => [1,2,3,5,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => {{1},{2},{3},{4,5},{6},{7},{8},{9}}

[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6,9,8] => [1,2,3,5,4,7,6,9,8] => {{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] => [1,2,4,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => {{1},{2},{3,4},{5},{6},{7},{8},{9}}

[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,8,7,9] => [1,2,4,3,6,5,8,7,9] => {{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] => [1,3,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => {{1},{2,3},{4},{5},{6},{7},{8},{9}}

[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,7,9,8] => [1,3,2,4,5,6,7,9,8] => {{1},{2,3},{4},{5},{6},{7},{8,9}}

[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,6,9,8,7] => [1,3,2,4,5,6,8,9,7] => {{1},{2,3},{4},{5},{6},{7,8,9}}

[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8,9] => [1,3,2,5,4,6,7,8,9] => {{1},{2,3},{4,5},{6},{7},{8},{9}}

[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8] => [1,3,2,5,4,7,6,9,8] => {{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] => [1,4,3,2,5,6,7,8,9] => [1,3,4,2,5,6,7,8,9] => {{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] => [1,7,6,5,4,3,2,8,9] => [1,3,4,5,6,7,2,8,9] => {{1},{2,3,4,5,6,7},{8},{9}}

[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,7,6,5,4,3,2,9,8] => [1,3,4,5,6,7,2,9,8] => {{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] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => {{1,2},{3},{4},{5},{6},{7},{8},{9}}

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,9,8] => [2,1,3,4,5,6,7,9,8] => {{1,2},{3},{4},{5},{6},{7},{8,9}}

[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,6,8,7,9] => [2,1,3,4,5,6,8,7,9] => {{1,2},{3},{4},{5},{6},{7,8},{9}}

[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,6,9,8,7] => [2,1,3,4,5,6,8,9,7] => {{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] => [2,1,4,3,5,6,7,8,9] => [2,1,4,3,5,6,7,8,9] => {{1,2},{3,4},{5},{6},{7},{8},{9}}

[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9] => [2,1,4,3,6,5,7,8,9] => {{1,2},{3,4},{5,6},{7},{8},{9}}

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,8,7,9] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}}

[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,4,3,9,8,7,6,5] => [2,1,4,3,6,7,8,9,5] => {{1,2},{3,4},{5,6,7,8,9}}

[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,7,6,5,4,3,9] => [2,1,4,5,6,7,8,3,9] => {{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] => [3,2,1,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => {{1,2,3},{4},{5},{6},{7},{8},{9}}

[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,7,9,8] => [2,3,1,4,5,6,7,9,8] => {{1,2,3},{4},{5},{6},{7},{8,9}}

[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8,9] => [2,3,1,5,4,6,7,8,9] => {{1,2,3},{4,5},{6},{7},{8},{9}}

[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6,9,8] => [2,3,1,5,4,7,6,9,8] => {{1,2,3},{4,5},{6,7},{8,9}}

[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => [2,3,1,5,6,7,8,9,4] => {{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] => [4,3,2,1,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => {{1,2,3,4},{5},{6},{7},{8},{9}}

[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,3,2,1,6,5,7,8,9] => [2,3,4,1,6,5,7,8,9] => {{1,2,3,4},{5,6},{7},{8},{9}}

[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,8,7,9] => [2,3,4,1,6,5,8,7,9] => {{1,2,3,4},{5,6},{7,8},{9}}

[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => [2,3,4,1,6,7,8,9,5] => {{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] => [5,4,3,2,1,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => {{1,2,3,4,5},{6},{7},{8},{9}}

[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,4,3,2,1,7,6,8,9] => [2,3,4,5,1,7,6,8,9] => {{1,2,3,4,5},{6,7},{8},{9}}

[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4,3,2,1,9,8,7,6] => [2,3,4,5,1,7,8,9,6] => {{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] => [6,5,4,3,2,1,7,8,9] => [2,3,4,5,6,1,7,8,9] => {{1,2,3,4,5,6},{7},{8},{9}}

[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,5,4,3,2,1,8,7,9] => [2,3,4,5,6,1,8,7,9] => {{1,2,3,4,5,6},{7,8},{9}}

[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,5,4,3,2,1,9,8,7] => [2,3,4,5,6,1,8,9,7] => {{1,2,3,4,5,6},{7,8,9}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,9,8,10] => {{1},{2},{3},{4},{5},{6},{7},{8,9},{10}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => {{1},{2},{3},{4},{5},{6},{7,8},{9},{10}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,5,6,8,7,10,9] => [1,2,3,4,5,6,8,7,10,9] => {{1},{2},{3},{4},{5},{6},{7,8},{9,10}}

[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => {{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] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => {{1},{2},{3},{4},{5,6},{7},{8},{9},{10}}

[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7,10,9] => [1,2,3,4,6,5,8,7,10,9] => {{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] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => {{1},{2},{3},{4,5},{6},{7},{8},{9},{10}}

[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,9,8,10] => [1,2,3,5,4,7,6,9,8,10] => {{1},{2},{3},{4,5},{6,7},{8,9},{10}}

[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,10,9,8,7,6,5,4] => [1,2,3,5,6,7,8,9,10,4] => {{1},{2},{3},{4,5,6,7,8,9,10}}

[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => {{1},{2},{3,4},{5},{6},{7},{8},{9},{10}}

[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7,10,9] => [1,2,4,3,6,5,8,7,10,9] => {{1},{2},{3,4},{5,6},{7,8},{9,10}}

[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => {{1},{2,3},{4},{5},{6},{7},{8},{9},{10}}

[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,9,8,10] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}

[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,7,6,10,9,8] => [1,3,2,5,4,7,6,9,10,8] => {{1},{2,3},{4,5},{6,7},{8,9,10}}

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,7,8,10,9] => [2,1,3,4,5,6,7,8,10,9] => {{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] => [2,1,4,3,5,6,7,8,9,10] => [2,1,4,3,5,6,7,8,9,10] => {{1,2},{3,4},{5},{6},{7},{8},{9},{10}}

[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7,8,9,10] => [2,1,4,3,6,5,7,8,9,10] => {{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] => [2,1,4,3,6,5,8,7,9,10] => [2,1,4,3,6,5,8,7,9,10] => {{1,2},{3,4},{5,6},{7,8},{9},{10}}

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => {{1,2},{3,4},{5,6},{7,8},{9,10}}

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,6,5,10,9,8,7] => [2,1,4,3,6,5,8,9,10,7] => {{1,2},{3,4},{5,6},{7,8,9,10}}

[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3,10,9,8,7] => [2,1,4,5,6,3,8,9,10,7] => {{1,2},{3,4,5,6},{7,8,9,10}}

[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,1,8,7,6,5,4,3,10,9] => [2,1,4,5,6,7,8,3,10,9] => {{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] => [3,2,1,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => {{1,2,3},{4},{5},{6},{7},{8},{9},{10}}

[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,9,8,10] => [2,3,1,5,4,7,6,9,8,10] => {{1,2,3},{4,5},{6,7},{8,9},{10}}

[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,1,10,9,8,7,6,5,4] => [2,3,1,5,6,7,8,9,10,4] => {{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] => [4,3,2,1,5,6,7,8,9,10] => [2,3,4,1,5,6,7,8,9,10] => {{1,2,3,4},{5},{6},{7},{8},{9},{10}}

[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7,10,9] => [2,3,4,1,6,5,8,7,10,9] => {{1,2,3,4},{5,6},{7,8},{9,10}}

[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,6,5,10,9,8,7] => [2,3,4,1,6,5,8,9,10,7] => {{1,2,3,4},{5,6},{7,8,9,10}}

[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,8,7,6,5,10,9] => [2,3,4,1,6,7,8,5,10,9] => {{1,2,3,4},{5,6,7,8},{9,10}}

[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,3,2,1,10,9,8,7,6,5] => [2,3,4,1,6,7,8,9,10,5] => {{1,2,3,4},{5,6,7,8,9,10}}

[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8,9,10] => [2,3,4,5,1,6,7,8,9,10] => {{1,2,3,4,5},{6},{7},{8},{9},{10}}

[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,9,8,10] => [2,3,4,5,1,7,6,9,8,10] => {{1,2,3,4,5},{6,7},{8,9},{10}}

[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1,10,9,8,7,6] => [2,3,4,5,1,7,8,9,10,6] => {{1,2,3,4,5},{6,7,8,9,10}}

[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1,7,8,9,10] => [2,3,4,5,6,1,7,8,9,10] => {{1,2,3,4,5,6},{7},{8},{9},{10}}

[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,5,4,3,2,1,10,9,8,7] => [2,3,4,5,6,1,8,9,10,7] => {{1,2,3,4,5,6},{7,8,9,10}}

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9,10] => [2,3,4,5,6,7,1,8,9,10] => {{1,2,3,4,5,6,7},{8},{9},{10}}

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [7,6,5,4,3,2,1,9,8,10] => [2,3,4,5,6,7,1,9,8,10] => {{1,2,3,4,5,6,7},{8,9},{10}}

[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [7,6,5,4,3,2,1,10,9,8] => [2,3,4,5,6,7,1,9,10,8] => {{1,2,3,4,5,6,7},{8,9,10}}

[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1] => {{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] => [2,3,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9] => {{1,3},{2},{4},{5},{6},{7},{8},{9}}

[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [4,2,3,1,5,6,7,8,9] => {{1,4},{2},{3},{5},{6},{7},{8},{9}}

[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [5,2,3,4,1,6,7,8,9] => {{1,5},{2},{3},{4},{6},{7},{8},{9}}

[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [6,2,3,4,5,1,7,8,9] => {{1,6},{2},{3},{4},{5},{7},{8},{9}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [7,2,3,4,5,6,1,8,9] => {{1,7},{2},{3},{4},{5},{6},{8},{9}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,1,9] => [8,2,3,4,5,6,7,1,9] => {{1,8},{2},{3},{4},{5},{6},{7},{9}}

[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10] => {{1,3},{2},{4},{5},{6},{7},{8},{9},{10}}

[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9] => [3,2,4,1,5,6,7,8,9] => {{1,3,4},{2},{5},{6},{7},{8},{9}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,1,10] => [9,2,3,4,5,6,7,8,1,10] => {{1,9},{2},{3},{4},{5},{6},{7},{8},{10}}

[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [2,1,3,4,5,6,7,8,9,10,11] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [9,2,3,4,5,6,7,8,10,1] => {{1,9,10},{2},{3},{4},{5},{6},{7},{8}}

[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,6,8,9,7] => [1,3,2,4,5,6,9,8,7] => {{1},{2,3},{4},{5},{6},{7,9},{8}}

[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8,9] => [3,4,2,1,5,6,7,8,9] => {{1,2,3,4},{5},{6},{7},{8},{9}}

[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,9,10,1] => {{1,3,4,5,6,7,8,9,10},{2}}

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [10,3,4,5,6,7,8,9,2,1] => {{1,10},{2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [11,3,4,5,6,7,8,9,10,2,1] => {{1,11},{2,3,4,5,6,7,8,9,10}}

[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9] => {{1,4},{2,3},{5},{6},{7},{8},{9}}

[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10,3,9,8,7,6,5,4,2,1] => [2,4,5,6,7,8,9,10,1,3] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [10,2,9,8,7,6,5,4,3,1] => [3,4,5,6,7,8,9,10,2,1] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,9,8,7,6,5,4] => [3,2,1,5,6,7,8,9,4] => {{1,3},{2},{4,5,6,7,8,9}}

[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,8,2] => [1,8,3,4,5,6,7,9,2] => {{1},{2,8,9},{3},{4},{5},{6},{7}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [7,2,3,4,5,6,1,9,8] => {{1,7},{2},{3},{4},{5},{6},{8,9}}

[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,9,3] => [2,1,9,4,5,6,7,8,3] => {{1,2},{3,9},{4},{5},{6},{7},{8}}

[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,6,1,9,8,7] => [6,2,3,4,5,1,8,9,7] => {{1,6},{2},{3},{4},{5},{7,8,9}}

[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,2,6,5,4,3,1,9,8] => [3,4,5,6,7,1,2,9,8] => {{1,2,3,4,5,6,7},{8,9}}

[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,5,4,3,2,1,8,9,7] => [2,3,4,5,6,1,9,8,7] => {{1,2,3,4,5,6},{7,9},{8}}

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [10,8,7,6,5,4,3,9,2,1] => [2,9,4,5,6,7,8,10,3,1] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,8,7,9] => [3,2,4,1,6,5,8,7,9] => {{1,3,4},{2},{5,6},{7,8},{9}}

[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6,9,8] => [3,2,1,5,4,7,6,9,8] => {{1,3},{2},{4,5},{6,7},{8,9}}

[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7,10,9] => [3,2,4,1,6,5,8,7,10,9] => {{1,3,4},{2},{5,6},{7,8},{9,10}}

[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,9,8,10] => [3,2,1,5,4,7,6,9,8,10] => {{1,3},{2},{4,5},{6,7},{8,9},{10}}

[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,9,11,10,1] => [10,2,3,4,5,6,7,8,9,11,1] => {{1,10,11},{2},{3},{4},{5},{6},{7},{8},{9}}

[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [10,9,8,5,4,7,6,3,2,1] => [2,3,6,5,7,8,1,9,10,4] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [10,5,4,3,2,9,8,7,6,1] => [6,3,4,5,7,8,9,10,1,2] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,1] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,11,10,9,8,7,6,5,4,3,1] => [3,2,4,5,6,7,8,9,10,11,1] => {{1,3,4,5,6,7,8,9,10,11},{2}}

[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,8,7,6,5,3] => [1,2,5,4,6,7,8,9,3] => {{1},{2},{3,5,6,7,8,9},{4}}

[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,5,9,8,7,6,4] => [1,2,3,6,5,7,8,9,4] => {{1},{2},{3},{4,6,7,8,9},{5}}

[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,9,8,7,5] => [1,2,3,4,7,6,8,9,5] => {{1},{2},{3},{4},{5,7,8,9},{6}}

[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => [1,2,3,4,5,8,7,9,6] => {{1},{2},{3},{4},{5},{6,8,9},{7}}

[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,8,7,6,5,4,3,2,1,11,10] => [2,3,4,5,6,7,8,9,1,11,10] => {{1,2,3,4,5,6,7,8,9},{10,11}}

[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [10,7,6,5,4,3,2,9,8,1] => [8,3,4,5,6,7,9,10,1,2] => {{1,2,3,4,5,6,7,8,9,10}}

[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [1,4,3,2,5,6,7,8,9] => {{1},{2,4},{3},{5},{6},{7},{8},{9}}

[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => [1,2,3,4,5,6,7,8,10,9,11] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10},{11}}

[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,2,10,9,8,7,6,5,4,1] => [4,3,2,5,6,7,8,9,10,1] => {{1,4,5,6,7,8,9,10},{2,3}}

[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => [1,3,2,5,4,7,6,9,8,11,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10,11}}

[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [4,2,3,1,6,5,8,7,10,9] => [3,4,2,1,6,5,8,7,10,9] => {{1,2,3,4},{5,6},{7,8},{9,10}}

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10,2,3,4,5,6,7,8,9,11,1] => [11,10,2,3,4,5,6,7,8,9,1] => {{1,11},{2,3,4,5,6,7,8,9,10}}

[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,8,7,9] => [4,3,2,1,6,5,8,7,9] => {{1,4},{2,3},{5,6},{7,8},{9}}

[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7,10,9] => [4,3,2,1,6,5,8,7,10,9] => {{1,4},{2,3},{5,6},{7,8},{9,10}}

[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [10,3,2,9,8,7,6,5,4,1] => [4,3,5,6,7,8,9,10,1,2] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,2,1,10,7,6,9,8,5] => [2,3,4,1,8,7,9,10,5,6] => {{1,2,3,4},{5,6,7,8,9,10}}

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,6,5,9,8,10,7] => [2,1,4,3,6,5,10,9,8,7] => {{1,2},{3,4},{5,6},{7,10},{8,9}}

[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [1,3,2,5,4,7,6,10,9,8] => {{1},{2,3},{4,5},{6,7},{8,10},{9}}

[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8,9,10] => [3,2,4,1,5,6,7,8,9,10] => {{1,3,4},{2},{5},{6},{7},{8},{9},{10}}

[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10] => {{1,4},{2,3},{5},{6},{7},{8},{9},{10}}

[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,7,6,8,5,10,9] => [4,3,2,1,8,7,6,5,10,9] => {{1,4},{2,3},{5,8},{6,7},{9,10}}

[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3,9,8,10,7] => [2,1,6,5,4,3,10,9,8,7] => {{1,2},{3,6},{4,5},{7,10},{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] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}

[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [10,3,2,5,4,7,6,9,8,1] => [8,3,9,5,1,7,4,10,6,2] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,9,8,7,6,5,4,3,2,1,12,11] => [2,3,4,5,6,7,8,9,10,1,12,11] => {{1,2,3,4,5,6,7,8,9,10},{11,12}}

[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7,10,9] => [2,1,5,4,6,3,8,7,10,9] => {{1,2},{3,5,6},{4},{7,8},{9,10}}

[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,3,6,8,7,5,10,9] => [2,1,4,3,7,6,8,5,10,9] => {{1,2},{3,4},{5,7,8},{6},{9,10}}

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,10,9,7] => [2,1,4,3,6,5,9,8,10,7] => {{1,2},{3,4},{5,6},{7,9,10},{8}}

[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3,8,10,9,7] => [2,1,5,4,6,3,9,8,10,7] => {{1,2},{3,5,6},{4},{7,9,10},{8}}

[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,5,8,10,9,7] => [3,2,4,1,6,5,9,8,10,7] => {{1,3,4},{2},{5,6},{7,9,10},{8}}

[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,8,7,5,10,9] => [3,2,4,1,7,6,8,5,10,9] => {{1,3,4},{2},{5,7,8},{6},{9,10}}

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,7,10,12,11,9] => [2,1,4,3,6,5,8,7,11,10,12,9] => {{1,2},{3,4},{5,6},{7,8},{9,11,12},{10}}

[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,3,6,5,8,10,9,7,12,11] => [2,1,4,3,6,5,9,8,10,7,12,11] => {{1,2},{3,4},{5,6},{7,9,10},{8},{11,12}}

[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,8,7,5,10,9,12,11] => [2,1,4,3,7,6,8,5,10,9,12,11] => {{1,2},{3,4},{5,7,8},{6},{9,10},{11,12}}

[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5,10,12,11,9] => [2,1,4,3,7,6,8,5,11,10,12,9] => {{1,2},{3,4},{5,7,8},{6},{9,11,12},{10}}

[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7,10,9,12,11] => [2,1,5,4,6,3,8,7,10,9,12,11] => {{1,2},{3,5,6},{4},{7,8},{9,10},{11,12}}

[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3,8,7,10,12,11,9] => [2,1,5,4,6,3,8,7,11,10,12,9] => {{1,2},{3,5,6},{4},{7,8},{9,11,12},{10}}

[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,10,9,7,12,11] => [2,1,5,4,6,3,9,8,10,7,12,11] => {{1,2},{3,5,6},{4},{7,9,10},{8},{11,12}}

[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7,10,9,12,11] => [3,2,4,1,6,5,8,7,10,9,12,11] => {{1,3,4},{2},{5,6},{7,8},{9,10},{11,12}}

[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,5,8,7,10,12,11,9] => [3,2,4,1,6,5,8,7,11,10,12,9] => {{1,3,4},{2},{5,6},{7,8},{9,11,12},{10}}

[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5,8,10,9,7,12,11] => [3,2,4,1,6,5,9,8,10,7,12,11] => {{1,3,4},{2},{5,6},{7,9,10},{8},{11,12}}

[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,8,7,5,10,9,12,11] => [3,2,4,1,7,6,8,5,10,9,12,11] => {{1,3,4},{2},{5,7,8},{6},{9,10},{11,12}}

[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5,10,12,11,9] => [3,2,4,1,7,6,8,5,11,10,12,9] => {{1,3,4},{2},{5,7,8},{6},{9,11,12},{10}}

[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,6,5,10,8,9,7] => [3,4,2,1,6,5,9,10,8,7] => {{1,2,3,4},{5,6},{7,8,9,10}}

[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [10,9,6,5,4,3,8,7,2,1] => [2,7,4,5,6,8,9,1,10,3] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7,10,9] => [4,3,5,6,1,2,8,7,10,9] => {{1,2,3,4,5,6},{7,8},{9,10}}

Map

to non-crossing permutation

Description

Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..

Map

descent views to invisible inversion bottoms

Description

Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that

the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.

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].