Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00069: Permutations —complement⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Images
[1,0] => [1] => [1] => {{1}}
[1,0,1,0] => [2,1] => [1,2] => {{1},{2}}
[1,1,0,0] => [1,2] => [2,1] => {{1,2}}
[1,0,1,0,1,0] => [3,2,1] => [1,2,3] => {{1},{2},{3}}
[1,0,1,1,0,0] => [2,3,1] => [2,1,3] => {{1,2},{3}}
[1,1,0,0,1,0] => [3,1,2] => [1,3,2] => {{1},{2,3}}
[1,1,0,1,0,0] => [2,1,3] => [2,3,1] => {{1,2,3}}
[1,1,1,0,0,0] => [1,2,3] => [3,2,1] => {{1,3},{2}}
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [1,2,3,4] => {{1},{2},{3},{4}}
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [2,1,3,4] => {{1,2},{3},{4}}
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [1,3,2,4] => {{1},{2,3},{4}}
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [2,3,1,4] => {{1,2,3},{4}}
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [3,2,1,4] => {{1,3},{2},{4}}
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [1,2,4,3] => {{1},{2},{3,4}}
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [2,1,4,3] => {{1,2},{3,4}}
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [1,3,4,2] => {{1},{2,3,4}}
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [2,3,4,1] => {{1,2,3,4}}
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [3,2,4,1] => {{1,3,4},{2}}
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [1,4,3,2] => {{1},{2,4},{3}}
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [2,4,3,1] => {{1,2,4},{3}}
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [3,4,2,1] => {{1,2,3,4}}
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [4,3,2,1] => {{1,4},{2,3}}
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [1,2,3,4,5] => {{1},{2},{3},{4},{5}}
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [2,1,3,4,5] => {{1,2},{3},{4},{5}}
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [1,3,2,4,5] => {{1},{2,3},{4},{5}}
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [2,3,1,4,5] => {{1,2,3},{4},{5}}
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [3,2,1,4,5] => {{1,3},{2},{4},{5}}
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [1,2,4,3,5] => {{1},{2},{3,4},{5}}
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [2,1,4,3,5] => {{1,2},{3,4},{5}}
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [1,3,4,2,5] => {{1},{2,3,4},{5}}
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [2,3,4,1,5] => {{1,2,3,4},{5}}
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [3,2,4,1,5] => {{1,3,4},{2},{5}}
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [1,4,3,2,5] => {{1},{2,4},{3},{5}}
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [2,4,3,1,5] => {{1,2,4},{3},{5}}
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [3,4,2,1,5] => {{1,2,3,4},{5}}
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [4,3,2,1,5] => {{1,4},{2,3},{5}}
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [1,2,3,5,4] => {{1},{2},{3},{4,5}}
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [2,1,3,5,4] => {{1,2},{3},{4,5}}
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [1,3,2,5,4] => {{1},{2,3},{4,5}}
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [2,3,1,5,4] => {{1,2,3},{4,5}}
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [3,2,1,5,4] => {{1,3},{2},{4,5}}
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [1,2,4,5,3] => {{1},{2},{3,4,5}}
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [2,1,4,5,3] => {{1,2},{3,4,5}}
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [1,3,4,5,2] => {{1},{2,3,4,5}}
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [2,3,4,5,1] => {{1,2,3,4,5}}
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [3,2,4,5,1] => {{1,3,4,5},{2}}
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [1,4,3,5,2] => {{1},{2,4,5},{3}}
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [2,4,3,5,1] => {{1,2,4,5},{3}}
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [3,4,2,5,1] => {{1,2,3,4,5}}
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [4,3,2,5,1] => {{1,4,5},{2,3}}
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [1,2,5,4,3] => {{1},{2},{3,5},{4}}
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [2,1,5,4,3] => {{1,2},{3,5},{4}}
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [1,3,5,4,2] => {{1},{2,3,5},{4}}
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [2,3,5,4,1] => {{1,2,3,5},{4}}
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [3,2,5,4,1] => {{1,3,5},{2},{4}}
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [1,4,5,3,2] => {{1},{2,3,4,5}}
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [2,4,5,3,1] => {{1,2,3,4,5}}
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [3,4,5,2,1] => {{1,3,5},{2,4}}
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [4,3,5,2,1] => {{1,2,3,4,5}}
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [1,5,4,3,2] => {{1},{2,5},{3,4}}
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [2,5,4,3,1] => {{1,2,5},{3,4}}
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [3,5,4,2,1] => {{1,2,3,4,5}}
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [4,5,3,2,1] => {{1,2,4,5},{3}}
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [5,4,3,2,1] => {{1,5},{2,4},{3}}
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => {{1},{2},{3},{4},{5},{6}}
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [2,1,3,4,5,6] => {{1,2},{3},{4},{5},{6}}
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [1,3,2,4,5,6] => {{1},{2,3},{4},{5},{6}}
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [2,3,1,4,5,6] => {{1,2,3},{4},{5},{6}}
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [3,2,1,4,5,6] => {{1,3},{2},{4},{5},{6}}
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [1,2,4,3,5,6] => {{1},{2},{3,4},{5},{6}}
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [2,1,4,3,5,6] => {{1,2},{3,4},{5},{6}}
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [1,3,4,2,5,6] => {{1},{2,3,4},{5},{6}}
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [2,3,4,1,5,6] => {{1,2,3,4},{5},{6}}
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [3,2,4,1,5,6] => {{1,3,4},{2},{5},{6}}
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [1,4,3,2,5,6] => {{1},{2,4},{3},{5},{6}}
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [2,4,3,1,5,6] => {{1,2,4},{3},{5},{6}}
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [3,4,2,1,5,6] => {{1,2,3,4},{5},{6}}
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [4,3,2,1,5,6] => {{1,4},{2,3},{5},{6}}
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [1,2,3,5,4,6] => {{1},{2},{3},{4,5},{6}}
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [2,1,3,5,4,6] => {{1,2},{3},{4,5},{6}}
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [1,3,2,5,4,6] => {{1},{2,3},{4,5},{6}}
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [2,3,1,5,4,6] => {{1,2,3},{4,5},{6}}
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [3,2,1,5,4,6] => {{1,3},{2},{4,5},{6}}
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [1,2,4,5,3,6] => {{1},{2},{3,4,5},{6}}
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [2,1,4,5,3,6] => {{1,2},{3,4,5},{6}}
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [1,3,4,5,2,6] => {{1},{2,3,4,5},{6}}
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [2,3,4,5,1,6] => {{1,2,3,4,5},{6}}
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [3,2,4,5,1,6] => {{1,3,4,5},{2},{6}}
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [1,4,3,5,2,6] => {{1},{2,4,5},{3},{6}}
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [2,4,3,5,1,6] => {{1,2,4,5},{3},{6}}
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [3,4,2,5,1,6] => {{1,2,3,4,5},{6}}
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [4,3,2,5,1,6] => {{1,4,5},{2,3},{6}}
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [1,2,5,4,3,6] => {{1},{2},{3,5},{4},{6}}
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [2,1,5,4,3,6] => {{1,2},{3,5},{4},{6}}
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [1,3,5,4,2,6] => {{1},{2,3,5},{4},{6}}
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [2,3,5,4,1,6] => {{1,2,3,5},{4},{6}}
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [3,2,5,4,1,6] => {{1,3,5},{2},{4},{6}}
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [1,4,5,3,2,6] => {{1},{2,3,4,5},{6}}
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [2,4,5,3,1,6] => {{1,2,3,4,5},{6}}
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [3,4,5,2,1,6] => {{1,3,5},{2,4},{6}}
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [4,3,5,2,1,6] => {{1,2,3,4,5},{6}}
>>> Load all 2095 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => {{1},{2,5},{3,4},{6}}
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [2,5,4,3,1,6] => {{1,2,5},{3,4},{6}}
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [3,5,4,2,1,6] => {{1,2,3,4,5},{6}}
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [4,5,3,2,1,6] => {{1,2,4,5},{3},{6}}
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [5,4,3,2,1,6] => {{1,5},{2,4},{3},{6}}
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [1,2,3,4,6,5] => {{1},{2},{3},{4},{5,6}}
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [2,1,3,4,6,5] => {{1,2},{3},{4},{5,6}}
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [1,3,2,4,6,5] => {{1},{2,3},{4},{5,6}}
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [2,3,1,4,6,5] => {{1,2,3},{4},{5,6}}
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [3,2,1,4,6,5] => {{1,3},{2},{4},{5,6}}
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [1,2,4,3,6,5] => {{1},{2},{3,4},{5,6}}
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}}
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [1,3,4,2,6,5] => {{1},{2,3,4},{5,6}}
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [2,3,4,1,6,5] => {{1,2,3,4},{5,6}}
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [3,2,4,1,6,5] => {{1,3,4},{2},{5,6}}
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [1,4,3,2,6,5] => {{1},{2,4},{3},{5,6}}
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [2,4,3,1,6,5] => {{1,2,4},{3},{5,6}}
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [3,4,2,1,6,5] => {{1,2,3,4},{5,6}}
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [4,3,2,1,6,5] => {{1,4},{2,3},{5,6}}
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [1,2,3,5,6,4] => {{1},{2},{3},{4,5,6}}
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [2,1,3,5,6,4] => {{1,2},{3},{4,5,6}}
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [1,3,2,5,6,4] => {{1},{2,3},{4,5,6}}
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [2,3,1,5,6,4] => {{1,2,3},{4,5,6}}
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [3,2,1,5,6,4] => {{1,3},{2},{4,5,6}}
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [1,2,4,5,6,3] => {{1},{2},{3,4,5,6}}
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [2,1,4,5,6,3] => {{1,2},{3,4,5,6}}
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [1,3,4,5,6,2] => {{1},{2,3,4,5,6}}
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [2,3,4,5,6,1] => {{1,2,3,4,5,6}}
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [3,2,4,5,6,1] => {{1,3,4,5,6},{2}}
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [1,4,3,5,6,2] => {{1},{2,4,5,6},{3}}
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [2,4,3,5,6,1] => {{1,2,4,5,6},{3}}
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [3,4,2,5,6,1] => {{1,2,3,4,5,6}}
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [4,3,2,5,6,1] => {{1,4,5,6},{2,3}}
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [1,2,5,4,6,3] => {{1},{2},{3,5,6},{4}}
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [2,1,5,4,6,3] => {{1,2},{3,5,6},{4}}
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [1,3,5,4,6,2] => {{1},{2,3,5,6},{4}}
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [2,3,5,4,6,1] => {{1,2,3,5,6},{4}}
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [3,2,5,4,6,1] => {{1,3,5,6},{2},{4}}
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [1,4,5,3,6,2] => {{1},{2,3,4,5,6}}
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [2,4,5,3,6,1] => {{1,2,3,4,5,6}}
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [3,4,5,2,6,1] => {{1,3,5,6},{2,4}}
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [4,3,5,2,6,1] => {{1,2,3,4,5,6}}
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [1,5,4,3,6,2] => {{1},{2,5,6},{3,4}}
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [2,5,4,3,6,1] => {{1,2,5,6},{3,4}}
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [3,5,4,2,6,1] => {{1,2,3,4,5,6}}
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [4,5,3,2,6,1] => {{1,2,4,5,6},{3}}
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [5,4,3,2,6,1] => {{1,5,6},{2,4},{3}}
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [1,2,3,6,5,4] => {{1},{2},{3},{4,6},{5}}
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [2,1,3,6,5,4] => {{1,2},{3},{4,6},{5}}
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [1,3,2,6,5,4] => {{1},{2,3},{4,6},{5}}
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [2,3,1,6,5,4] => {{1,2,3},{4,6},{5}}
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => {{1,3},{2},{4,6},{5}}
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [1,2,4,6,5,3] => {{1},{2},{3,4,6},{5}}
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [2,1,4,6,5,3] => {{1,2},{3,4,6},{5}}
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [1,3,4,6,5,2] => {{1},{2,3,4,6},{5}}
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [2,3,4,6,5,1] => {{1,2,3,4,6},{5}}
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [3,2,4,6,5,1] => {{1,3,4,6},{2},{5}}
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [1,4,3,6,5,2] => {{1},{2,4,6},{3},{5}}
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [2,4,3,6,5,1] => {{1,2,4,6},{3},{5}}
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [3,4,2,6,5,1] => {{1,2,3,4,6},{5}}
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [4,3,2,6,5,1] => {{1,4,6},{2,3},{5}}
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [1,2,5,6,4,3] => {{1},{2},{3,4,5,6}}
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [2,1,5,6,4,3] => {{1,2},{3,4,5,6}}
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [1,3,5,6,4,2] => {{1},{2,3,4,5,6}}
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [2,3,5,6,4,1] => {{1,2,3,4,5,6}}
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [3,2,5,6,4,1] => {{1,3,4,5,6},{2}}
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [1,4,5,6,3,2] => {{1},{2,4,6},{3,5}}
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [2,4,5,6,3,1] => {{1,2,4,6},{3,5}}
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [3,4,5,6,2,1] => {{1,2,3,4,5,6}}
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [4,3,5,6,2,1] => {{1,4,6},{2,3,5}}
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [1,5,4,6,3,2] => {{1},{2,3,4,5,6}}
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [2,5,4,6,3,1] => {{1,2,3,4,5,6}}
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [3,5,4,6,2,1] => {{1,3,4,6},{2,5}}
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [4,5,3,6,2,1] => {{1,4,6},{2,5},{3}}
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [5,4,3,6,2,1] => {{1,2,4,5,6},{3}}
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [1,2,6,5,4,3] => {{1},{2},{3,6},{4,5}}
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [2,1,6,5,4,3] => {{1,2},{3,6},{4,5}}
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [1,3,6,5,4,2] => {{1},{2,3,6},{4,5}}
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [2,3,6,5,4,1] => {{1,2,3,6},{4,5}}
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [3,2,6,5,4,1] => {{1,3,6},{2},{4,5}}
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [1,4,6,5,3,2] => {{1},{2,3,4,5,6}}
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [2,4,6,5,3,1] => {{1,2,3,4,5,6}}
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [3,4,6,5,2,1] => {{1,3,6},{2,4,5}}
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,3,6,5,2,1] => {{1,2,3,4,5,6}}
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [1,5,6,4,3,2] => {{1},{2,3,5,6},{4}}
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [2,5,6,4,3,1] => {{1,2,3,5,6},{4}}
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [3,5,6,4,2,1] => {{1,3,6},{2,5},{4}}
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [4,5,6,3,2,1] => {{1,3,4,6},{2,5}}
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [5,4,6,3,2,1] => {{1,2,3,4,5,6}}
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [1,6,5,4,3,2] => {{1},{2,6},{3,5},{4}}
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [2,6,5,4,3,1] => {{1,2,6},{3,5},{4}}
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [3,6,5,4,2,1] => {{1,2,3,5,6},{4}}
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [4,6,5,3,2,1] => {{1,2,3,4,5,6}}
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [5,6,4,3,2,1] => {{1,2,5,6},{3,4}}
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => {{1,6},{2,5},{3,4}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => {{1},{2},{3},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [2,1,3,4,5,6,7] => {{1,2},{3},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [1,3,2,4,5,6,7] => {{1},{2,3},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [2,3,1,4,5,6,7] => {{1,2,3},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [3,2,1,4,5,6,7] => {{1,3},{2},{4},{5},{6},{7}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [1,2,4,3,5,6,7] => {{1},{2},{3,4},{5},{6},{7}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [2,1,4,3,5,6,7] => {{1,2},{3,4},{5},{6},{7}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [1,3,4,2,5,6,7] => {{1},{2,3,4},{5},{6},{7}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [2,3,4,1,5,6,7] => {{1,2,3,4},{5},{6},{7}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [3,2,4,1,5,6,7] => {{1,3,4},{2},{5},{6},{7}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [1,4,3,2,5,6,7] => {{1},{2,4},{3},{5},{6},{7}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [2,4,3,1,5,6,7] => {{1,2,4},{3},{5},{6},{7}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [3,4,2,1,5,6,7] => {{1,2,3,4},{5},{6},{7}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [4,3,2,1,5,6,7] => {{1,4},{2,3},{5},{6},{7}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [1,2,3,5,4,6,7] => {{1},{2},{3},{4,5},{6},{7}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [2,1,3,5,4,6,7] => {{1,2},{3},{4,5},{6},{7}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [1,3,2,5,4,6,7] => {{1},{2,3},{4,5},{6},{7}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [2,3,1,5,4,6,7] => {{1,2,3},{4,5},{6},{7}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [3,2,1,5,4,6,7] => {{1,3},{2},{4,5},{6},{7}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [1,2,4,5,3,6,7] => {{1},{2},{3,4,5},{6},{7}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [2,1,4,5,3,6,7] => {{1,2},{3,4,5},{6},{7}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [1,3,4,5,2,6,7] => {{1},{2,3,4,5},{6},{7}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [2,3,4,5,1,6,7] => {{1,2,3,4,5},{6},{7}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [3,2,4,5,1,6,7] => {{1,3,4,5},{2},{6},{7}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [1,4,3,5,2,6,7] => {{1},{2,4,5},{3},{6},{7}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [2,4,3,5,1,6,7] => {{1,2,4,5},{3},{6},{7}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [3,4,2,5,1,6,7] => {{1,2,3,4,5},{6},{7}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [4,3,2,5,1,6,7] => {{1,4,5},{2,3},{6},{7}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [1,2,5,4,3,6,7] => {{1},{2},{3,5},{4},{6},{7}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [2,1,5,4,3,6,7] => {{1,2},{3,5},{4},{6},{7}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [1,3,5,4,2,6,7] => {{1},{2,3,5},{4},{6},{7}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [2,3,5,4,1,6,7] => {{1,2,3,5},{4},{6},{7}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [3,2,5,4,1,6,7] => {{1,3,5},{2},{4},{6},{7}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [1,4,5,3,2,6,7] => {{1},{2,3,4,5},{6},{7}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [2,4,5,3,1,6,7] => {{1,2,3,4,5},{6},{7}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [3,4,5,2,1,6,7] => {{1,3,5},{2,4},{6},{7}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [4,3,5,2,1,6,7] => {{1,2,3,4,5},{6},{7}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [1,5,4,3,2,6,7] => {{1},{2,5},{3,4},{6},{7}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [2,5,4,3,1,6,7] => {{1,2,5},{3,4},{6},{7}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [3,5,4,2,1,6,7] => {{1,2,3,4,5},{6},{7}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [4,5,3,2,1,6,7] => {{1,2,4,5},{3},{6},{7}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [5,4,3,2,1,6,7] => {{1,5},{2,4},{3},{6},{7}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [1,2,3,4,6,5,7] => {{1},{2},{3},{4},{5,6},{7}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [2,1,3,4,6,5,7] => {{1,2},{3},{4},{5,6},{7}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [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] => [6,5,7,4,2,3,1] => [2,3,1,4,6,5,7] => {{1,2,3},{4},{5,6},{7}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [3,2,1,4,6,5,7] => {{1,3},{2},{4},{5,6},{7}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [1,2,4,3,6,5,7] => {{1},{2},{3,4},{5,6},{7}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [2,1,4,3,6,5,7] => {{1,2},{3,4},{5,6},{7}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [1,3,4,2,6,5,7] => {{1},{2,3,4},{5,6},{7}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [2,3,4,1,6,5,7] => {{1,2,3,4},{5,6},{7}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [3,2,4,1,6,5,7] => {{1,3,4},{2},{5,6},{7}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [1,4,3,2,6,5,7] => {{1},{2,4},{3},{5,6},{7}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [2,4,3,1,6,5,7] => {{1,2,4},{3},{5,6},{7}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [3,4,2,1,6,5,7] => {{1,2,3,4},{5,6},{7}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [4,3,2,1,6,5,7] => {{1,4},{2,3},{5,6},{7}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [1,2,3,5,6,4,7] => {{1},{2},{3},{4,5,6},{7}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [2,1,3,5,6,4,7] => {{1,2},{3},{4,5,6},{7}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [1,3,2,5,6,4,7] => {{1},{2,3},{4,5,6},{7}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [2,3,1,5,6,4,7] => {{1,2,3},{4,5,6},{7}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [3,2,1,5,6,4,7] => {{1,3},{2},{4,5,6},{7}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [1,2,4,5,6,3,7] => {{1},{2},{3,4,5,6},{7}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [2,1,4,5,6,3,7] => {{1,2},{3,4,5,6},{7}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [1,3,4,5,6,2,7] => {{1},{2,3,4,5,6},{7}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [2,3,4,5,6,1,7] => {{1,2,3,4,5,6},{7}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [3,2,4,5,6,1,7] => {{1,3,4,5,6},{2},{7}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [1,4,3,5,6,2,7] => {{1},{2,4,5,6},{3},{7}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [2,4,3,5,6,1,7] => {{1,2,4,5,6},{3},{7}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [3,4,2,5,6,1,7] => {{1,2,3,4,5,6},{7}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [4,3,2,5,6,1,7] => {{1,4,5,6},{2,3},{7}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [1,2,5,4,6,3,7] => {{1},{2},{3,5,6},{4},{7}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [2,1,5,4,6,3,7] => {{1,2},{3,5,6},{4},{7}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [1,3,5,4,6,2,7] => {{1},{2,3,5,6},{4},{7}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [2,3,5,4,6,1,7] => {{1,2,3,5,6},{4},{7}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [3,2,5,4,6,1,7] => {{1,3,5,6},{2},{4},{7}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [1,4,5,3,6,2,7] => {{1},{2,3,4,5,6},{7}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [2,4,5,3,6,1,7] => {{1,2,3,4,5,6},{7}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [3,4,5,2,6,1,7] => {{1,3,5,6},{2,4},{7}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [4,3,5,2,6,1,7] => {{1,2,3,4,5,6},{7}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [1,5,4,3,6,2,7] => {{1},{2,5,6},{3,4},{7}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [2,5,4,3,6,1,7] => {{1,2,5,6},{3,4},{7}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [3,5,4,2,6,1,7] => {{1,2,3,4,5,6},{7}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [4,5,3,2,6,1,7] => {{1,2,4,5,6},{3},{7}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [5,4,3,2,6,1,7] => {{1,5,6},{2,4},{3},{7}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [1,2,3,6,5,4,7] => {{1},{2},{3},{4,6},{5},{7}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [2,1,3,6,5,4,7] => {{1,2},{3},{4,6},{5},{7}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [1,3,2,6,5,4,7] => {{1},{2,3},{4,6},{5},{7}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [2,3,1,6,5,4,7] => {{1,2,3},{4,6},{5},{7}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [3,2,1,6,5,4,7] => {{1,3},{2},{4,6},{5},{7}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [1,2,4,6,5,3,7] => {{1},{2},{3,4,6},{5},{7}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [2,1,4,6,5,3,7] => {{1,2},{3,4,6},{5},{7}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [1,3,4,6,5,2,7] => {{1},{2,3,4,6},{5},{7}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [2,3,4,6,5,1,7] => {{1,2,3,4,6},{5},{7}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [3,2,4,6,5,1,7] => {{1,3,4,6},{2},{5},{7}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [1,4,3,6,5,2,7] => {{1},{2,4,6},{3},{5},{7}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [2,4,3,6,5,1,7] => {{1,2,4,6},{3},{5},{7}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [3,4,2,6,5,1,7] => {{1,2,3,4,6},{5},{7}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [4,3,2,6,5,1,7] => {{1,4,6},{2,3},{5},{7}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [1,2,5,6,4,3,7] => {{1},{2},{3,4,5,6},{7}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [2,1,5,6,4,3,7] => {{1,2},{3,4,5,6},{7}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [1,3,5,6,4,2,7] => {{1},{2,3,4,5,6},{7}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [2,3,5,6,4,1,7] => {{1,2,3,4,5,6},{7}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [3,2,5,6,4,1,7] => {{1,3,4,5,6},{2},{7}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [1,4,5,6,3,2,7] => {{1},{2,4,6},{3,5},{7}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [2,4,5,6,3,1,7] => {{1,2,4,6},{3,5},{7}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [3,4,5,6,2,1,7] => {{1,2,3,4,5,6},{7}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [4,3,5,6,2,1,7] => {{1,4,6},{2,3,5},{7}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [1,5,4,6,3,2,7] => {{1},{2,3,4,5,6},{7}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [2,5,4,6,3,1,7] => {{1,2,3,4,5,6},{7}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [3,5,4,6,2,1,7] => {{1,3,4,6},{2,5},{7}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [4,5,3,6,2,1,7] => {{1,4,6},{2,5},{3},{7}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [5,4,3,6,2,1,7] => {{1,2,4,5,6},{3},{7}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [1,2,6,5,4,3,7] => {{1},{2},{3,6},{4,5},{7}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [2,1,6,5,4,3,7] => {{1,2},{3,6},{4,5},{7}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [1,3,6,5,4,2,7] => {{1},{2,3,6},{4,5},{7}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [2,3,6,5,4,1,7] => {{1,2,3,6},{4,5},{7}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [3,2,6,5,4,1,7] => {{1,3,6},{2},{4,5},{7}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [1,4,6,5,3,2,7] => {{1},{2,3,4,5,6},{7}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [2,4,6,5,3,1,7] => {{1,2,3,4,5,6},{7}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [3,4,6,5,2,1,7] => {{1,3,6},{2,4,5},{7}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [4,3,6,5,2,1,7] => {{1,2,3,4,5,6},{7}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [1,5,6,4,3,2,7] => {{1},{2,3,5,6},{4},{7}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [2,5,6,4,3,1,7] => {{1,2,3,5,6},{4},{7}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [3,5,6,4,2,1,7] => {{1,3,6},{2,5},{4},{7}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [4,5,6,3,2,1,7] => {{1,3,4,6},{2,5},{7}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [5,4,6,3,2,1,7] => {{1,2,3,4,5,6},{7}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [1,6,5,4,3,2,7] => {{1},{2,6},{3,5},{4},{7}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [2,6,5,4,3,1,7] => {{1,2,6},{3,5},{4},{7}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [3,6,5,4,2,1,7] => {{1,2,3,5,6},{4},{7}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [4,6,5,3,2,1,7] => {{1,2,3,4,5,6},{7}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [5,6,4,3,2,1,7] => {{1,2,5,6},{3,4},{7}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [6,5,4,3,2,1,7] => {{1,6},{2,5},{3,4},{7}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [1,2,3,4,5,7,6] => {{1},{2},{3},{4},{5},{6,7}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [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] => [7,5,6,4,3,1,2] => [1,3,2,4,5,7,6] => {{1},{2,3},{4},{5},{6,7}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [2,3,1,4,5,7,6] => {{1,2,3},{4},{5},{6,7}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [3,2,1,4,5,7,6] => {{1,3},{2},{4},{5},{6,7}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [1,2,4,3,5,7,6] => {{1},{2},{3,4},{5},{6,7}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [2,1,4,3,5,7,6] => {{1,2},{3,4},{5},{6,7}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [1,3,4,2,5,7,6] => {{1},{2,3,4},{5},{6,7}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [2,3,4,1,5,7,6] => {{1,2,3,4},{5},{6,7}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [3,2,4,1,5,7,6] => {{1,3,4},{2},{5},{6,7}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [1,4,3,2,5,7,6] => {{1},{2,4},{3},{5},{6,7}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [2,4,3,1,5,7,6] => {{1,2,4},{3},{5},{6,7}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [3,4,2,1,5,7,6] => {{1,2,3,4},{5},{6,7}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [4,3,2,1,5,7,6] => {{1,4},{2,3},{5},{6,7}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [1,2,3,5,4,7,6] => {{1},{2},{3},{4,5},{6,7}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [2,1,3,5,4,7,6] => {{1,2},{3},{4,5},{6,7}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [1,3,2,5,4,7,6] => {{1},{2,3},{4,5},{6,7}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [2,3,1,5,4,7,6] => {{1,2,3},{4,5},{6,7}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [3,2,1,5,4,7,6] => {{1,3},{2},{4,5},{6,7}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [1,2,4,5,3,7,6] => {{1},{2},{3,4,5},{6,7}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [2,1,4,5,3,7,6] => {{1,2},{3,4,5},{6,7}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [1,3,4,5,2,7,6] => {{1},{2,3,4,5},{6,7}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [2,3,4,5,1,7,6] => {{1,2,3,4,5},{6,7}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [3,2,4,5,1,7,6] => {{1,3,4,5},{2},{6,7}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [1,4,3,5,2,7,6] => {{1},{2,4,5},{3},{6,7}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [2,4,3,5,1,7,6] => {{1,2,4,5},{3},{6,7}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [3,4,2,5,1,7,6] => {{1,2,3,4,5},{6,7}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [4,3,2,5,1,7,6] => {{1,4,5},{2,3},{6,7}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [1,2,5,4,3,7,6] => {{1},{2},{3,5},{4},{6,7}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [2,1,5,4,3,7,6] => {{1,2},{3,5},{4},{6,7}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [1,3,5,4,2,7,6] => {{1},{2,3,5},{4},{6,7}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [2,3,5,4,1,7,6] => {{1,2,3,5},{4},{6,7}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [3,2,5,4,1,7,6] => {{1,3,5},{2},{4},{6,7}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [1,4,5,3,2,7,6] => {{1},{2,3,4,5},{6,7}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [2,4,5,3,1,7,6] => {{1,2,3,4,5},{6,7}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [3,4,5,2,1,7,6] => {{1,3,5},{2,4},{6,7}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [4,3,5,2,1,7,6] => {{1,2,3,4,5},{6,7}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [1,5,4,3,2,7,6] => {{1},{2,5},{3,4},{6,7}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [2,5,4,3,1,7,6] => {{1,2,5},{3,4},{6,7}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [3,5,4,2,1,7,6] => {{1,2,3,4,5},{6,7}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [4,5,3,2,1,7,6] => {{1,2,4,5},{3},{6,7}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [5,4,3,2,1,7,6] => {{1,5},{2,4},{3},{6,7}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [1,2,3,4,6,7,5] => {{1},{2},{3},{4},{5,6,7}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [2,1,3,4,6,7,5] => {{1,2},{3},{4},{5,6,7}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [1,3,2,4,6,7,5] => {{1},{2,3},{4},{5,6,7}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [2,3,1,4,6,7,5] => {{1,2,3},{4},{5,6,7}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [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] => [7,6,4,5,2,1,3] => [1,2,4,3,6,7,5] => {{1},{2},{3,4},{5,6,7}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [2,1,4,3,6,7,5] => {{1,2},{3,4},{5,6,7}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [1,3,4,2,6,7,5] => {{1},{2,3,4},{5,6,7}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [2,3,4,1,6,7,5] => {{1,2,3,4},{5,6,7}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [3,2,4,1,6,7,5] => {{1,3,4},{2},{5,6,7}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [1,4,3,2,6,7,5] => {{1},{2,4},{3},{5,6,7}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [2,4,3,1,6,7,5] => {{1,2,4},{3},{5,6,7}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [3,4,2,1,6,7,5] => {{1,2,3,4},{5,6,7}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [4,3,2,1,6,7,5] => {{1,4},{2,3},{5,6,7}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [1,2,3,5,6,7,4] => {{1},{2},{3},{4,5,6,7}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [2,1,3,5,6,7,4] => {{1,2},{3},{4,5,6,7}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [1,3,2,5,6,7,4] => {{1},{2,3},{4,5,6,7}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [2,3,1,5,6,7,4] => {{1,2,3},{4,5,6,7}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [3,2,1,5,6,7,4] => {{1,3},{2},{4,5,6,7}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [1,2,4,5,6,7,3] => {{1},{2},{3,4,5,6,7}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [2,1,4,5,6,7,3] => {{1,2},{3,4,5,6,7}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [1,3,4,5,6,7,2] => {{1},{2,3,4,5,6,7}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [2,3,4,5,6,7,1] => {{1,2,3,4,5,6,7}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [3,2,4,5,6,7,1] => {{1,3,4,5,6,7},{2}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [1,4,3,5,6,7,2] => {{1},{2,4,5,6,7},{3}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [2,4,3,5,6,7,1] => {{1,2,4,5,6,7},{3}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [3,4,2,5,6,7,1] => {{1,2,3,4,5,6,7}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [4,3,2,5,6,7,1] => {{1,4,5,6,7},{2,3}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [1,2,5,4,6,7,3] => {{1},{2},{3,5,6,7},{4}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [2,1,5,4,6,7,3] => {{1,2},{3,5,6,7},{4}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [1,3,5,4,6,7,2] => {{1},{2,3,5,6,7},{4}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [2,3,5,4,6,7,1] => {{1,2,3,5,6,7},{4}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [3,2,5,4,6,7,1] => {{1,3,5,6,7},{2},{4}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [1,4,5,3,6,7,2] => {{1},{2,3,4,5,6,7}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [2,4,5,3,6,7,1] => {{1,2,3,4,5,6,7}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [3,4,5,2,6,7,1] => {{1,3,5,6,7},{2,4}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [4,3,5,2,6,7,1] => {{1,2,3,4,5,6,7}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [1,5,4,3,6,7,2] => {{1},{2,5,6,7},{3,4}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [2,5,4,3,6,7,1] => {{1,2,5,6,7},{3,4}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [3,5,4,2,6,7,1] => {{1,2,3,4,5,6,7}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [4,5,3,2,6,7,1] => {{1,2,4,5,6,7},{3}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [5,4,3,2,6,7,1] => {{1,5,6,7},{2,4},{3}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [1,2,3,6,5,7,4] => {{1},{2},{3},{4,6,7},{5}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [2,1,3,6,5,7,4] => {{1,2},{3},{4,6,7},{5}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [1,3,2,6,5,7,4] => {{1},{2,3},{4,6,7},{5}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [2,3,1,6,5,7,4] => {{1,2,3},{4,6,7},{5}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [3,2,1,6,5,7,4] => {{1,3},{2},{4,6,7},{5}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [1,2,4,6,5,7,3] => {{1},{2},{3,4,6,7},{5}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [2,1,4,6,5,7,3] => {{1,2},{3,4,6,7},{5}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [1,3,4,6,5,7,2] => {{1},{2,3,4,6,7},{5}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [2,3,4,6,5,7,1] => {{1,2,3,4,6,7},{5}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [3,2,4,6,5,7,1] => {{1,3,4,6,7},{2},{5}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [1,4,3,6,5,7,2] => {{1},{2,4,6,7},{3},{5}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [2,4,3,6,5,7,1] => {{1,2,4,6,7},{3},{5}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [3,4,2,6,5,7,1] => {{1,2,3,4,6,7},{5}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [4,3,2,6,5,7,1] => {{1,4,6,7},{2,3},{5}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [1,2,5,6,4,7,3] => {{1},{2},{3,4,5,6,7}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [2,1,5,6,4,7,3] => {{1,2},{3,4,5,6,7}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [1,3,5,6,4,7,2] => {{1},{2,3,4,5,6,7}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [2,3,5,6,4,7,1] => {{1,2,3,4,5,6,7}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [3,2,5,6,4,7,1] => {{1,3,4,5,6,7},{2}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [1,4,5,6,3,7,2] => {{1},{2,4,6,7},{3,5}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [2,4,5,6,3,7,1] => {{1,2,4,6,7},{3,5}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [3,4,5,6,2,7,1] => {{1,2,3,4,5,6,7}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [4,3,5,6,2,7,1] => {{1,4,6,7},{2,3,5}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [1,5,4,6,3,7,2] => {{1},{2,3,4,5,6,7}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [2,5,4,6,3,7,1] => {{1,2,3,4,5,6,7}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [3,5,4,6,2,7,1] => {{1,3,4,6,7},{2,5}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [4,5,3,6,2,7,1] => {{1,4,6,7},{2,5},{3}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [5,4,3,6,2,7,1] => {{1,2,4,5,6,7},{3}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [1,2,6,5,4,7,3] => {{1},{2},{3,6,7},{4,5}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [2,1,6,5,4,7,3] => {{1,2},{3,6,7},{4,5}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [1,3,6,5,4,7,2] => {{1},{2,3,6,7},{4,5}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [2,3,6,5,4,7,1] => {{1,2,3,6,7},{4,5}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [3,2,6,5,4,7,1] => {{1,3,6,7},{2},{4,5}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [1,4,6,5,3,7,2] => {{1},{2,3,4,5,6,7}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [2,4,6,5,3,7,1] => {{1,2,3,4,5,6,7}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [3,4,6,5,2,7,1] => {{1,3,6,7},{2,4,5}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [4,3,6,5,2,7,1] => {{1,2,3,4,5,6,7}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [1,5,6,4,3,7,2] => {{1},{2,3,5,6,7},{4}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [2,5,6,4,3,7,1] => {{1,2,3,5,6,7},{4}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [3,5,6,4,2,7,1] => {{1,3,6,7},{2,5},{4}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [4,5,6,3,2,7,1] => {{1,3,4,6,7},{2,5}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [5,4,6,3,2,7,1] => {{1,2,3,4,5,6,7}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [1,6,5,4,3,7,2] => {{1},{2,6,7},{3,5},{4}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [2,6,5,4,3,7,1] => {{1,2,6,7},{3,5},{4}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [3,6,5,4,2,7,1] => {{1,2,3,5,6,7},{4}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [4,6,5,3,2,7,1] => {{1,2,3,4,5,6,7}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [5,6,4,3,2,7,1] => {{1,2,5,6,7},{3,4}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [6,5,4,3,2,7,1] => {{1,6,7},{2,5},{3,4}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [1,2,3,4,7,6,5] => {{1},{2},{3},{4},{5,7},{6}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [2,1,3,4,7,6,5] => {{1,2},{3},{4},{5,7},{6}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [1,3,2,4,7,6,5] => {{1},{2,3},{4},{5,7},{6}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [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] => [5,6,7,4,1,2,3] => [3,2,1,4,7,6,5] => {{1,3},{2},{4},{5,7},{6}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [1,2,4,3,7,6,5] => {{1},{2},{3,4},{5,7},{6}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [2,1,4,3,7,6,5] => {{1,2},{3,4},{5,7},{6}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [1,3,4,2,7,6,5] => {{1},{2,3,4},{5,7},{6}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [2,3,4,1,7,6,5] => {{1,2,3,4},{5,7},{6}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [3,2,4,1,7,6,5] => {{1,3,4},{2},{5,7},{6}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [1,4,3,2,7,6,5] => {{1},{2,4},{3},{5,7},{6}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [2,4,3,1,7,6,5] => {{1,2,4},{3},{5,7},{6}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [3,4,2,1,7,6,5] => {{1,2,3,4},{5,7},{6}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [4,3,2,1,7,6,5] => {{1,4},{2,3},{5,7},{6}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [1,2,3,5,7,6,4] => {{1},{2},{3},{4,5,7},{6}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [2,1,3,5,7,6,4] => {{1,2},{3},{4,5,7},{6}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [1,3,2,5,7,6,4] => {{1},{2,3},{4,5,7},{6}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [2,3,1,5,7,6,4] => {{1,2,3},{4,5,7},{6}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [3,2,1,5,7,6,4] => {{1,3},{2},{4,5,7},{6}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [1,2,4,5,7,6,3] => {{1},{2},{3,4,5,7},{6}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [2,1,4,5,7,6,3] => {{1,2},{3,4,5,7},{6}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [1,3,4,5,7,6,2] => {{1},{2,3,4,5,7},{6}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [2,3,4,5,7,6,1] => {{1,2,3,4,5,7},{6}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [3,2,4,5,7,6,1] => {{1,3,4,5,7},{2},{6}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [1,4,3,5,7,6,2] => {{1},{2,4,5,7},{3},{6}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [2,4,3,5,7,6,1] => {{1,2,4,5,7},{3},{6}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [3,4,2,5,7,6,1] => {{1,2,3,4,5,7},{6}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [4,3,2,5,7,6,1] => {{1,4,5,7},{2,3},{6}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [1,2,5,4,7,6,3] => {{1},{2},{3,5,7},{4},{6}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [2,1,5,4,7,6,3] => {{1,2},{3,5,7},{4},{6}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [1,3,5,4,7,6,2] => {{1},{2,3,5,7},{4},{6}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [2,3,5,4,7,6,1] => {{1,2,3,5,7},{4},{6}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [3,2,5,4,7,6,1] => {{1,3,5,7},{2},{4},{6}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [1,4,5,3,7,6,2] => {{1},{2,3,4,5,7},{6}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [2,4,5,3,7,6,1] => {{1,2,3,4,5,7},{6}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [3,4,5,2,7,6,1] => {{1,3,5,7},{2,4},{6}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [4,3,5,2,7,6,1] => {{1,2,3,4,5,7},{6}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [1,5,4,3,7,6,2] => {{1},{2,5,7},{3,4},{6}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [2,5,4,3,7,6,1] => {{1,2,5,7},{3,4},{6}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [3,5,4,2,7,6,1] => {{1,2,3,4,5,7},{6}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [4,5,3,2,7,6,1] => {{1,2,4,5,7},{3},{6}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [5,4,3,2,7,6,1] => {{1,5,7},{2,4},{3},{6}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [1,2,3,6,7,5,4] => {{1},{2},{3},{4,5,6,7}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [2,1,3,6,7,5,4] => {{1,2},{3},{4,5,6,7}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [1,3,2,6,7,5,4] => {{1},{2,3},{4,5,6,7}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [2,3,1,6,7,5,4] => {{1,2,3},{4,5,6,7}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [3,2,1,6,7,5,4] => {{1,3},{2},{4,5,6,7}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [1,2,4,6,7,5,3] => {{1},{2},{3,4,5,6,7}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [2,1,4,6,7,5,3] => {{1,2},{3,4,5,6,7}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [1,3,4,6,7,5,2] => {{1},{2,3,4,5,6,7}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [2,3,4,6,7,5,1] => {{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [3,2,4,6,7,5,1] => {{1,3,4,5,6,7},{2}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [1,4,3,6,7,5,2] => {{1},{2,4,5,6,7},{3}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [2,4,3,6,7,5,1] => {{1,2,4,5,6,7},{3}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [3,4,2,6,7,5,1] => {{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [4,3,2,6,7,5,1] => {{1,4,5,6,7},{2,3}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [1,2,5,6,7,4,3] => {{1},{2},{3,5,7},{4,6}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [2,1,5,6,7,4,3] => {{1,2},{3,5,7},{4,6}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [1,3,5,6,7,4,2] => {{1},{2,3,5,7},{4,6}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [2,3,5,6,7,4,1] => {{1,2,3,5,7},{4,6}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [3,2,5,6,7,4,1] => {{1,3,5,7},{2},{4,6}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [1,4,5,6,7,3,2] => {{1},{2,3,4,5,6,7}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [2,4,5,6,7,3,1] => {{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [3,4,5,6,7,2,1] => {{1,3,5,7},{2,4,6}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [4,3,5,6,7,2,1] => {{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [1,5,4,6,7,3,2] => {{1},{2,5,7},{3,4,6}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [2,5,4,6,7,3,1] => {{1,2,5,7},{3,4,6}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [3,5,4,6,7,2,1] => {{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [4,5,3,6,7,2,1] => {{1,2,4,5,6,7},{3}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [5,4,3,6,7,2,1] => {{1,5,7},{2,4,6},{3}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [1,2,6,5,7,4,3] => {{1},{2},{3,4,5,6,7}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [2,1,6,5,7,4,3] => {{1,2},{3,4,5,6,7}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [1,3,6,5,7,4,2] => {{1},{2,3,4,5,6,7}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [2,3,6,5,7,4,1] => {{1,2,3,4,5,6,7}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [3,2,6,5,7,4,1] => {{1,3,4,5,6,7},{2}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [1,4,6,5,7,3,2] => {{1},{2,4,5,7},{3,6}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [2,4,6,5,7,3,1] => {{1,2,4,5,7},{3,6}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [3,4,6,5,7,2,1] => {{1,2,3,4,5,6,7}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [4,3,6,5,7,2,1] => {{1,4,5,7},{2,3,6}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [1,5,6,4,7,3,2] => {{1},{2,5,7},{3,6},{4}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [2,5,6,4,7,3,1] => {{1,2,5,7},{3,6},{4}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [3,5,6,4,7,2,1] => {{1,2,3,5,6,7},{4}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [4,5,6,3,7,2,1] => {{1,2,3,4,5,6,7}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [5,4,6,3,7,2,1] => {{1,5,7},{2,3,4,6}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [1,6,5,4,7,3,2] => {{1},{2,3,5,6,7},{4}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [2,6,5,4,7,3,1] => {{1,2,3,5,6,7},{4}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [3,6,5,4,7,2,1] => {{1,3,5,7},{2,6},{4}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [4,6,5,3,7,2,1] => {{1,3,4,5,7},{2,6}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [5,6,4,3,7,2,1] => {{1,5,7},{2,6},{3,4}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [6,5,4,3,7,2,1] => {{1,2,5,6,7},{3,4}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [1,2,3,7,6,5,4] => {{1},{2},{3},{4,7},{5,6}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [2,1,3,7,6,5,4] => {{1,2},{3},{4,7},{5,6}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [1,3,2,7,6,5,4] => {{1},{2,3},{4,7},{5,6}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [2,3,1,7,6,5,4] => {{1,2,3},{4,7},{5,6}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [3,2,1,7,6,5,4] => {{1,3},{2},{4,7},{5,6}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [1,2,4,7,6,5,3] => {{1},{2},{3,4,7},{5,6}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [2,1,4,7,6,5,3] => {{1,2},{3,4,7},{5,6}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [1,3,4,7,6,5,2] => {{1},{2,3,4,7},{5,6}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [2,3,4,7,6,5,1] => {{1,2,3,4,7},{5,6}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [3,2,4,7,6,5,1] => {{1,3,4,7},{2},{5,6}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [1,4,3,7,6,5,2] => {{1},{2,4,7},{3},{5,6}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [2,4,3,7,6,5,1] => {{1,2,4,7},{3},{5,6}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [3,4,2,7,6,5,1] => {{1,2,3,4,7},{5,6}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [4,3,2,7,6,5,1] => {{1,4,7},{2,3},{5,6}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [1,2,5,7,6,4,3] => {{1},{2},{3,4,5,6,7}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [2,1,5,7,6,4,3] => {{1,2},{3,4,5,6,7}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [1,3,5,7,6,4,2] => {{1},{2,3,4,5,6,7}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [2,3,5,7,6,4,1] => {{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [3,2,5,7,6,4,1] => {{1,3,4,5,6,7},{2}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [1,4,5,7,6,3,2] => {{1},{2,4,7},{3,5,6}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [2,4,5,7,6,3,1] => {{1,2,4,7},{3,5,6}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [3,4,5,7,6,2,1] => {{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [4,3,5,7,6,2,1] => {{1,4,7},{2,3,5,6}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [1,5,4,7,6,3,2] => {{1},{2,3,4,5,6,7}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [2,5,4,7,6,3,1] => {{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [3,5,4,7,6,2,1] => {{1,3,4,7},{2,5,6}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [4,5,3,7,6,2,1] => {{1,4,7},{2,5,6},{3}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [5,4,3,7,6,2,1] => {{1,2,4,5,6,7},{3}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [1,2,6,7,5,4,3] => {{1},{2},{3,4,6,7},{5}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [2,1,6,7,5,4,3] => {{1,2},{3,4,6,7},{5}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [1,3,6,7,5,4,2] => {{1},{2,3,4,6,7},{5}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [2,3,6,7,5,4,1] => {{1,2,3,4,6,7},{5}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [3,2,6,7,5,4,1] => {{1,3,4,6,7},{2},{5}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [1,4,6,7,5,3,2] => {{1},{2,4,7},{3,6},{5}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [2,4,6,7,5,3,1] => {{1,2,4,7},{3,6},{5}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [3,4,6,7,5,2,1] => {{1,2,3,4,6,7},{5}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [4,3,6,7,5,2,1] => {{1,4,7},{2,3,6},{5}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [1,5,6,7,4,3,2] => {{1},{2,4,5,7},{3,6}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [2,5,6,7,4,3,1] => {{1,2,4,5,7},{3,6}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [3,5,6,7,4,2,1] => {{1,2,3,4,5,6,7}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [4,5,6,7,3,2,1] => {{1,4,7},{2,3,5,6}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [5,4,6,7,3,2,1] => {{1,2,3,4,5,6,7}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [1,6,5,7,4,3,2] => {{1},{2,3,4,5,6,7}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [2,6,5,7,4,3,1] => {{1,2,3,4,5,6,7}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [3,6,5,7,4,2,1] => {{1,3,4,5,7},{2,6}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [4,6,5,7,3,2,1] => {{1,4,7},{2,6},{3,5}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [5,6,4,7,3,2,1] => {{1,3,4,5,7},{2,6}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [6,5,4,7,3,2,1] => {{1,2,3,4,5,6,7}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [1,2,7,6,5,4,3] => {{1},{2},{3,7},{4,6},{5}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [2,1,7,6,5,4,3] => {{1,2},{3,7},{4,6},{5}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [1,3,7,6,5,4,2] => {{1},{2,3,7},{4,6},{5}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [2,3,7,6,5,4,1] => {{1,2,3,7},{4,6},{5}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [3,2,7,6,5,4,1] => {{1,3,7},{2},{4,6},{5}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [1,4,7,6,5,3,2] => {{1},{2,3,4,6,7},{5}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [2,4,7,6,5,3,1] => {{1,2,3,4,6,7},{5}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [3,4,7,6,5,2,1] => {{1,3,7},{2,4,6},{5}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [4,3,7,6,5,2,1] => {{1,2,3,4,6,7},{5}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [1,5,7,6,4,3,2] => {{1},{2,3,4,5,6,7}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [2,5,7,6,4,3,1] => {{1,2,3,4,5,6,7}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [3,5,7,6,4,2,1] => {{1,3,7},{2,4,5,6}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [4,5,7,6,3,2,1] => {{1,2,3,4,5,6,7}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [5,4,7,6,3,2,1] => {{1,3,5,7},{2,4,6}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [1,6,7,5,4,3,2] => {{1},{2,3,6,7},{4,5}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [2,6,7,5,4,3,1] => {{1,2,3,6,7},{4,5}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [3,6,7,5,4,2,1] => {{1,3,7},{2,6},{4,5}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [4,6,7,5,3,2,1] => {{1,3,4,5,7},{2,6}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [5,6,7,4,3,2,1] => {{1,3,5,7},{2,6},{4}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [6,5,7,4,3,2,1] => {{1,2,3,5,6,7},{4}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [1,7,6,5,4,3,2] => {{1},{2,7},{3,6},{4,5}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [2,7,6,5,4,3,1] => {{1,2,7},{3,6},{4,5}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [3,7,6,5,4,2,1] => {{1,2,3,6,7},{4,5}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [4,7,6,5,3,2,1] => {{1,2,3,4,5,6,7}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [5,7,6,4,3,2,1] => {{1,2,3,5,6,7},{4}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [6,7,5,4,3,2,1] => {{1,2,6,7},{3,5},{4}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [7,6,5,4,3,2,1] => {{1,7},{2,6},{3,5},{4}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => {{1},{2},{3},{4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => [2,1,3,4,5,6,7,8] => {{1,2},{3},{4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,2,1] => [1,3,2,4,5,6,7,8] => {{1},{2,3},{4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => [2,3,1,4,5,6,7,8] => {{1,2,3},{4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [3,2,1,4,5,6,7,8] => {{1,3},{2},{4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,2,1] => [1,2,4,3,5,6,7,8] => {{1},{2},{3,4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => [2,1,4,3,5,6,7,8] => {{1,2},{3,4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,2,1] => [1,3,4,2,5,6,7,8] => {{1},{2,3,4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => [2,3,4,1,5,6,7,8] => {{1,2,3,4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,2,1] => [3,2,4,1,5,6,7,8] => {{1,3,4},{2},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,2,1] => [1,4,3,2,5,6,7,8] => {{1},{2,4},{3},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => [2,4,3,1,5,6,7,8] => {{1,2,4},{3},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => [3,4,2,1,5,6,7,8] => {{1,2,3,4},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [4,3,2,1,5,6,7,8] => {{1,4},{2,3},{5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,2,1] => [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] => [7,8,6,4,5,3,2,1] => [2,1,3,5,4,6,7,8] => {{1,2},{3},{4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [1,3,2,5,4,6,7,8] => {{1},{2,3},{4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,3,2,1] => [2,3,1,5,4,6,7,8] => {{1,2,3},{4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,2,1] => [3,2,1,5,4,6,7,8] => {{1,3},{2},{4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,3,2,1] => [2,1,4,5,3,6,7,8] => {{1,2},{3,4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,3,2,1] => [1,3,4,5,2,6,7,8] => {{1},{2,3,4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => [2,3,4,5,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,3,2,1] => [3,2,4,5,1,6,7,8] => {{1,3,4,5},{2},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,2,1] => [2,4,3,5,1,6,7,8] => {{1,2,4,5},{3},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => [3,4,2,5,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [4,3,2,5,1,6,7,8] => {{1,4,5},{2,3},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,2,1] => [1,2,5,4,3,6,7,8] => {{1},{2},{3,5},{4},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,2,1] => [2,1,5,4,3,6,7,8] => {{1,2},{3,5},{4},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => [2,3,5,4,1,6,7,8] => {{1,2,3,5},{4},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,2,1] => [3,2,5,4,1,6,7,8] => {{1,3,5},{2},{4},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,2,1] => [1,4,5,3,2,6,7,8] => {{1},{2,3,4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => [2,4,5,3,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,2,1] => [3,4,5,2,1,6,7,8] => {{1,3,5},{2,4},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [4,3,5,2,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,3,2,1] => [1,5,4,3,2,6,7,8] => {{1},{2,5},{3,4},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => [2,5,4,3,1,6,7,8] => {{1,2,5},{3,4},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,3,2,1] => [3,5,4,2,1,6,7,8] => {{1,2,3,4,5},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [4,5,3,2,1,6,7,8] => {{1,2,4,5},{3},{6},{7},{8}}
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [5,4,3,2,1,6,7,8] => {{1,5},{2,4},{3},{6},{7},{8}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => [1,2,3,4,6,5,7,8] => {{1},{2},{3},{4},{5,6},{7},{8}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => [2,1,3,4,6,5,7,8] => {{1,2},{3},{4},{5,6},{7},{8}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => [1,3,2,4,6,5,7,8] => {{1},{2,3},{4},{5,6},{7},{8}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [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] => [7,8,5,6,3,4,2,1] => [2,1,4,3,6,5,7,8] => {{1,2},{3,4},{5,6},{7},{8}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,2,1] => [2,3,4,1,6,5,7,8] => {{1,2,3,4},{5,6},{7},{8}}
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,2,1] => [3,2,4,1,6,5,7,8] => {{1,3,4},{2},{5,6},{7},{8}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,2,1] => [2,4,3,1,6,5,7,8] => {{1,2,4},{3},{5,6},{7},{8}}
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => [4,3,2,1,6,5,7,8] => {{1,4},{2,3},{5,6},{7},{8}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,5,2,1] => [1,2,3,5,6,4,7,8] => {{1},{2},{3},{4,5,6},{7},{8}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,5,2,1] => [1,3,2,5,6,4,7,8] => {{1},{2,3},{4,5,6},{7},{8}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,5,2,1] => [2,3,1,5,6,4,7,8] => {{1,2,3},{4,5,6},{7},{8}}
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,2,1] => [3,2,1,5,6,4,7,8] => {{1,3},{2},{4,5,6},{7},{8}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,2,1] => [1,2,4,5,6,3,7,8] => {{1},{2},{3,4,5,6},{7},{8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,2,1] => [1,3,4,5,6,2,7,8] => {{1},{2,3,4,5,6},{7},{8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => [2,3,4,5,6,1,7,8] => {{1,2,3,4,5,6},{7},{8}}
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,8,2,1] => [3,2,4,5,6,1,7,8] => {{1,3,4,5,6},{2},{7},{8}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,7,2,1] => [1,4,3,5,6,2,7,8] => {{1},{2,4,5,6},{3},{7},{8}}
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [3,4,2,5,6,1,7,8] => {{1,2,3,4,5,6},{7},{8}}
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,2,1] => [4,3,2,5,6,1,7,8] => {{1,4,5,6},{2,3},{7},{8}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,8,2,1] => [2,3,5,4,6,1,7,8] => {{1,2,3,5,6},{4},{7},{8}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,2,1] => [1,4,5,3,6,2,7,8] => {{1},{2,3,4,5,6},{7},{8}}
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [3,4,5,2,6,1,7,8] => {{1,3,5,6},{2,4},{7},{8}}
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,2,1] => [4,3,5,2,6,1,7,8] => {{1,2,3,4,5,6},{7},{8}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,7,2,1] => [1,5,4,3,6,2,7,8] => {{1},{2,5,6},{3,4},{7},{8}}
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,2,1] => [3,5,4,2,6,1,7,8] => {{1,2,3,4,5,6},{7},{8}}
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => [4,5,3,2,6,1,7,8] => {{1,2,4,5,6},{3},{7},{8}}
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => [5,4,3,2,6,1,7,8] => {{1,5,6},{2,4},{3},{7},{8}}
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,2,1] => [1,2,3,6,5,4,7,8] => {{1},{2},{3},{4,6},{5},{7},{8}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,2,1] => [1,3,2,6,5,4,7,8] => {{1},{2,3},{4,6},{5},{7},{8}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,5,2,1] => [2,3,1,6,5,4,7,8] => {{1,2,3},{4,6},{5},{7},{8}}
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => [3,2,1,6,5,4,7,8] => {{1,3},{2},{4,6},{5},{7},{8}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,6,2,1] => [1,2,4,6,5,3,7,8] => {{1},{2},{3,4,6},{5},{7},{8}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,2,1] => [2,1,4,6,5,3,7,8] => {{1,2},{3,4,6},{5},{7},{8}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,2,1] => [2,3,4,6,5,1,7,8] => {{1,2,3,4,6},{5},{7},{8}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,7,2,1] => [1,4,3,6,5,2,7,8] => {{1},{2,4,6},{3},{5},{7},{8}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,8,2,1] => [2,4,3,6,5,1,7,8] => {{1,2,4,6},{3},{5},{7},{8}}
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,8,2,1] => [4,3,2,6,5,1,7,8] => {{1,4,6},{2,3},{5},{7},{8}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,2,1] => [1,2,5,6,4,3,7,8] => {{1},{2},{3,4,5,6},{7},{8}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,2,1] => [2,1,5,6,4,3,7,8] => {{1,2},{3,4,5,6},{7},{8}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,2,1] => [1,3,5,6,4,2,7,8] => {{1},{2,3,4,5,6},{7},{8}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,2,1] => [2,3,5,6,4,1,7,8] => {{1,2,3,4,5,6},{7},{8}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,2,1] => [1,4,5,6,3,2,7,8] => {{1},{2,4,6},{3,5},{7},{8}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,2,1] => [2,4,5,6,3,1,7,8] => {{1,2,4,6},{3,5},{7},{8}}
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [3,4,5,6,2,1,7,8] => {{1,2,3,4,5,6},{7},{8}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,7,2,1] => [1,5,4,6,3,2,7,8] => {{1},{2,3,4,5,6},{7},{8}}
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,2,1] => [5,4,3,6,2,1,7,8] => {{1,2,4,5,6},{3},{7},{8}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,2,1] => [1,2,6,5,4,3,7,8] => {{1},{2},{3,6},{4,5},{7},{8}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,2,1] => [2,3,6,5,4,1,7,8] => {{1,2,3,6},{4,5},{7},{8}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,2,1] => [1,4,6,5,3,2,7,8] => {{1},{2,3,4,5,6},{7},{8}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,2,1] => [2,4,6,5,3,1,7,8] => {{1,2,3,4,5,6},{7},{8}}
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,2,1] => [4,3,6,5,2,1,7,8] => {{1,2,3,4,5,6},{7},{8}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,2,1] => [1,5,6,4,3,2,7,8] => {{1},{2,3,5,6},{4},{7},{8}}
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,2,1] => [4,5,6,3,2,1,7,8] => {{1,3,4,6},{2,5},{7},{8}}
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,2,1] => [5,4,6,3,2,1,7,8] => {{1,2,3,4,5,6},{7},{8}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => [1,6,5,4,3,2,7,8] => {{1},{2,6},{3,5},{4},{7},{8}}
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,2,1] => [3,6,5,4,2,1,7,8] => {{1,2,3,5,6},{4},{7},{8}}
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => [5,6,4,3,2,1,7,8] => {{1,2,5,6},{3,4},{7},{8}}
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => [6,5,4,3,2,1,7,8] => {{1,6},{2,5},{3,4},{7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => [1,2,3,4,5,7,6,8] => {{1},{2},{3},{4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => [2,1,3,4,5,7,6,8] => {{1,2},{3},{4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [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] => [7,6,8,5,4,2,3,1] => [2,3,1,4,5,7,6,8] => {{1,2,3},{4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,2,3,1] => [3,2,1,4,5,7,6,8] => {{1,3},{2},{4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => [1,2,4,3,5,7,6,8] => {{1},{2},{3,4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,3,1] => [1,3,4,2,5,7,6,8] => {{1},{2,3,4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,3,1] => [2,3,4,1,5,7,6,8] => {{1,2,3,4},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,3,1] => [3,2,4,1,5,7,6,8] => {{1,3,4},{2},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,3,1] => [1,4,3,2,5,7,6,8] => {{1},{2,4},{3},{5},{6,7},{8}}
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [4,3,2,1,5,7,6,8] => {{1,4},{2,3},{5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => [1,2,3,5,4,7,6,8] => {{1},{2},{3},{4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [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] => [7,6,8,4,5,2,3,1] => [2,3,1,5,4,7,6,8] => {{1,2,3},{4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,2,3,1] => [3,2,1,5,4,7,6,8] => {{1,3},{2},{4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,2,3,1] => [1,2,4,5,3,7,6,8] => {{1},{2},{3,4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,3,1] => [1,3,4,5,2,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,3,1] => [2,3,4,5,1,7,6,8] => {{1,2,3,4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,2,3,1] => [1,4,3,5,2,7,6,8] => {{1},{2,4,5},{3},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,3,1] => [2,4,3,5,1,7,6,8] => {{1,2,4,5},{3},{6,7},{8}}
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,3,1] => [3,4,2,5,1,7,6,8] => {{1,2,3,4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,3,1] => [2,1,5,4,3,7,6,8] => {{1,2},{3,5},{4},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,3,1] => [1,3,5,4,2,7,6,8] => {{1},{2,3,5},{4},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,3,1] => [2,3,5,4,1,7,6,8] => {{1,2,3,5},{4},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,3,1] => [3,2,5,4,1,7,6,8] => {{1,3,5},{2},{4},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,2,3,1] => [1,4,5,3,2,7,6,8] => {{1},{2,3,4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,2,3,1] => [2,4,5,3,1,7,6,8] => {{1,2,3,4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,2,3,1] => [3,4,5,2,1,7,6,8] => {{1,3,5},{2,4},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,3,1] => [1,5,4,3,2,7,6,8] => {{1},{2,5},{3,4},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,2,3,1] => [2,5,4,3,1,7,6,8] => {{1,2,5},{3,4},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,2,3,1] => [3,5,4,2,1,7,6,8] => {{1,2,3,4,5},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,2,3,1] => [4,5,3,2,1,7,6,8] => {{1,2,4,5},{3},{6,7},{8}}
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => [5,4,3,2,1,7,6,8] => {{1,5},{2,4},{3},{6,7},{8}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,4,1] => [1,2,3,4,6,7,5,8] => {{1},{2},{3},{4},{5,6,7},{8}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,4,1] => [2,3,1,4,6,7,5,8] => {{1,2,3},{4},{5,6,7},{8}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,4,1] => [1,2,4,3,6,7,5,8] => {{1},{2},{3,4},{5,6,7},{8}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,4,1] => [2,1,4,3,6,7,5,8] => {{1,2},{3,4},{5,6,7},{8}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => [1,3,4,2,6,7,5,8] => {{1},{2,3,4},{5,6,7},{8}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,4,1] => [2,3,4,1,6,7,5,8] => {{1,2,3,4},{5,6,7},{8}}
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,4,1] => [3,2,4,1,6,7,5,8] => {{1,3,4},{2},{5,6,7},{8}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,4,1] => [1,4,3,2,6,7,5,8] => {{1},{2,4},{3},{5,6,7},{8}}
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => [4,3,2,1,6,7,5,8] => {{1,4},{2,3},{5,6,7},{8}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,5,1] => [1,2,3,5,6,7,4,8] => {{1},{2},{3},{4,5,6,7},{8}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,5,1] => [1,3,2,5,6,7,4,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,5,1] => [2,3,1,5,6,7,4,8] => {{1,2,3},{4,5,6,7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,6,1] => [1,2,4,5,6,7,3,8] => {{1},{2},{3,4,5,6,7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,6,1] => [2,1,4,5,6,7,3,8] => {{1,2},{3,4,5,6,7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,7,1] => [1,3,4,5,6,7,2,8] => {{1},{2,3,4,5,6,7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => [2,3,4,5,6,7,1,8] => {{1,2,3,4,5,6,7},{8}}
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => [3,2,4,5,6,7,1,8] => {{1,3,4,5,6,7},{2},{8}}
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => [3,4,2,5,6,7,1,8] => {{1,2,3,4,5,6,7},{8}}
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,8,1] => [4,3,2,5,6,7,1,8] => {{1,4,5,6,7},{2,3},{8}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,2,6,1] => [1,2,5,4,6,7,3,8] => {{1},{2},{3,5,6,7},{4},{8}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,2,6,1] => [2,1,5,4,6,7,3,8] => {{1,2},{3,5,6,7},{4},{8}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,8,1] => [2,3,5,4,6,7,1,8] => {{1,2,3,5,6,7},{4},{8}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,7,1] => [1,4,5,3,6,7,2,8] => {{1},{2,3,4,5,6,7},{8}}
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,8,1] => [3,4,5,2,6,7,1,8] => {{1,3,5,6,7},{2,4},{8}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,7,1] => [1,5,4,3,6,7,2,8] => {{1},{2,5,6,7},{3,4},{8}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,8,1] => [2,5,4,3,6,7,1,8] => {{1,2,5,6,7},{3,4},{8}}
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,8,1] => [3,5,4,2,6,7,1,8] => {{1,2,3,4,5,6,7},{8}}
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => [5,4,3,2,6,7,1,8] => {{1,5,6,7},{2,4},{3},{8}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,5,1] => [1,2,3,6,5,7,4,8] => {{1},{2},{3},{4,6,7},{5},{8}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,2,5,1] => [1,3,2,6,5,7,4,8] => {{1},{2,3},{4,6,7},{5},{8}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,2,5,1] => [2,3,1,6,5,7,4,8] => {{1,2,3},{4,6,7},{5},{8}}
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,5,1] => [3,2,1,6,5,7,4,8] => {{1,3},{2},{4,6,7},{5},{8}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,8,1] => [2,3,4,6,5,7,1,8] => {{1,2,3,4,6,7},{5},{8}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,7,1] => [1,4,3,6,5,7,2,8] => {{1},{2,4,6,7},{3},{5},{8}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,8,1] => [2,4,3,6,5,7,1,8] => {{1,2,4,6,7},{3},{5},{8}}
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,8,1] => [3,4,2,6,5,7,1,8] => {{1,2,3,4,6,7},{5},{8}}
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,8,1] => [4,3,2,6,5,7,1,8] => {{1,4,6,7},{2,3},{5},{8}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,6,1] => [1,2,5,6,4,7,3,8] => {{1},{2},{3,4,5,6,7},{8}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,7,1] => [1,3,5,6,4,7,2,8] => {{1},{2,3,4,5,6,7},{8}}
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => [3,4,5,6,2,7,1,8] => {{1,2,3,4,5,6,7},{8}}
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,8,1] => [4,3,5,6,2,7,1,8] => {{1,4,6,7},{2,3,5},{8}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,7,1] => [1,5,4,6,3,7,2,8] => {{1},{2,3,4,5,6,7},{8}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,8,1] => [2,5,4,6,3,7,1,8] => {{1,2,3,4,5,6,7},{8}}
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,2,8,1] => [3,5,4,6,2,7,1,8] => {{1,3,4,6,7},{2,5},{8}}
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => [4,5,3,6,2,7,1,8] => {{1,4,6,7},{2,5},{3},{8}}
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,2,8,1] => [5,4,3,6,2,7,1,8] => {{1,2,4,5,6,7},{3},{8}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,2,7,1] => [1,3,6,5,4,7,2,8] => {{1},{2,3,6,7},{4,5},{8}}
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,2,8,1] => [3,2,6,5,4,7,1,8] => {{1,3,6,7},{2},{4,5},{8}}
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,8,1] => [3,4,6,5,2,7,1,8] => {{1,3,6,7},{2,4,5},{8}}
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,8,1] => [3,5,6,4,2,7,1,8] => {{1,3,6,7},{2,5},{4},{8}}
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,2,8,1] => [5,4,6,3,2,7,1,8] => {{1,2,3,4,5,6,7},{8}}
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,2,8,1] => [3,6,5,4,2,7,1,8] => {{1,2,3,5,6,7},{4},{8}}
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,2,8,1] => [5,6,4,3,2,7,1,8] => {{1,2,5,6,7},{3,4},{8}}
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,8,1] => [6,5,4,3,2,7,1,8] => {{1,6,7},{2,5},{3,4},{8}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => [1,2,3,4,7,6,5,8] => {{1},{2},{3},{4},{5,7},{6},{8}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,4,1] => [1,3,2,4,7,6,5,8] => {{1},{2,3},{4},{5,7},{6},{8}}
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [3,2,1,4,7,6,5,8] => {{1,3},{2},{4},{5,7},{6},{8}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,4,1] => [2,3,4,1,7,6,5,8] => {{1,2,3,4},{5,7},{6},{8}}
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,4,1] => [3,2,4,1,7,6,5,8] => {{1,3,4},{2},{5,7},{6},{8}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [1,4,3,2,7,6,5,8] => {{1},{2,4},{3},{5,7},{6},{8}}
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [4,3,2,1,7,6,5,8] => {{1,4},{2,3},{5,7},{6},{8}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,5,1] => [1,2,3,5,7,6,4,8] => {{1},{2},{3},{4,5,7},{6},{8}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,3,5,1] => [1,3,2,5,7,6,4,8] => {{1},{2,3},{4,5,7},{6},{8}}
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,5,1] => [3,2,1,5,7,6,4,8] => {{1,3},{2},{4,5,7},{6},{8}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,7,1] => [1,3,4,5,7,6,2,8] => {{1},{2,3,4,5,7},{6},{8}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => [2,3,4,5,7,6,1,8] => {{1,2,3,4,5,7},{6},{8}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,7,1] => [1,4,3,5,7,6,2,8] => {{1},{2,4,5,7},{3},{6},{8}}
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,3,8,1] => [3,4,2,5,7,6,1,8] => {{1,2,3,4,5,7},{6},{8}}
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,8,1] => [4,3,2,5,7,6,1,8] => {{1,4,5,7},{2,3},{6},{8}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,3,7,1] => [1,3,5,4,7,6,2,8] => {{1},{2,3,5,7},{4},{6},{8}}
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => [3,2,5,4,7,6,1,8] => {{1,3,5,7},{2},{4},{6},{8}}
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,8,1] => [3,4,5,2,7,6,1,8] => {{1,3,5,7},{2,4},{6},{8}}
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,8,1] => [4,3,5,2,7,6,1,8] => {{1,2,3,4,5,7},{6},{8}}
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,2,3,8,1] => [3,5,4,2,7,6,1,8] => {{1,2,3,4,5,7},{6},{8}}
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,8,1] => [4,5,3,2,7,6,1,8] => {{1,2,4,5,7},{3},{6},{8}}
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => [5,4,3,2,7,6,1,8] => {{1,5,7},{2,4},{3},{6},{8}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,5,1] => [1,2,3,6,7,5,4,8] => {{1},{2},{3},{4,5,6,7},{8}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,4,5,1] => [2,1,3,6,7,5,4,8] => {{1,2},{3},{4,5,6,7},{8}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,5,1] => [1,3,2,6,7,5,4,8] => {{1},{2,3},{4,5,6,7},{8}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,4,5,1] => [2,3,1,6,7,5,4,8] => {{1,2,3},{4,5,6,7},{8}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,6,1] => [1,2,4,6,7,5,3,8] => {{1},{2},{3,4,5,6,7},{8}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,7,1] => [1,3,4,6,7,5,2,8] => {{1},{2,3,4,5,6,7},{8}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => [2,3,4,6,7,5,1,8] => {{1,2,3,4,5,6,7},{8}}
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,2,4,8,1] => [3,2,4,6,7,5,1,8] => {{1,3,4,5,6,7},{2},{8}}
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,8,1] => [3,4,2,6,7,5,1,8] => {{1,2,3,4,5,6,7},{8}}
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,8,1] => [4,3,2,6,7,5,1,8] => {{1,4,5,6,7},{2,3},{8}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,6,1] => [1,2,5,6,7,4,3,8] => {{1},{2},{3,5,7},{4,6},{8}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,6,1] => [2,1,5,6,7,4,3,8] => {{1,2},{3,5,7},{4,6},{8}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,7,1] => [1,3,5,6,7,4,2,8] => {{1},{2,3,5,7},{4,6},{8}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,8,1] => [2,3,5,6,7,4,1,8] => {{1,2,3,5,7},{4,6},{8}}
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,8,1] => [3,2,5,6,7,4,1,8] => {{1,3,5,7},{2},{4,6},{8}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,7,1] => [1,4,5,6,7,3,2,8] => {{1},{2,3,4,5,6,7},{8}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => [2,4,5,6,7,3,1,8] => {{1,2,3,4,5,6,7},{8}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,8,1] => [3,4,5,6,7,2,1,8] => {{1,3,5,7},{2,4,6},{8}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,6,7,1] => [1,5,4,6,7,3,2,8] => {{1},{2,5,7},{3,4,6},{8}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,8,1] => [2,5,4,6,7,3,1,8] => {{1,2,5,7},{3,4,6},{8}}
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,7,8,1] => [5,4,3,6,7,2,1,8] => {{1,5,7},{2,4,6},{3},{8}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,5,7,1] => [1,3,6,5,7,4,2,8] => {{1},{2,3,4,5,6,7},{8}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,5,8,1] => [2,3,6,5,7,4,1,8] => {{1,2,3,4,5,6,7},{8}}
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,8,1] => [3,2,6,5,7,4,1,8] => {{1,3,4,5,6,7},{2},{8}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,7,1] => [1,4,6,5,7,3,2,8] => {{1},{2,4,5,7},{3,6},{8}}
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,8,1] => [4,3,6,5,7,2,1,8] => {{1,4,5,7},{2,3,6},{8}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,7,1] => [1,5,6,4,7,3,2,8] => {{1},{2,5,7},{3,6},{4},{8}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [2,5,6,4,7,3,1,8] => {{1,2,5,7},{3,6},{4},{8}}
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,2,7,8,1] => [3,5,6,4,7,2,1,8] => {{1,2,3,5,6,7},{4},{8}}
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,8,1] => [5,4,6,3,7,2,1,8] => {{1,5,7},{2,3,4,6},{8}}
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,8,1] => [5,6,4,3,7,2,1,8] => {{1,5,7},{2,6},{3,4},{8}}
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,8,1] => [6,5,4,3,7,2,1,8] => {{1,2,5,6,7},{3,4},{8}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => [1,2,3,7,6,5,4,8] => {{1},{2},{3},{4,7},{5,6},{8}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,5,1] => [1,3,2,7,6,5,4,8] => {{1},{2,3},{4,7},{5,6},{8}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => [3,2,1,7,6,5,4,8] => {{1,3},{2},{4,7},{5,6},{8}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => [2,3,4,7,6,5,1,8] => {{1,2,3,4,7},{5,6},{8}}
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,8,1] => [3,4,2,7,6,5,1,8] => {{1,2,3,4,7},{5,6},{8}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,3,5,6,1] => [1,2,5,7,6,4,3,8] => {{1},{2},{3,4,5,6,7},{8}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,7,1] => [1,3,5,7,6,4,2,8] => {{1},{2,3,4,5,6,7},{8}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,8,1] => [2,3,5,7,6,4,1,8] => {{1,2,3,4,5,6,7},{8}}
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,8,1] => [3,2,5,7,6,4,1,8] => {{1,3,4,5,6,7},{2},{8}}
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,3,7,8,1] => [4,3,5,7,6,2,1,8] => {{1,4,7},{2,3,5,6},{8}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,8,1] => [2,5,4,7,6,3,1,8] => {{1,2,3,4,5,6,7},{8}}
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,7,8,1] => [3,5,4,7,6,2,1,8] => {{1,3,4,7},{2,5,6},{8}}
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,8,1] => [4,5,3,7,6,2,1,8] => {{1,4,7},{2,5,6},{3},{8}}
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,7,8,1] => [5,4,3,7,6,2,1,8] => {{1,2,4,5,6,7},{3},{8}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,4,5,6,1] => [1,2,6,7,5,4,3,8] => {{1},{2},{3,4,6,7},{5},{8}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => [2,1,6,7,5,4,3,8] => {{1,2},{3,4,6,7},{5},{8}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,8,1] => [2,3,6,7,5,4,1,8] => {{1,2,3,4,6,7},{5},{8}}
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,8,1] => [3,2,6,7,5,4,1,8] => {{1,3,4,6,7},{2},{5},{8}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,6,7,1] => [1,4,6,7,5,3,2,8] => {{1},{2,4,7},{3,6},{5},{8}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,8,1] => [2,4,6,7,5,3,1,8] => {{1,2,4,7},{3,6},{5},{8}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,5,6,7,1] => [1,5,6,7,4,3,2,8] => {{1},{2,4,5,7},{3,6},{8}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [2,5,6,7,4,3,1,8] => {{1,2,4,5,7},{3,6},{8}}
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,7,8,1] => [3,5,6,7,4,2,1,8] => {{1,2,3,4,5,6,7},{8}}
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => [4,5,6,7,3,2,1,8] => {{1,4,7},{2,3,5,6},{8}}
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,7,8,1] => [5,4,6,7,3,2,1,8] => {{1,2,3,4,5,6,7},{8}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,7,1] => [1,6,5,7,4,3,2,8] => {{1},{2,3,4,5,6,7},{8}}
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,8,1] => [4,6,5,7,3,2,1,8] => {{1,4,7},{2,6},{3,5},{8}}
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,7,8,1] => [5,6,4,7,3,2,1,8] => {{1,3,4,5,7},{2,6},{8}}
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => [6,5,4,7,3,2,1,8] => {{1,2,3,4,5,6,7},{8}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => [1,2,7,6,5,4,3,8] => {{1},{2},{3,7},{4,6},{5},{8}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,6,1] => [2,1,7,6,5,4,3,8] => {{1,2},{3,7},{4,6},{5},{8}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,8,1] => [2,3,7,6,5,4,1,8] => {{1,2,3,7},{4,6},{5},{8}}
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => [3,2,7,6,5,4,1,8] => {{1,3,7},{2},{4,6},{5},{8}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,6,7,1] => [1,4,7,6,5,3,2,8] => {{1},{2,3,4,6,7},{5},{8}}
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,7,8,1] => [3,4,7,6,5,2,1,8] => {{1,3,7},{2,4,6},{5},{8}}
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,7,8,1] => [4,3,7,6,5,2,1,8] => {{1,2,3,4,6,7},{5},{8}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,8,1] => [2,5,7,6,4,3,1,8] => {{1,2,3,4,5,6,7},{8}}
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,8,1] => [3,5,7,6,4,2,1,8] => {{1,3,7},{2,4,5,6},{8}}
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,8,1] => [4,5,7,6,3,2,1,8] => {{1,2,3,4,5,6,7},{8}}
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,8,1] => [5,4,7,6,3,2,1,8] => {{1,3,5,7},{2,4,6},{8}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,7,1] => [1,6,7,5,4,3,2,8] => {{1},{2,3,6,7},{4,5},{8}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [2,6,7,5,4,3,1,8] => {{1,2,3,6,7},{4,5},{8}}
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,8,1] => [4,6,7,5,3,2,1,8] => {{1,3,4,5,7},{2,6},{8}}
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => [5,6,7,4,3,2,1,8] => {{1,3,5,7},{2,6},{4},{8}}
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => [6,5,7,4,3,2,1,8] => {{1,2,3,5,6,7},{4},{8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,7,1] => [1,7,6,5,4,3,2,8] => {{1},{2,7},{3,6},{4,5},{8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [2,7,6,5,4,3,1,8] => {{1,2,7},{3,6},{4,5},{8}}
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => [4,7,6,5,3,2,1,8] => {{1,2,3,4,5,6,7},{8}}
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => [5,7,6,4,3,2,1,8] => {{1,2,3,5,6,7},{4},{8}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => [6,7,5,4,3,2,1,8] => {{1,2,6,7},{3,5},{4},{8}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [7,6,5,4,3,2,1,8] => {{1,7},{2,6},{3,5},{4},{8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,8,7] => {{1},{2},{3},{4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => [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] => [8,6,7,5,4,3,1,2] => [1,3,2,4,5,6,8,7] => {{1},{2,3},{4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,1,2] => [2,3,1,4,5,6,8,7] => {{1,2,3},{4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,1,2] => [3,2,1,4,5,6,8,7] => {{1,3},{2},{4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => [1,2,4,3,5,6,8,7] => {{1},{2},{3,4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,1,2] => [2,1,4,3,5,6,8,7] => {{1,2},{3,4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,1,2] => [1,3,4,2,5,6,8,7] => {{1},{2,3,4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,1,2] => [2,3,4,1,5,6,8,7] => {{1,2,3,4},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,1,2] => [3,2,4,1,5,6,8,7] => {{1,3,4},{2},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,1,2] => [1,4,3,2,5,6,8,7] => {{1},{2,4},{3},{5},{6},{7,8}}
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [4,3,2,1,5,6,8,7] => {{1,4},{2,3},{5},{6},{7,8}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => [1,2,3,5,4,6,8,7] => {{1},{2},{3},{4,5},{6},{7,8}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => [2,1,3,5,4,6,8,7] => {{1,2},{3},{4,5},{6},{7,8}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,3,1,2] => [2,1,4,5,3,6,8,7] => {{1,2},{3,4,5},{6},{7,8}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,1,2] => [2,3,4,5,1,6,8,7] => {{1,2,3,4,5},{6},{7,8}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,1,2] => [2,4,3,5,1,6,8,7] => {{1,2,4,5},{3},{6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,1,2] => [1,2,5,4,3,6,8,7] => {{1},{2},{3,5},{4},{6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,1,2] => [2,1,5,4,3,6,8,7] => {{1,2},{3,5},{4},{6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,1,2] => [1,3,5,4,2,6,8,7] => {{1},{2,3,5},{4},{6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,1,2] => [2,3,5,4,1,6,8,7] => {{1,2,3,5},{4},{6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,1,2] => [3,2,5,4,1,6,8,7] => {{1,3,5},{2},{4},{6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,1,2] => [1,4,5,3,2,6,8,7] => {{1},{2,3,4,5},{6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,1,2] => [2,4,5,3,1,6,8,7] => {{1,2,3,4,5},{6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,1,2] => [3,4,5,2,1,6,8,7] => {{1,3,5},{2,4},{6},{7,8}}
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,1,2] => [4,3,5,2,1,6,8,7] => {{1,2,3,4,5},{6},{7,8}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,1,2] => [2,5,4,3,1,6,8,7] => {{1,2,5},{3,4},{6},{7,8}}
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,1,2] => [4,5,3,2,1,6,8,7] => {{1,2,4,5},{3},{6},{7,8}}
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => [5,4,3,2,1,6,8,7] => {{1,5},{2,4},{3},{6},{7,8}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => [1,2,3,4,6,5,8,7] => {{1},{2},{3},{4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,1,2] => [2,1,3,4,6,5,8,7] => {{1,2},{3},{4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,1,2] => [1,3,2,4,6,5,8,7] => {{1},{2,3},{4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,1,2] => [2,3,1,4,6,5,8,7] => {{1,2,3},{4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => [1,2,4,3,6,5,8,7] => {{1},{2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,4,1,2] => [1,3,4,2,6,5,8,7] => {{1},{2,3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,1,2] => [2,3,4,1,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => [3,2,4,1,6,5,8,7] => {{1,3,4},{2},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => [2,4,3,1,6,5,8,7] => {{1,2,4},{3},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => [3,4,2,1,6,5,8,7] => {{1,2,3,4},{5,6},{7,8}}
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [4,3,2,1,6,5,8,7] => {{1,4},{2,3},{5,6},{7,8}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,5,1,2] => [1,2,3,5,6,4,8,7] => {{1},{2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,5,1,2] => [2,1,3,5,6,4,8,7] => {{1,2},{3},{4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,5,1,2] => [1,3,2,5,6,4,8,7] => {{1},{2,3},{4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,1,2] => [1,2,4,5,6,3,8,7] => {{1},{2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => [2,1,4,5,6,3,8,7] => {{1,2},{3,4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,1,2] => [1,3,4,5,6,2,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => [2,3,4,5,6,1,8,7] => {{1,2,3,4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,1,2] => [2,4,3,5,6,1,8,7] => {{1,2,4,5,6},{3},{7,8}}
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,1,2] => [3,4,2,5,6,1,8,7] => {{1,2,3,4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => [4,3,2,5,6,1,8,7] => {{1,4,5,6},{2,3},{7,8}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,6,1,2] => [2,1,5,4,6,3,8,7] => {{1,2},{3,5,6},{4},{7,8}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => [3,2,5,4,6,1,8,7] => {{1,3,5,6},{2},{4},{7,8}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,1,2] => [2,4,5,3,6,1,8,7] => {{1,2,3,4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,1,2] => [3,4,5,2,6,1,8,7] => {{1,3,5,6},{2,4},{7,8}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => [4,3,5,2,6,1,8,7] => {{1,2,3,4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,8,1,2] => [2,5,4,3,6,1,8,7] => {{1,2,5,6},{3,4},{7,8}}
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,1,2] => [3,5,4,2,6,1,8,7] => {{1,2,3,4,5,6},{7,8}}
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,1,2] => [4,5,3,2,6,1,8,7] => {{1,2,4,5,6},{3},{7,8}}
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => [5,4,3,2,6,1,8,7] => {{1,5,6},{2,4},{3},{7,8}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,1,2] => [1,2,3,6,5,4,8,7] => {{1},{2},{3},{4,6},{5},{7,8}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,1,2] => [2,1,3,6,5,4,8,7] => {{1,2},{3},{4,6},{5},{7,8}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,1,2] => [1,3,2,6,5,4,8,7] => {{1},{2,3},{4,6},{5},{7,8}}
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,5,1,2] => [2,3,1,6,5,4,8,7] => {{1,2,3},{4,6},{5},{7,8}}
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,1,2] => [3,2,1,6,5,4,8,7] => {{1,3},{2},{4,6},{5},{7,8}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,1,2] => [2,1,4,6,5,3,8,7] => {{1,2},{3,4,6},{5},{7,8}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,8,1,2] => [2,4,3,6,5,1,8,7] => {{1,2,4,6},{3},{5},{7,8}}
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,8,1,2] => [3,4,2,6,5,1,8,7] => {{1,2,3,4,6},{5},{7,8}}
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,8,1,2] => [4,3,2,6,5,1,8,7] => {{1,4,6},{2,3},{5},{7,8}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => [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] => [7,6,4,3,5,8,1,2] => [2,3,5,6,4,1,8,7] => {{1,2,3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,8,1,2] => [3,2,5,6,4,1,8,7] => {{1,3,4,5,6},{2},{7,8}}
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,1,2] => [3,4,5,6,2,1,8,7] => {{1,2,3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,1,2] => [4,3,5,6,2,1,8,7] => {{1,4,6},{2,3,5},{7,8}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,7,1,2] => [1,5,4,6,3,2,8,7] => {{1},{2,3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,1,2] => [4,5,3,6,2,1,8,7] => {{1,4,6},{2,5},{3},{7,8}}
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,1,2] => [5,4,3,6,2,1,8,7] => {{1,2,4,5,6},{3},{7,8}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => [2,1,6,5,4,3,8,7] => {{1,2},{3,6},{4,5},{7,8}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,7,1,2] => [1,3,6,5,4,2,8,7] => {{1},{2,3,6},{4,5},{7,8}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,1,2] => [2,3,6,5,4,1,8,7] => {{1,2,3,6},{4,5},{7,8}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,1,2] => [2,4,6,5,3,1,8,7] => {{1,2,3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,8,1,2] => [3,4,6,5,2,1,8,7] => {{1,3,6},{2,4,5},{7,8}}
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => [4,3,6,5,2,1,8,7] => {{1,2,3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => [1,5,6,4,3,2,8,7] => {{1},{2,3,5,6},{4},{7,8}}
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => [3,5,6,4,2,1,8,7] => {{1,3,6},{2,5},{4},{7,8}}
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => [4,5,6,3,2,1,8,7] => {{1,3,4,6},{2,5},{7,8}}
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => [5,4,6,3,2,1,8,7] => {{1,2,3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [1,6,5,4,3,2,8,7] => {{1},{2,6},{3,5},{4},{7,8}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,1,2] => [2,6,5,4,3,1,8,7] => {{1,2,6},{3,5},{4},{7,8}}
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => [3,6,5,4,2,1,8,7] => {{1,2,3,5,6},{4},{7,8}}
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,1,2] => [4,6,5,3,2,1,8,7] => {{1,2,3,4,5,6},{7,8}}
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => [5,6,4,3,2,1,8,7] => {{1,2,5,6},{3,4},{7,8}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [6,5,4,3,2,1,8,7] => {{1,6},{2,5},{3,4},{7,8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => [1,2,3,4,5,7,8,6] => {{1},{2},{3},{4},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,1,3] => [2,1,3,4,5,7,8,6] => {{1,2},{3},{4},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,1,3] => [1,3,2,4,5,7,8,6] => {{1},{2,3},{4},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => [2,3,1,4,5,7,8,6] => {{1,2,3},{4},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,2,1,3] => [3,2,1,4,5,7,8,6] => {{1,3},{2},{4},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,1,3] => [1,2,4,3,5,7,8,6] => {{1},{2},{3,4},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,1,3] => [2,1,4,3,5,7,8,6] => {{1,2},{3,4},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,1,3] => [1,3,4,2,5,7,8,6] => {{1},{2,3,4},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,1,3] => [2,3,4,1,5,7,8,6] => {{1,2,3,4},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,1,3] => [3,2,4,1,5,7,8,6] => {{1,3,4},{2},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,1,3] => [1,4,3,2,5,7,8,6] => {{1},{2,4},{3},{5},{6,7,8}}
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => [4,3,2,1,5,7,8,6] => {{1,4},{2,3},{5},{6,7,8}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,1,3] => [1,2,3,5,4,7,8,6] => {{1},{2},{3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,2,1,3] => [2,1,3,5,4,7,8,6] => {{1,2},{3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,1,3] => [1,3,2,5,4,7,8,6] => {{1},{2,3},{4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,2,1,3] => [1,2,4,5,3,7,8,6] => {{1},{2},{3,4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,1,3] => [1,3,4,5,2,7,8,6] => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,1,3] => [2,3,4,5,1,7,8,6] => {{1,2,3,4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,1,3] => [2,4,3,5,1,7,8,6] => {{1,2,4,5},{3},{6,7,8}}
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,1,3] => [3,4,2,5,1,7,8,6] => {{1,2,3,4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,2,1,3] => [4,3,2,5,1,7,8,6] => {{1,4,5},{2,3},{6,7,8}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,1,3] => [1,2,5,4,3,7,8,6] => {{1},{2},{3,5},{4},{6,7,8}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,1,3] => [1,3,5,4,2,7,8,6] => {{1},{2,3,5},{4},{6,7,8}}
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,1,3] => [3,2,5,4,1,7,8,6] => {{1,3,5},{2},{4},{6,7,8}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,2,1,3] => [1,4,5,3,2,7,8,6] => {{1},{2,3,4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,2,1,3] => [2,4,5,3,1,7,8,6] => {{1,2,3,4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,1,3] => [1,5,4,3,2,7,8,6] => {{1},{2,5},{3,4},{6,7,8}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,2,1,3] => [2,5,4,3,1,7,8,6] => {{1,2,5},{3,4},{6,7,8}}
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,2,1,3] => [3,5,4,2,1,7,8,6] => {{1,2,3,4,5},{6,7,8}}
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => [5,4,3,2,1,7,8,6] => {{1,5},{2,4},{3},{6,7,8}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,4] => [1,2,3,4,6,7,8,5] => {{1},{2},{3},{4},{5,6,7,8}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,1,4] => [2,1,3,4,6,7,8,5] => {{1,2},{3},{4},{5,6,7,8}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,1,4] => [1,3,2,4,6,7,8,5] => {{1},{2,3},{4},{5,6,7,8}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,1,4] => [2,3,1,4,6,7,8,5] => {{1,2,3},{4},{5,6,7,8}}
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,1,4] => [3,2,1,4,6,7,8,5] => {{1,3},{2},{4},{5,6,7,8}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,1,4] => [1,2,4,3,6,7,8,5] => {{1},{2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,1,4] => [2,1,4,3,6,7,8,5] => {{1,2},{3,4},{5,6,7,8}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,1,4] => [1,3,4,2,6,7,8,5] => {{1},{2,3,4},{5,6,7,8}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => [2,3,4,1,6,7,8,5] => {{1,2,3,4},{5,6,7,8}}
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,1,4] => [3,2,4,1,6,7,8,5] => {{1,3,4},{2},{5,6,7,8}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,1,4] => [1,4,3,2,6,7,8,5] => {{1},{2,4},{3},{5,6,7,8}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,2,1,4] => [2,4,3,1,6,7,8,5] => {{1,2,4},{3},{5,6,7,8}}
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,2,1,4] => [3,4,2,1,6,7,8,5] => {{1,2,3,4},{5,6,7,8}}
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => [4,3,2,1,6,7,8,5] => {{1,4},{2,3},{5,6,7,8}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => [1,2,3,5,6,7,8,4] => {{1},{2},{3},{4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,1,5] => [2,1,3,5,6,7,8,4] => {{1,2},{3},{4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,1,5] => [1,3,2,5,6,7,8,4] => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,1,5] => [2,3,1,5,6,7,8,4] => {{1,2,3},{4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => [3,2,1,5,6,7,8,4] => {{1,3},{2},{4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,1,6] => [1,2,4,5,6,7,8,3] => {{1},{2},{3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => [2,1,4,5,6,7,8,3] => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => [1,3,4,5,6,7,8,2] => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [2,3,4,5,6,7,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [3,2,4,5,6,7,8,1] => {{1,3,4,5,6,7,8},{2}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,1,7] => [1,4,3,5,6,7,8,2] => {{1},{2,4,5,6,7,8},{3}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,1,8] => [2,4,3,5,6,7,8,1] => {{1,2,4,5,6,7,8},{3}}
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => [3,4,2,5,6,7,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [4,3,2,5,6,7,8,1] => {{1,4,5,6,7,8},{2,3}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,2,1,6] => [1,2,5,4,6,7,8,3] => {{1},{2},{3,5,6,7,8},{4}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,2,1,6] => [2,1,5,4,6,7,8,3] => {{1,2},{3,5,6,7,8},{4}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => [2,3,5,4,6,7,8,1] => {{1,2,3,5,6,7,8},{4}}
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,1,8] => [3,2,5,4,6,7,8,1] => {{1,3,5,6,7,8},{2},{4}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,1,7] => [1,4,5,3,6,7,8,2] => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,1,8] => [2,4,5,3,6,7,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => [3,4,5,2,6,7,8,1] => {{1,3,5,6,7,8},{2,4}}
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,2,1,8] => [4,3,5,2,6,7,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => [1,5,4,3,6,7,8,2] => {{1},{2,5,6,7,8},{3,4}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => [2,5,4,3,6,7,8,1] => {{1,2,5,6,7,8},{3,4}}
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,1,8] => [3,5,4,2,6,7,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1,8] => [4,5,3,2,6,7,8,1] => {{1,2,4,5,6,7,8},{3}}
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => [5,4,3,2,6,7,8,1] => {{1,5,6,7,8},{2,4},{3}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => [1,2,3,6,5,7,8,4] => {{1},{2},{3},{4,6,7,8},{5}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,2,1,5] => [1,3,2,6,5,7,8,4] => {{1},{2,3},{4,6,7,8},{5}}
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,1,5] => [3,2,1,6,5,7,8,4] => {{1,3},{2},{4,6,7,8},{5}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,1,7] => [1,3,4,6,5,7,8,2] => {{1},{2,3,4,6,7,8},{5}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,1,8] => [2,3,4,6,5,7,8,1] => {{1,2,3,4,6,7,8},{5}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,1,7] => [1,4,3,6,5,7,8,2] => {{1},{2,4,6,7,8},{3},{5}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => [2,4,3,6,5,7,8,1] => {{1,2,4,6,7,8},{3},{5}}
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,1,8] => [3,4,2,6,5,7,8,1] => {{1,2,3,4,6,7,8},{5}}
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => [4,3,2,6,5,7,8,1] => {{1,4,6,7,8},{2,3},{5}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,1,6] => [1,2,5,6,4,7,8,3] => {{1},{2},{3,4,5,6,7,8}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,2,1,6] => [2,1,5,6,4,7,8,3] => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => [2,3,5,6,4,7,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,1,8] => [3,2,5,6,4,7,8,1] => {{1,3,4,5,6,7,8},{2}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => [2,4,5,6,3,7,8,1] => {{1,2,4,6,7,8},{3,5}}
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,1,8] => [3,4,5,6,2,7,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,1,8] => [4,3,5,6,2,7,8,1] => {{1,4,6,7,8},{2,3,5}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,1,7] => [1,5,4,6,3,7,8,2] => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,2,1,8] => [3,5,4,6,2,7,8,1] => {{1,3,4,6,7,8},{2,5}}
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,2,1,8] => [5,4,3,6,2,7,8,1] => {{1,2,4,5,6,7,8},{3}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,2,1,6] => [1,2,6,5,4,7,8,3] => {{1},{2},{3,6,7,8},{4,5}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => [2,3,6,5,4,7,8,1] => {{1,2,3,6,7,8},{4,5}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,2,1,8] => [2,4,6,5,3,7,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,1,8] => [3,4,6,5,2,7,8,1] => {{1,3,6,7,8},{2,4,5}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,6,2,1,8] => [2,5,6,4,3,7,8,1] => {{1,2,3,5,6,7,8},{4}}
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,1,8] => [3,5,6,4,2,7,8,1] => {{1,3,6,7,8},{2,5},{4}}
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,1,8] => [4,5,6,3,2,7,8,1] => {{1,3,4,6,7,8},{2,5}}
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,2,1,8] => [5,4,6,3,2,7,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,1,8] => [2,6,5,4,3,7,8,1] => {{1,2,6,7,8},{3,5},{4}}
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,2,1,8] => [3,6,5,4,2,7,8,1] => {{1,2,3,5,6,7,8},{4}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8] => [6,5,4,3,2,7,8,1] => {{1,6,7,8},{2,5},{3,4}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => [1,2,3,4,7,6,8,5] => {{1},{2},{3},{4},{5,7,8},{6}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,3,1,4] => [2,1,3,4,7,6,8,5] => {{1,2},{3},{4},{5,7,8},{6}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,1,4] => [1,3,2,4,7,6,8,5] => {{1},{2,3},{4},{5,7,8},{6}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,1,4] => [2,3,1,4,7,6,8,5] => {{1,2,3},{4},{5,7,8},{6}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,1,4] => [1,2,4,3,7,6,8,5] => {{1},{2},{3,4},{5,7,8},{6}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,1,4] => [2,1,4,3,7,6,8,5] => {{1,2},{3,4},{5,7,8},{6}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,1,4] => [1,3,4,2,7,6,8,5] => {{1},{2,3,4},{5,7,8},{6}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,1,4] => [2,3,4,1,7,6,8,5] => {{1,2,3,4},{5,7,8},{6}}
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => [3,2,4,1,7,6,8,5] => {{1,3,4},{2},{5,7,8},{6}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,1,4] => [1,4,3,2,7,6,8,5] => {{1},{2,4},{3},{5,7,8},{6}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => [2,4,3,1,7,6,8,5] => {{1,2,4},{3},{5,7,8},{6}}
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,1,4] => [3,4,2,1,7,6,8,5] => {{1,2,3,4},{5,7,8},{6}}
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => [4,3,2,1,7,6,8,5] => {{1,4},{2,3},{5,7,8},{6}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,1,5] => [1,2,3,5,7,6,8,4] => {{1},{2},{3},{4,5,7,8},{6}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,1,5] => [2,3,1,5,7,6,8,4] => {{1,2,3},{4,5,7,8},{6}}
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => [3,2,1,5,7,6,8,4] => {{1,3},{2},{4,5,7,8},{6}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,1,7] => [1,3,4,5,7,6,8,2] => {{1},{2,3,4,5,7,8},{6}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,1,8] => [2,3,4,5,7,6,8,1] => {{1,2,3,4,5,7,8},{6}}
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => [3,2,4,5,7,6,8,1] => {{1,3,4,5,7,8},{2},{6}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => [2,4,3,5,7,6,8,1] => {{1,2,4,5,7,8},{3},{6}}
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,3,1,8] => [3,4,2,5,7,6,8,1] => {{1,2,3,4,5,7,8},{6}}
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => [4,3,2,5,7,6,8,1] => {{1,4,5,7,8},{2,3},{6}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,3,1,6] => [1,2,5,4,7,6,8,3] => {{1},{2},{3,5,7,8},{4},{6}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,1,6] => [2,1,5,4,7,6,8,3] => {{1,2},{3,5,7,8},{4},{6}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,2,3,1,7] => [1,3,5,4,7,6,8,2] => {{1},{2,3,5,7,8},{4},{6}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => [2,3,5,4,7,6,8,1] => {{1,2,3,5,7,8},{4},{6}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [3,2,5,4,7,6,8,1] => {{1,3,5,7,8},{2},{4},{6}}
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,1,8] => [3,4,5,2,7,6,8,1] => {{1,3,5,7,8},{2,4},{6}}
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [4,3,5,2,7,6,8,1] => {{1,2,3,4,5,7,8},{6}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,1,8] => [2,5,4,3,7,6,8,1] => {{1,2,5,7,8},{3,4},{6}}
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,2,3,1,8] => [3,5,4,2,7,6,8,1] => {{1,2,3,4,5,7,8},{6}}
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => [5,4,3,2,7,6,8,1] => {{1,5,7,8},{2,4},{3},{6}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => [1,2,3,6,7,5,8,4] => {{1},{2},{3},{4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,1,5] => [1,3,2,6,7,5,8,4] => {{1},{2,3},{4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,4,1,5] => [2,3,1,6,7,5,8,4] => {{1,2,3},{4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => [3,2,1,6,7,5,8,4] => {{1,3},{2},{4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,4,1,6] => [2,1,4,6,7,5,8,3] => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,1,7] => [1,3,4,6,7,5,8,2] => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,1,8] => [2,3,4,6,7,5,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,2,4,1,8] => [2,4,3,6,7,5,8,1] => {{1,2,4,5,6,7,8},{3}}
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => [3,4,2,6,7,5,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => [4,3,2,6,7,5,8,1] => {{1,4,5,6,7,8},{2,3}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,1,6] => [1,2,5,6,7,4,8,3] => {{1},{2},{3,5,7,8},{4,6}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,1,6] => [2,1,5,6,7,4,8,3] => {{1,2},{3,5,7,8},{4,6}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,1,7] => [1,3,5,6,7,4,8,2] => {{1},{2,3,5,7,8},{4,6}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,1,8] => [2,3,5,6,7,4,8,1] => {{1,2,3,5,7,8},{4,6}}
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,1,8] => [3,2,5,6,7,4,8,1] => {{1,3,5,7,8},{2},{4,6}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,1,7] => [1,4,5,6,7,3,8,2] => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,1,8] => [2,4,5,6,7,3,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,1,8] => [3,4,5,6,7,2,8,1] => {{1,3,5,7,8},{2,4,6}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,6,1,7] => [1,5,4,6,7,3,8,2] => {{1},{2,5,7,8},{3,4,6}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,1,8] => [2,5,4,6,7,3,8,1] => {{1,2,5,7,8},{3,4,6}}
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,2,7,1,8] => [3,5,4,6,7,2,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,1,8] => [4,5,3,6,7,2,8,1] => {{1,2,4,5,6,7,8},{3}}
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,7,1,8] => [5,4,3,6,7,2,8,1] => {{1,5,7,8},{2,4,6},{3}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,1,6] => [2,1,6,5,7,4,8,3] => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => [3,2,6,5,7,4,8,1] => {{1,3,4,5,6,7,8},{2}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,1,7] => [1,4,6,5,7,3,8,2] => {{1},{2,4,5,7,8},{3,6}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,1,8] => [2,4,6,5,7,3,8,1] => {{1,2,4,5,7,8},{3,6}}
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,7,1,8] => [3,4,6,5,7,2,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [4,3,6,5,7,2,8,1] => {{1,4,5,7,8},{2,3,6}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,1,7] => [1,5,6,4,7,3,8,2] => {{1},{2,5,7,8},{3,6},{4}}
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,2,7,1,8] => [3,5,6,4,7,2,8,1] => {{1,2,3,5,6,7,8},{4}}
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,1,8] => [4,5,6,3,7,2,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [5,4,6,3,7,2,8,1] => {{1,5,7,8},{2,3,4,6}}
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,1,8] => [3,6,5,4,7,2,8,1] => {{1,3,5,7,8},{2,6},{4}}
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,1,8] => [4,6,5,3,7,2,8,1] => {{1,3,4,5,7,8},{2,6}}
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => [6,5,4,3,7,2,8,1] => {{1,2,5,6,7,8},{3,4}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => [1,2,3,7,6,5,8,4] => {{1},{2},{3},{4,7,8},{5,6}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,1,5] => [1,3,2,7,6,5,8,4] => {{1},{2,3},{4,7,8},{5,6}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,1,5] => [2,3,1,7,6,5,8,4] => {{1,2,3},{4,7,8},{5,6}}
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,1,5] => [3,2,1,7,6,5,8,4] => {{1,3},{2},{4,7,8},{5,6}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,3,4,1,6] => [1,2,4,7,6,5,8,3] => {{1},{2},{3,4,7,8},{5,6}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,4,1,6] => [2,1,4,7,6,5,8,3] => {{1,2},{3,4,7,8},{5,6}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,4,1,7] => [1,3,4,7,6,5,8,2] => {{1},{2,3,4,7,8},{5,6}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => [2,3,4,7,6,5,8,1] => {{1,2,3,4,7,8},{5,6}}
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => [3,2,4,7,6,5,8,1] => {{1,3,4,7,8},{2},{5,6}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => [2,4,3,7,6,5,8,1] => {{1,2,4,7,8},{3},{5,6}}
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => [3,4,2,7,6,5,8,1] => {{1,2,3,4,7,8},{5,6}}
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => [4,3,2,7,6,5,8,1] => {{1,4,7,8},{2,3},{5,6}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,3,5,1,6] => [1,2,5,7,6,4,8,3] => {{1},{2},{3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,5,1,6] => [2,1,5,7,6,4,8,3] => {{1,2},{3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,1,8] => [2,3,5,7,6,4,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,1,8] => [3,2,5,7,6,4,8,1] => {{1,3,4,5,6,7,8},{2}}
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,7,1,8] => [3,4,5,7,6,2,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,1,8] => [2,5,4,7,6,3,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,7,1,8] => [3,5,4,7,6,2,8,1] => {{1,3,4,7,8},{2,5,6}}
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,7,1,8] => [5,4,3,7,6,2,8,1] => {{1,2,4,5,6,7,8},{3}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,1,6] => [2,1,6,7,5,4,8,3] => {{1,2},{3,4,6,7,8},{5}}
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,1,8] => [3,2,6,7,5,4,8,1] => {{1,3,4,6,7,8},{2},{5}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,6,1,7] => [1,4,6,7,5,3,8,2] => {{1},{2,4,7,8},{3,6},{5}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,1,8] => [2,4,6,7,5,3,8,1] => {{1,2,4,7,8},{3,6},{5}}
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,1,8] => [3,4,6,7,5,2,8,1] => {{1,2,3,4,6,7,8},{5}}
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,7,1,8] => [4,3,6,7,5,2,8,1] => {{1,4,7,8},{2,3,6},{5}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,5,6,1,7] => [1,5,6,7,4,3,8,2] => {{1},{2,4,5,7,8},{3,6}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,6,1,8] => [2,5,6,7,4,3,8,1] => {{1,2,4,5,7,8},{3,6}}
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,7,1,8] => [3,5,6,7,4,2,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => [4,5,6,7,3,2,8,1] => {{1,4,7,8},{2,3,5,6}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,1,7] => [1,6,5,7,4,3,8,2] => {{1},{2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [7,3,4,2,5,6,1,8] => [2,6,5,7,4,3,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,1,8] => [4,6,5,7,3,2,8,1] => {{1,4,7,8},{2,6},{3,5}}
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,1,8] => [6,5,4,7,3,2,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,1,6] => [1,2,7,6,5,4,8,3] => {{1},{2},{3,7,8},{4,6},{5}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,1,6] => [2,1,7,6,5,4,8,3] => {{1,2},{3,7,8},{4,6},{5}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,1,8] => [2,3,7,6,5,4,8,1] => {{1,2,3,7,8},{4,6},{5}}
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,1,8] => [3,2,7,6,5,4,8,1] => {{1,3,7,8},{2},{4,6},{5}}
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,7,1,8] => [3,4,7,6,5,2,8,1] => {{1,3,7,8},{2,4,6},{5}}
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,7,1,8] => [4,3,7,6,5,2,8,1] => {{1,2,3,4,6,7,8},{5}}
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,1,8] => [3,5,7,6,4,2,8,1] => {{1,3,7,8},{2,4,5,6}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,1,7] => [1,6,7,5,4,3,8,2] => {{1},{2,3,6,7,8},{4,5}}
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,1,8] => [4,6,7,5,3,2,8,1] => {{1,3,4,5,7,8},{2,6}}
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,1,8] => [5,6,7,4,3,2,8,1] => {{1,3,5,7,8},{2,6},{4}}
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,1,8] => [6,5,7,4,3,2,8,1] => {{1,2,3,5,6,7,8},{4}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,1,7] => [1,7,6,5,4,3,8,2] => {{1},{2,7,8},{3,6},{4,5}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,1,8] => [2,7,6,5,4,3,8,1] => {{1,2,7,8},{3,6},{4,5}}
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,1,8] => [4,7,6,5,3,2,8,1] => {{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,1,8] => [5,7,6,4,3,2,8,1] => {{1,2,3,5,6,7,8},{4}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => [6,7,5,4,3,2,8,1] => {{1,2,6,7,8},{3,5},{4}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [7,6,5,4,3,2,8,1] => {{1,7,8},{2,6},{3,5},{4}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => [1,2,3,4,5,8,7,6] => {{1},{2},{3},{4},{5},{6,8},{7}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,1,2,3] => [2,1,3,4,5,8,7,6] => {{1,2},{3},{4},{5},{6,8},{7}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,1,2,3] => [1,3,2,4,5,8,7,6] => {{1},{2,3},{4},{5},{6,8},{7}}
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [3,2,1,4,5,8,7,6] => {{1,3},{2},{4},{5},{6,8},{7}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,1,2,3] => [1,2,4,3,5,8,7,6] => {{1},{2},{3,4},{5},{6,8},{7}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,1,2,3] => [2,1,4,3,5,8,7,6] => {{1,2},{3,4},{5},{6,8},{7}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,1,2,3] => [2,3,4,1,5,8,7,6] => {{1,2,3,4},{5},{6,8},{7}}
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,1,2,3] => [3,2,4,1,5,8,7,6] => {{1,3,4},{2},{5},{6,8},{7}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => [1,4,3,2,5,8,7,6] => {{1},{2,4},{3},{5},{6,8},{7}}
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,1,2,3] => [2,4,3,1,5,8,7,6] => {{1,2,4},{3},{5},{6,8},{7}}
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => [4,3,2,1,5,8,7,6] => {{1,4},{2,3},{5},{6,8},{7}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => [1,2,3,5,4,8,7,6] => {{1},{2},{3},{4,5},{6,8},{7}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,1,2,3] => [2,1,3,5,4,8,7,6] => {{1,2},{3},{4,5},{6,8},{7}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => [1,3,2,5,4,8,7,6] => {{1},{2,3},{4,5},{6,8},{7}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,1,2,3] => [1,2,4,5,3,8,7,6] => {{1},{2},{3,4,5},{6,8},{7}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,1,2,3] => [2,1,4,5,3,8,7,6] => {{1,2},{3,4,5},{6,8},{7}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,1,2,3] => [1,3,4,5,2,8,7,6] => {{1},{2,3,4,5},{6,8},{7}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,1,2,3] => [2,3,4,5,1,8,7,6] => {{1,2,3,4,5},{6,8},{7}}
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,1,2,3] => [3,2,4,5,1,8,7,6] => {{1,3,4,5},{2},{6,8},{7}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,1,2,3] => [2,4,3,5,1,8,7,6] => {{1,2,4,5},{3},{6,8},{7}}
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,1,2,3] => [3,4,2,5,1,8,7,6] => {{1,2,3,4,5},{6,8},{7}}
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,1,2,3] => [4,3,2,5,1,8,7,6] => {{1,4,5},{2,3},{6,8},{7}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => [1,2,5,4,3,8,7,6] => {{1},{2},{3,5},{4},{6,8},{7}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => [2,1,5,4,3,8,7,6] => {{1,2},{3,5},{4},{6,8},{7}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,1,2,3] => [2,3,5,4,1,8,7,6] => {{1,2,3,5},{4},{6,8},{7}}
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => [3,2,5,4,1,8,7,6] => {{1,3,5},{2},{4},{6,8},{7}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,1,2,3] => [1,4,5,3,2,8,7,6] => {{1},{2,3,4,5},{6,8},{7}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,1,2,3] => [2,4,5,3,1,8,7,6] => {{1,2,3,4,5},{6,8},{7}}
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => [3,4,5,2,1,8,7,6] => {{1,3,5},{2,4},{6,8},{7}}
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,1,2,3] => [4,3,5,2,1,8,7,6] => {{1,2,3,4,5},{6,8},{7}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,1,2,3] => [1,5,4,3,2,8,7,6] => {{1},{2,5},{3,4},{6,8},{7}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,1,2,3] => [2,5,4,3,1,8,7,6] => {{1,2,5},{3,4},{6,8},{7}}
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,1,2,3] => [3,5,4,2,1,8,7,6] => {{1,2,3,4,5},{6,8},{7}}
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,1,2,3] => [4,5,3,2,1,8,7,6] => {{1,2,4,5},{3},{6,8},{7}}
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [5,4,3,2,1,8,7,6] => {{1,5},{2,4},{3},{6,8},{7}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => [1,2,3,4,6,8,7,5] => {{1},{2},{3},{4},{5,6,8},{7}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,1,2,4] => [1,3,2,4,6,8,7,5] => {{1},{2,3},{4},{5,6,8},{7}}
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,1,2,4] => [3,2,1,4,6,8,7,5] => {{1,3},{2},{4},{5,6,8},{7}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,1,2,4] => [1,2,4,3,6,8,7,5] => {{1},{2},{3,4},{5,6,8},{7}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => [2,1,4,3,6,8,7,5] => {{1,2},{3,4},{5,6,8},{7}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,1,2,4] => [1,3,4,2,6,8,7,5] => {{1},{2,3,4},{5,6,8},{7}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,1,2,4] => [2,3,4,1,6,8,7,5] => {{1,2,3,4},{5,6,8},{7}}
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => [3,2,4,1,6,8,7,5] => {{1,3,4},{2},{5,6,8},{7}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,1,2,4] => [1,4,3,2,6,8,7,5] => {{1},{2,4},{3},{5,6,8},{7}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => [2,4,3,1,6,8,7,5] => {{1,2,4},{3},{5,6,8},{7}}
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,1,2,4] => [3,4,2,1,6,8,7,5] => {{1,2,3,4},{5,6,8},{7}}
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => [4,3,2,1,6,8,7,5] => {{1,4},{2,3},{5,6,8},{7}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => [1,2,3,5,6,8,7,4] => {{1},{2},{3},{4,5,6,8},{7}}
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => [3,2,1,5,6,8,7,4] => {{1,3},{2},{4,5,6,8},{7}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,1,2,6] => [1,2,4,5,6,8,7,3] => {{1},{2},{3,4,5,6,8},{7}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,1,2,6] => [2,1,4,5,6,8,7,3] => {{1,2},{3,4,5,6,8},{7}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => [1,3,4,5,6,8,7,2] => {{1},{2,3,4,5,6,8},{7}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => [2,3,4,5,6,8,7,1] => {{1,2,3,4,5,6,8},{7}}
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,1,2,8] => [3,2,4,5,6,8,7,1] => {{1,3,4,5,6,8},{2},{7}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => [2,4,3,5,6,8,7,1] => {{1,2,4,5,6,8},{3},{7}}
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,1,2,8] => [3,4,2,5,6,8,7,1] => {{1,2,3,4,5,6,8},{7}}
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,1,2,8] => [4,3,2,5,6,8,7,1] => {{1,4,5,6,8},{2,3},{7}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,1,2,6] => [1,2,5,4,6,8,7,3] => {{1},{2},{3,5,6,8},{4},{7}}
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,1,2,8] => [3,2,5,4,6,8,7,1] => {{1,3,5,6,8},{2},{4},{7}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,1,2,7] => [1,4,5,3,6,8,7,2] => {{1},{2,3,4,5,6,8},{7}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,1,2,8] => [2,4,5,3,6,8,7,1] => {{1,2,3,4,5,6,8},{7}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,1,2,7] => [1,5,4,3,6,8,7,2] => {{1},{2,5,6,8},{3,4},{7}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,1,2,8] => [2,5,4,3,6,8,7,1] => {{1,2,5,6,8},{3,4},{7}}
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => [5,4,3,2,6,8,7,1] => {{1,5,6,8},{2,4},{3},{7}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => [1,2,3,6,5,8,7,4] => {{1},{2},{3},{4,6,8},{5},{7}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,1,2,5] => [2,1,3,6,5,8,7,4] => {{1,2},{3},{4,6,8},{5},{7}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,1,2,5] => [1,3,2,6,5,8,7,4] => {{1},{2,3},{4,6,8},{5},{7}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,1,2,5] => [2,3,1,6,5,8,7,4] => {{1,2,3},{4,6,8},{5},{7}}
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => [3,2,1,6,5,8,7,4] => {{1,3},{2},{4,6,8},{5},{7}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,1,2,6] => [1,2,4,6,5,8,7,3] => {{1},{2},{3,4,6,8},{5},{7}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,1,2,6] => [2,1,4,6,5,8,7,3] => {{1,2},{3,4,6,8},{5},{7}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,1,2,8] => [2,3,4,6,5,8,7,1] => {{1,2,3,4,6,8},{5},{7}}
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,1,2,8] => [3,2,4,6,5,8,7,1] => {{1,3,4,6,8},{2},{5},{7}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => [1,4,3,6,5,8,7,2] => {{1},{2,4,6,8},{3},{5},{7}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,1,2,8] => [2,4,3,6,5,8,7,1] => {{1,2,4,6,8},{3},{5},{7}}
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,1,2,8] => [3,4,2,6,5,8,7,1] => {{1,2,3,4,6,8},{5},{7}}
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,1,2,8] => [4,3,2,6,5,8,7,1] => {{1,4,6,8},{2,3},{5},{7}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,1,2,6] => [2,1,5,6,4,8,7,3] => {{1,2},{3,4,5,6,8},{7}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,1,2,8] => [2,3,5,6,4,8,7,1] => {{1,2,3,4,5,6,8},{7}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,1,2,7] => [1,4,5,6,3,8,7,2] => {{1},{2,4,6,8},{3,5},{7}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,1,2,8] => [2,4,5,6,3,8,7,1] => {{1,2,4,6,8},{3,5},{7}}
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,1,2,8] => [3,4,5,6,2,8,7,1] => {{1,2,3,4,5,6,8},{7}}
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,1,2,8] => [4,5,3,6,2,8,7,1] => {{1,4,6,8},{2,5},{3},{7}}
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,1,2,8] => [5,4,3,6,2,8,7,1] => {{1,2,4,5,6,8},{3},{7}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,1,2,6] => [1,2,6,5,4,8,7,3] => {{1},{2},{3,6,8},{4,5},{7}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,1,2,7] => [1,3,6,5,4,8,7,2] => {{1},{2,3,6,8},{4,5},{7}}
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,1,2,8] => [3,2,6,5,4,8,7,1] => {{1,3,6,8},{2},{4,5},{7}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,1,2,7] => [1,4,6,5,3,8,7,2] => {{1},{2,3,4,5,6,8},{7}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,1,2,8] => [2,4,6,5,3,8,7,1] => {{1,2,3,4,5,6,8},{7}}
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,1,2,8] => [4,3,6,5,2,8,7,1] => {{1,2,3,4,5,6,8},{7}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,1,2,7] => [1,5,6,4,3,8,7,2] => {{1},{2,3,5,6,8},{4},{7}}
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,1,2,8] => [3,5,6,4,2,8,7,1] => {{1,3,6,8},{2,5},{4},{7}}
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,1,2,8] => [4,5,6,3,2,8,7,1] => {{1,3,4,6,8},{2,5},{7}}
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,1,2,8] => [5,4,6,3,2,8,7,1] => {{1,2,3,4,5,6,8},{7}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [1,6,5,4,3,8,7,2] => {{1},{2,6,8},{3,5},{4},{7}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,1,2,8] => [2,6,5,4,3,8,7,1] => {{1,2,6,8},{3,5},{4},{7}}
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,1,2,8] => [3,6,5,4,2,8,7,1] => {{1,2,3,5,6,8},{4},{7}}
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,1,2,8] => [4,6,5,3,2,8,7,1] => {{1,2,3,4,5,6,8},{7}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [6,5,4,3,2,8,7,1] => {{1,6,8},{2,5},{3,4},{7}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => [1,2,3,4,7,8,6,5] => {{1},{2},{3},{4},{5,6,7,8}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => [2,1,3,4,7,8,6,5] => {{1,2},{3},{4},{5,6,7,8}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,1,3,4] => [2,3,1,4,7,8,6,5] => {{1,2,3},{4},{5,6,7,8}}
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => [3,2,1,4,7,8,6,5] => {{1,3},{2},{4},{5,6,7,8}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,1,3,4] => [1,2,4,3,7,8,6,5] => {{1},{2},{3,4},{5,6,7,8}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => [2,1,4,3,7,8,6,5] => {{1,2},{3,4},{5,6,7,8}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,1,3,4] => [1,3,4,2,7,8,6,5] => {{1},{2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,1,3,4] => [2,3,4,1,7,8,6,5] => {{1,2,3,4},{5,6,7,8}}
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,1,3,4] => [3,2,4,1,7,8,6,5] => {{1,3,4},{2},{5,6,7,8}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,1,3,4] => [2,4,3,1,7,8,6,5] => {{1,2,4},{3},{5,6,7,8}}
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => [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] => [5,6,7,8,2,1,3,4] => [4,3,2,1,7,8,6,5] => {{1,4},{2,3},{5,6,7,8}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => [1,2,3,5,7,8,6,4] => {{1},{2},{3},{4,5,6,7,8}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,1,3,5] => [1,3,2,5,7,8,6,4] => {{1},{2,3},{4,5,6,7,8}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,1,3,5] => [2,3,1,5,7,8,6,4] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => [3,2,1,5,7,8,6,4] => {{1,3},{2},{4,5,6,7,8}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,2,1,3,6] => [1,2,4,5,7,8,6,3] => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => [2,1,4,5,7,8,6,3] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => [1,3,4,5,7,8,6,2] => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => [2,3,4,5,7,8,6,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,1,3,8] => [3,2,4,5,7,8,6,1] => {{1,3,4,5,6,7,8},{2}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,1,3,7] => [1,4,3,5,7,8,6,2] => {{1},{2,4,5,6,7,8},{3}}
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => [3,4,2,5,7,8,6,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,1,3,8] => [4,3,2,5,7,8,6,1] => {{1,4,5,6,7,8},{2,3}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,1,3,6] => [1,2,5,4,7,8,6,3] => {{1},{2},{3,5,6,7,8},{4}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,1,3,6] => [2,1,5,4,7,8,6,3] => {{1,2},{3,5,6,7,8},{4}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,1,3,8] => [2,3,5,4,7,8,6,1] => {{1,2,3,5,6,7,8},{4}}
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,1,3,8] => [3,2,5,4,7,8,6,1] => {{1,3,5,6,7,8},{2},{4}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,2,1,3,7] => [1,4,5,3,7,8,6,2] => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => [2,4,5,3,7,8,6,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,1,3,8] => [3,4,5,2,7,8,6,1] => {{1,3,5,6,7,8},{2,4}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,1,3,8] => [2,5,4,3,7,8,6,1] => {{1,2,5,6,7,8},{3,4}}
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => [5,4,3,2,7,8,6,1] => {{1,5,6,7,8},{2,4},{3}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => [1,2,3,6,7,8,5,4] => {{1},{2},{3},{4,6,8},{5,7}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,1,4,5] => [2,1,3,6,7,8,5,4] => {{1,2},{3},{4,6,8},{5,7}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,1,4,5] => [1,3,2,6,7,8,5,4] => {{1},{2,3},{4,6,8},{5,7}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,1,4,5] => [2,3,1,6,7,8,5,4] => {{1,2,3},{4,6,8},{5,7}}
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => [3,2,1,6,7,8,5,4] => {{1,3},{2},{4,6,8},{5,7}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,1,4,6] => [1,2,4,6,7,8,5,3] => {{1},{2},{3,4,6,8},{5,7}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,1,4,6] => [2,1,4,6,7,8,5,3] => {{1,2},{3,4,6,8},{5,7}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,1,4,7] => [1,3,4,6,7,8,5,2] => {{1},{2,3,4,6,8},{5,7}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => [2,3,4,6,7,8,5,1] => {{1,2,3,4,6,8},{5,7}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,2,1,4,7] => [1,4,3,6,7,8,5,2] => {{1},{2,4,6,8},{3},{5,7}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,2,1,4,8] => [2,4,3,6,7,8,5,1] => {{1,2,4,6,8},{3},{5,7}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => [1,2,5,6,7,8,4,3] => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => [2,1,5,6,7,8,4,3] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => [1,3,5,6,7,8,4,2] => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => [2,3,5,6,7,8,4,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,1,5,8] => [3,2,5,6,7,8,4,1] => {{1,3,4,5,6,7,8},{2}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,6,7] => [1,4,5,6,7,8,3,2] => {{1},{2,4,6,8},{3,5,7}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,6,8] => [2,4,5,6,7,8,3,1] => {{1,2,4,6,8},{3,5,7}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [3,4,5,6,7,8,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => [4,3,5,6,7,8,2,1] => {{1,4,6,8},{2,3,5,7}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,1,6,7] => [1,5,4,6,7,8,3,2] => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,1,6,8] => [2,5,4,6,7,8,3,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,2,1,7,8] => [3,5,4,6,7,8,2,1] => {{1,3,4,6,8},{2,5,7}}
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => [5,4,3,6,7,8,2,1] => {{1,2,4,5,6,7,8},{3}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,1,5,6] => [1,2,6,5,7,8,4,3] => {{1},{2},{3,6,8},{4,5,7}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,1,5,6] => [2,1,6,5,7,8,4,3] => {{1,2},{3,6,8},{4,5,7}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => [1,3,6,5,7,8,4,2] => {{1},{2,3,6,8},{4,5,7}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,1,6,8] => [2,4,6,5,7,8,3,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,1,7,8] => [3,4,6,5,7,8,2,1] => {{1,3,6,8},{2,4,5,7}}
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,1,7,8] => [4,3,6,5,7,8,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,1,6,7] => [1,5,6,4,7,8,3,2] => {{1},{2,3,5,6,7,8},{4}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,1,6,8] => [2,5,6,4,7,8,3,1] => {{1,2,3,5,6,7,8},{4}}
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,2,1,7,8] => [3,5,6,4,7,8,2,1] => {{1,3,6,8},{2,5,7},{4}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,1,6,7] => [1,6,5,4,7,8,3,2] => {{1},{2,6,8},{3,5,7},{4}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,1,6,8] => [2,6,5,4,7,8,3,1] => {{1,2,6,8},{3,5,7},{4}}
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,1,7,8] => [3,6,5,4,7,8,2,1] => {{1,2,3,5,6,7,8},{4}}
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => [6,5,4,3,7,8,2,1] => {{1,6,8},{2,5,7},{3,4}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => [1,2,3,7,6,8,5,4] => {{1},{2},{3},{4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,1,4,5] => [1,3,2,7,6,8,5,4] => {{1},{2,3},{4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,1,4,5] => [2,3,1,7,6,8,5,4] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,1,4,5] => [3,2,1,7,6,8,5,4] => {{1,3},{2},{4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => [1,3,4,7,6,8,5,2] => {{1},{2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,1,4,8] => [2,3,4,7,6,8,5,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => [1,4,3,7,6,8,5,2] => {{1},{2,4,5,6,7,8},{3}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,1,5,6] => [2,1,5,7,6,8,4,3] => {{1,2},{3,5,6,8},{4,7}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,1,5,8] => [2,3,5,7,6,8,4,1] => {{1,2,3,5,6,8},{4,7}}
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,1,5,8] => [3,2,5,7,6,8,4,1] => {{1,3,5,6,8},{2},{4,7}}
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,1,7,8] => [3,4,5,7,6,8,2,1] => {{1,3,5,6,8},{2,4,7}}
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,3,1,7,8] => [4,3,5,7,6,8,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,1,6,8] => [2,5,4,7,6,8,3,1] => {{1,2,5,6,8},{3,4,7}}
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,1,7,8] => [3,5,4,7,6,8,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,1,7,8] => [4,5,3,7,6,8,2,1] => {{1,2,4,5,6,7,8},{3}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,1,5,6] => [2,1,6,7,5,8,4,3] => {{1,2},{3,6,8},{4,7},{5}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,1,5,7] => [1,3,6,7,5,8,4,2] => {{1},{2,3,6,8},{4,7},{5}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,1,6,7] => [1,4,6,7,5,8,3,2] => {{1},{2,3,4,6,7,8},{5}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,1,6,8] => [2,4,6,7,5,8,3,1] => {{1,2,3,4,6,7,8},{5}}
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,1,7,8] => [3,4,6,7,5,8,2,1] => {{1,3,6,8},{2,4,7},{5}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,1,6,8] => [2,5,6,7,4,8,3,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,1,7,8] => [3,5,6,7,4,8,2,1] => {{1,3,6,8},{2,4,5,7}}
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => [4,5,6,7,3,8,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,1,7,8] => [5,4,6,7,3,8,2,1] => {{1,3,5,6,8},{2,4,7}}
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,1,7,8] => [6,5,4,7,3,8,2,1] => {{1,6,8},{2,3,4,5,7}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,1,5,6] => [1,2,7,6,5,8,4,3] => {{1},{2},{3,4,6,7,8},{5}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,1,5,6] => [2,1,7,6,5,8,4,3] => {{1,2},{3,4,6,7,8},{5}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,1,5,8] => [2,3,7,6,5,8,4,1] => {{1,2,3,4,6,7,8},{5}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,1,6,7] => [1,4,7,6,5,8,3,2] => {{1},{2,4,6,8},{3,7},{5}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,1,6,8] => [2,4,7,6,5,8,3,1] => {{1,2,4,6,8},{3,7},{5}}
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,1,7,8] => [3,4,7,6,5,8,2,1] => {{1,2,3,4,6,7,8},{5}}
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,1,7,8] => [4,3,7,6,5,8,2,1] => {{1,4,6,8},{2,3,7},{5}}
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,1,7,8] => [3,5,7,6,4,8,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,1,7,8] => [5,4,7,6,3,8,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,1,7,8] => [5,6,7,4,3,8,2,1] => {{1,2,3,5,6,7,8},{4}}
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => [6,5,7,4,3,8,2,1] => {{1,6,8},{2,3,5,7},{4}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,1,6,7] => [1,7,6,5,4,8,3,2] => {{1},{2,3,6,7,8},{4,5}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,1,6,8] => [2,7,6,5,4,8,3,1] => {{1,2,3,6,7,8},{4,5}}
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,1,7,8] => [3,7,6,5,4,8,2,1] => {{1,3,6,8},{2,7},{4,5}}
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => [4,7,6,5,3,8,2,1] => {{1,3,4,5,6,8},{2,7}}
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => [5,7,6,4,3,8,2,1] => {{1,3,5,6,8},{2,7},{4}}
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,1,7,8] => [6,7,5,4,3,8,2,1] => {{1,6,8},{2,7},{3,5},{4}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [7,6,5,4,3,8,2,1] => {{1,2,6,7,8},{3,5},{4}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => [1,2,3,4,8,7,6,5] => {{1},{2},{3},{4},{5,8},{6,7}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => [2,1,3,4,8,7,6,5] => {{1,2},{3},{4},{5,8},{6,7}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => [1,3,2,4,8,7,6,5] => {{1},{2,3},{4},{5,8},{6,7}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => [2,3,1,4,8,7,6,5] => {{1,2,3},{4},{5,8},{6,7}}
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => [3,2,1,4,8,7,6,5] => {{1,3},{2},{4},{5,8},{6,7}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => [1,2,4,3,8,7,6,5] => {{1},{2},{3,4},{5,8},{6,7}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => [2,1,4,3,8,7,6,5] => {{1,2},{3,4},{5,8},{6,7}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => [1,3,4,2,8,7,6,5] => {{1},{2,3,4},{5,8},{6,7}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => [2,3,4,1,8,7,6,5] => {{1,2,3,4},{5,8},{6,7}}
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => [3,2,4,1,8,7,6,5] => {{1,3,4},{2},{5,8},{6,7}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => [1,4,3,2,8,7,6,5] => {{1},{2,4},{3},{5,8},{6,7}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => [2,4,3,1,8,7,6,5] => {{1,2,4},{3},{5,8},{6,7}}
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => [3,4,2,1,8,7,6,5] => {{1,2,3,4},{5,8},{6,7}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [4,3,2,1,8,7,6,5] => {{1,4},{2,3},{5,8},{6,7}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,1,2,3,5] => [1,2,3,5,8,7,6,4] => {{1},{2},{3},{4,5,8},{6,7}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,1,2,3,5] => [1,3,2,5,8,7,6,4] => {{1},{2,3},{4,5,8},{6,7}}
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,1,2,3,5] => [3,2,1,5,8,7,6,4] => {{1,3},{2},{4,5,8},{6,7}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,1,2,3,6] => [1,2,4,5,8,7,6,3] => {{1},{2},{3,4,5,8},{6,7}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => [2,1,4,5,8,7,6,3] => {{1,2},{3,4,5,8},{6,7}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,1,2,3,7] => [1,3,4,5,8,7,6,2] => {{1},{2,3,4,5,8},{6,7}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => [2,3,4,5,8,7,6,1] => {{1,2,3,4,5,8},{6,7}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,1,2,3,7] => [1,4,3,5,8,7,6,2] => {{1},{2,4,5,8},{3},{6,7}}
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,1,2,3,8] => [3,4,2,5,8,7,6,1] => {{1,2,3,4,5,8},{6,7}}
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => [4,3,2,5,8,7,6,1] => {{1,4,5,8},{2,3},{6,7}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,1,2,3,6] => [1,2,5,4,8,7,6,3] => {{1},{2},{3,5,8},{4},{6,7}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,1,2,3,6] => [2,1,5,4,8,7,6,3] => {{1,2},{3,5,8},{4},{6,7}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,1,2,3,7] => [1,3,5,4,8,7,6,2] => {{1},{2,3,5,8},{4},{6,7}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,1,2,3,8] => [2,3,5,4,8,7,6,1] => {{1,2,3,5,8},{4},{6,7}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,1,2,3,7] => [1,4,5,3,8,7,6,2] => {{1},{2,3,4,5,8},{6,7}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,1,2,3,8] => [2,4,5,3,8,7,6,1] => {{1,2,3,4,5,8},{6,7}}
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,1,2,3,8] => [4,3,5,2,8,7,6,1] => {{1,2,3,4,5,8},{6,7}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,1,2,3,7] => [1,5,4,3,8,7,6,2] => {{1},{2,5,8},{3,4},{6,7}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,1,2,3,8] => [2,5,4,3,8,7,6,1] => {{1,2,5,8},{3,4},{6,7}}
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => [4,5,3,2,8,7,6,1] => {{1,2,4,5,8},{3},{6,7}}
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,1,2,3,8] => [5,4,3,2,8,7,6,1] => {{1,5,8},{2,4},{3},{6,7}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,1,2,4,5] => [1,2,3,6,8,7,5,4] => {{1},{2},{3},{4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,1,2,4,5] => [2,1,3,6,8,7,5,4] => {{1,2},{3},{4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,1,2,4,5] => [1,3,2,6,8,7,5,4] => {{1},{2,3},{4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,1,2,4,5] => [2,3,1,6,8,7,5,4] => {{1,2,3},{4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,1,2,4,5] => [3,2,1,6,8,7,5,4] => {{1,3},{2},{4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,1,2,4,6] => [1,2,4,6,8,7,5,3] => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,1,2,4,6] => [2,1,4,6,8,7,5,3] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,1,2,4,8] => [2,3,4,6,8,7,5,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,1,2,4,7] => [1,4,3,6,8,7,5,2] => {{1},{2,4,5,6,7,8},{3}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,1,2,4,8] => [2,4,3,6,8,7,5,1] => {{1,2,4,5,6,7,8},{3}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => [4,3,2,6,8,7,5,1] => {{1,4,5,6,7,8},{2,3}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,1,2,5,6] => [1,2,5,6,8,7,4,3] => {{1},{2},{3,5,8},{4,6,7}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,1,2,5,6] => [2,1,5,6,8,7,4,3] => {{1,2},{3,5,8},{4,6,7}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,1,2,5,7] => [1,3,5,6,8,7,4,2] => {{1},{2,3,5,8},{4,6,7}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => [2,3,5,6,8,7,4,1] => {{1,2,3,5,8},{4,6,7}}
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,2,7,8] => [3,4,5,6,8,7,2,1] => {{1,3,5,8},{2,4,6,7}}
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => [4,3,5,6,8,7,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => [4,5,3,6,8,7,2,1] => {{1,2,4,5,6,7,8},{3}}
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,1,2,7,8] => [5,4,3,6,8,7,2,1] => {{1,5,8},{2,4,6,7},{3}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,1,2,5,6] => [1,2,6,5,8,7,4,3] => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,1,2,5,6] => [2,1,6,5,8,7,4,3] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,1,2,5,8] => [2,3,6,5,8,7,4,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,1,2,6,7] => [1,4,6,5,8,7,3,2] => {{1},{2,4,5,8},{3,6,7}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,1,2,6,8] => [2,4,6,5,8,7,3,1] => {{1,2,4,5,8},{3,6,7}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => [4,3,6,5,8,7,2,1] => {{1,4,5,8},{2,3,6,7}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,1,2,6,8] => [2,5,6,4,8,7,3,1] => {{1,2,5,8},{3,6,7},{4}}
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => [4,5,6,3,8,7,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,1,2,6,8] => [2,6,5,4,8,7,3,1] => {{1,2,3,5,6,7,8},{4}}
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,1,2,7,8] => [3,6,5,4,8,7,2,1] => {{1,3,5,8},{2,6,7},{4}}
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,1,2,7,8] => [5,6,4,3,8,7,2,1] => {{1,5,8},{2,6,7},{3,4}}
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => [6,5,4,3,8,7,2,1] => {{1,2,5,6,7,8},{3,4}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => [1,2,3,7,8,6,5,4] => {{1},{2},{3},{4,5,7,8},{6}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,1,3,4,5] => [2,1,3,7,8,6,5,4] => {{1,2},{3},{4,5,7,8},{6}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,1,3,4,5] => [2,3,1,7,8,6,5,4] => {{1,2,3},{4,5,7,8},{6}}
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => [3,2,1,7,8,6,5,4] => {{1,3},{2},{4,5,7,8},{6}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => [1,2,4,7,8,6,5,3] => {{1},{2},{3,4,5,7,8},{6}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => [2,1,4,7,8,6,5,3] => {{1,2},{3,4,5,7,8},{6}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,1,3,4,8] => [2,3,4,7,8,6,5,1] => {{1,2,3,4,5,7,8},{6}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => [1,4,3,7,8,6,5,2] => {{1},{2,4,5,7,8},{3},{6}}
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,1,3,4,8] => [3,4,2,7,8,6,5,1] => {{1,2,3,4,5,7,8},{6}}
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => [4,3,2,7,8,6,5,1] => {{1,4,5,7,8},{2,3},{6}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => [2,1,5,7,8,6,4,3] => {{1,2},{3,5,8},{4,7},{6}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => [1,3,5,7,8,6,4,2] => {{1},{2,3,5,8},{4,7},{6}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,1,3,5,8] => [2,3,5,7,8,6,4,1] => {{1,2,3,5,8},{4,7},{6}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,1,3,5,8] => [3,2,5,7,8,6,4,1] => {{1,3,5,8},{2},{4,7},{6}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,1,3,6,8] => [2,4,5,7,8,6,3,1] => {{1,2,3,4,5,7,8},{6}}
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1,3,7,8] => [3,4,5,7,8,6,2,1] => {{1,3,5,8},{2,4,7},{6}}
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => [4,3,5,7,8,6,2,1] => {{1,2,3,4,5,7,8},{6}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,1,3,6,7] => [1,5,4,7,8,6,3,2] => {{1},{2,5,8},{3,4,7},{6}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,1,3,6,8] => [2,5,4,7,8,6,3,1] => {{1,2,5,8},{3,4,7},{6}}
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,1,3,7,8] => [3,5,4,7,8,6,2,1] => {{1,2,3,4,5,7,8},{6}}
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,1,3,7,8] => [4,5,3,7,8,6,2,1] => {{1,2,4,5,7,8},{3},{6}}
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,1,3,7,8] => [5,4,3,7,8,6,2,1] => {{1,5,8},{2,4,7},{3},{6}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => [1,2,6,7,8,5,4,3] => {{1},{2},{3,5,6,8},{4,7}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => [2,1,6,7,8,5,4,3] => {{1,2},{3,5,6,8},{4,7}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,1,4,5,7] => [1,3,6,7,8,5,4,2] => {{1},{2,3,5,6,8},{4,7}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => [2,3,6,7,8,5,4,1] => {{1,2,3,5,6,8},{4,7}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,1,4,6,7] => [1,4,6,7,8,5,3,2] => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,1,4,6,8] => [2,4,6,7,8,5,3,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1,4,7,8] => [3,4,6,7,8,5,2,1] => {{1,3,5,6,8},{2,4,7}}
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => [4,3,6,7,8,5,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => [1,5,6,7,8,4,3,2] => {{1},{2,5,8},{3,4,6,7}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [2,5,6,7,8,4,3,1] => {{1,2,5,8},{3,4,6,7}}
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => [3,5,6,7,8,4,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [4,5,6,7,8,3,2,1] => {{1,2,4,5,7,8},{3,6}}
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,1,6,7,8] => [5,4,6,7,8,3,2,1] => {{1,5,8},{2,4,7},{3,6}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,1,5,6,7] => [1,6,5,7,8,4,3,2] => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,1,6,7,8] => [4,6,5,7,8,3,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,1,6,7,8] => [5,6,4,7,8,3,2,1] => {{1,5,8},{2,3,4,6,7}}
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8] => [6,5,4,7,8,3,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,1,4,5,6] => [1,2,7,6,8,5,4,3] => {{1},{2},{3,4,5,6,7,8}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,1,4,5,6] => [2,1,7,6,8,5,4,3] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,1,5,6,7] => [1,5,7,6,8,4,3,2] => {{1},{2,5,8},{3,7},{4,6}}
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,1,5,7,8] => [3,5,7,6,8,4,2,1] => {{1,2,3,5,7,8},{4,6}}
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,1,6,7,8] => [4,5,7,6,8,3,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => [5,4,7,6,8,3,2,1] => {{1,5,8},{2,3,4,6,7}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,1,5,6,7] => [1,6,7,5,8,4,3,2] => {{1},{2,4,5,6,8},{3,7}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,1,5,6,8] => [2,6,7,5,8,4,3,1] => {{1,2,4,5,6,8},{3,7}}
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,1,6,7,8] => [4,6,7,5,8,3,2,1] => {{1,4,5,8},{2,3,6,7}}
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,1,6,7,8] => [5,6,7,4,8,3,2,1] => {{1,5,8},{2,3,6,7},{4}}
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8] => [6,5,7,4,8,3,2,1] => {{1,2,3,5,6,7,8},{4}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => [1,7,6,5,8,4,3,2] => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,1,5,7,8] => [3,7,6,5,8,4,2,1] => {{1,3,4,5,6,8},{2,7}}
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => [4,7,6,5,8,3,2,1] => {{1,4,5,8},{2,7},{3,6}}
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,1,6,7,8] => [5,7,6,4,8,3,2,1] => {{1,5,8},{2,7},{3,6},{4}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8] => [6,7,5,4,8,3,2,1] => {{1,3,5,6,8},{2,7},{4}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [7,6,5,4,8,3,2,1] => {{1,2,3,5,6,7,8},{4}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => [1,2,3,8,7,6,5,4] => {{1},{2},{3},{4,8},{5,7},{6}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => [2,1,3,8,7,6,5,4] => {{1,2},{3},{4,8},{5,7},{6}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => [1,3,2,8,7,6,5,4] => {{1},{2,3},{4,8},{5,7},{6}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [7,6,8,1,2,3,4,5] => [2,3,1,8,7,6,5,4] => {{1,2,3},{4,8},{5,7},{6}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [3,2,1,8,7,6,5,4] => {{1,3},{2},{4,8},{5,7},{6}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5,1,2,3,4,6] => [1,2,4,8,7,6,5,3] => {{1},{2},{3,4,8},{5,7},{6}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => [2,1,4,8,7,6,5,3] => {{1,2},{3,4,8},{5,7},{6}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => [1,3,4,8,7,6,5,2] => {{1},{2,3,4,8},{5,7},{6}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => [2,3,4,8,7,6,5,1] => {{1,2,3,4,8},{5,7},{6}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => [3,2,4,8,7,6,5,1] => {{1,3,4,8},{2},{5,7},{6}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => [1,4,3,8,7,6,5,2] => {{1},{2,4,8},{3},{5,7},{6}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => [2,4,3,8,7,6,5,1] => {{1,2,4,8},{3},{5,7},{6}}
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => [3,4,2,8,7,6,5,1] => {{1,2,3,4,8},{5,7},{6}}
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => [4,3,2,8,7,6,5,1] => {{1,4,8},{2,3},{5,7},{6}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => [1,2,5,8,7,6,4,3] => {{1},{2},{3,4,5,7,8},{6}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [7,8,4,1,2,3,5,6] => [2,1,5,8,7,6,4,3] => {{1,2},{3,4,5,7,8},{6}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [8,6,4,1,2,3,5,7] => [1,3,5,8,7,6,4,2] => {{1},{2,3,4,5,7,8},{6}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [7,6,4,1,2,3,5,8] => [2,3,5,8,7,6,4,1] => {{1,2,3,4,5,7,8},{6}}
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3,7,8] => [3,4,5,8,7,6,2,1] => {{1,2,3,4,5,7,8},{6}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,5,1,2,3,6,8] => [2,5,4,8,7,6,3,1] => {{1,2,3,4,5,7,8},{6}}
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [5,4,3,8,7,6,2,1] => {{1,2,4,5,7,8},{3},{6}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [7,8,3,1,2,4,5,6] => [2,1,6,8,7,5,4,3] => {{1,2},{3,4,5,6,7,8}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [8,6,3,1,2,4,5,7] => [1,3,6,8,7,5,4,2] => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [6,7,3,1,2,4,5,8] => [3,2,6,8,7,5,4,1] => {{1,3,4,5,6,7,8},{2}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3,1,2,4,6,7] => [1,4,6,8,7,5,3,2] => {{1},{2,4,8},{3,5,6,7}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => [2,4,6,8,7,5,3,1] => {{1,2,4,8},{3,5,6,7}}
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => [3,5,6,8,7,4,2,1] => {{1,3,4,6,8},{2,5,7}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => [4,5,6,8,7,3,2,1] => {{1,4,8},{2,5,7},{3,6}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,4,1,2,5,6,7] => [1,6,5,8,7,4,3,2] => {{1},{2,4,6,8},{3,5,7}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,3,4,1,2,6,7,8] => [4,6,5,8,7,3,2,1] => {{1,4,8},{2,3,5,6,7}}
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,5,1,2,6,7,8] => [5,6,4,8,7,3,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2,1,3,4,5,6] => [1,2,7,8,6,5,4,3] => {{1},{2},{3,4,7,8},{5,6}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => [2,1,7,8,6,5,4,3] => {{1,2},{3,4,7,8},{5,6}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [8,6,2,1,3,4,5,7] => [1,3,7,8,6,5,4,2] => {{1},{2,3,4,7,8},{5,6}}
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [6,7,2,1,3,4,5,8] => [3,2,7,8,6,5,4,1] => {{1,3,4,7,8},{2},{5,6}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1,3,4,6,7] => [1,4,7,8,6,5,3,2] => {{1},{2,4,8},{3,7},{5,6}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [7,5,2,1,3,4,6,8] => [2,4,7,8,6,5,3,1] => {{1,2,4,8},{3,7},{5,6}}
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,2,1,3,4,7,8] => [4,3,7,8,6,5,2,1] => {{1,4,8},{2,3,7},{5,6}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,3,5,7,8] => [3,5,7,8,6,4,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => [4,5,7,8,6,3,2,1] => {{1,4,8},{2,3,5,6,7}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [4,5,2,1,3,6,7,8] => [5,4,7,8,6,3,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => [1,6,7,8,5,4,3,2] => {{1},{2,4,6,8},{3,7},{5}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => [2,6,7,8,5,4,3,1] => {{1,2,4,6,8},{3,7},{5}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => [4,6,7,8,5,3,2,1] => {{1,4,8},{2,3,6,7},{5}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [5,6,7,8,4,3,2,1] => {{1,4,5,8},{2,3,6,7}}
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8] => [6,5,7,8,4,3,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [1,7,6,8,5,4,3,2] => {{1},{2,3,4,6,7,8},{5}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => [2,7,6,8,5,4,3,1] => {{1,2,3,4,6,7,8},{5}}
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => [3,7,6,8,5,4,2,1] => {{1,3,4,6,8},{2,7},{5}}
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => [4,7,6,8,5,3,2,1] => {{1,4,8},{2,7},{3,6},{5}}
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,3,1,5,6,7,8] => [5,7,6,8,4,3,2,1] => {{1,4,5,8},{2,7},{3,6}}
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [6,7,5,8,4,3,2,1] => {{1,3,4,5,6,8},{2,7}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [7,6,5,8,4,3,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => [1,2,8,7,6,5,4,3] => {{1},{2},{3,8},{4,7},{5,6}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [2,1,8,7,6,5,4,3] => {{1,2},{3,8},{4,7},{5,6}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [1,3,8,7,6,5,4,2] => {{1},{2,3,8},{4,7},{5,6}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,2,3,4,5,8] => [2,3,8,7,6,5,4,1] => {{1,2,3,8},{4,7},{5,6}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => [3,2,8,7,6,5,4,1] => {{1,3,8},{2},{4,7},{5,6}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,2,3,4,6,7] => [1,4,8,7,6,5,3,2] => {{1},{2,3,4,7,8},{5,6}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => [2,4,8,7,6,5,3,1] => {{1,2,3,4,7,8},{5,6}}
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,2,3,4,7,8] => [3,4,8,7,6,5,2,1] => {{1,3,8},{2,4,7},{5,6}}
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,6,1,2,3,4,7,8] => [4,3,8,7,6,5,2,1] => {{1,2,3,4,7,8},{5,6}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => [1,5,8,7,6,4,3,2] => {{1},{2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,2,3,5,6,8] => [2,5,8,7,6,4,3,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => [3,5,8,7,6,4,2,1] => {{1,3,8},{2,4,5,6,7}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => [4,5,8,7,6,3,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => [1,6,8,7,5,4,3,2] => {{1},{2,3,4,6,7,8},{5}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [2,6,8,7,5,4,3,1] => {{1,2,3,4,6,7,8},{5}}
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => [3,6,8,7,5,4,2,1] => {{1,3,8},{2,4,6,7},{5}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => [4,6,8,7,5,3,2,1] => {{1,2,3,4,6,7,8},{5}}
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,2,5,6,7,8] => [5,6,8,7,4,3,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [6,5,8,7,4,3,2,1] => {{1,3,6,8},{2,4,5,7}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [1,7,8,6,5,4,3,2] => {{1},{2,3,7,8},{4,6},{5}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [2,7,8,6,5,4,3,1] => {{1,2,3,7,8},{4,6},{5}}
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,3,4,5,7,8] => [3,7,8,6,5,4,2,1] => {{1,3,8},{2,7},{4,6},{5}}
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => [4,7,8,6,5,3,2,1] => {{1,3,4,6,8},{2,7},{5}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => [5,7,8,6,4,3,2,1] => {{1,3,4,5,6,8},{2,7}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [6,7,8,5,4,3,2,1] => {{1,3,6,8},{2,7},{4,5}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [7,6,8,5,4,3,2,1] => {{1,2,3,6,7,8},{4,5}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [1,8,7,6,5,4,3,2] => {{1},{2,8},{3,7},{4,6},{5}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => [2,8,7,6,5,4,3,1] => {{1,2,8},{3,7},{4,6},{5}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => [3,8,7,6,5,4,2,1] => {{1,2,3,7,8},{4,6},{5}}
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [4,8,7,6,5,3,2,1] => {{1,2,3,4,6,7,8},{5}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [5,8,7,6,4,3,2,1] => {{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [6,8,7,5,4,3,2,1] => {{1,2,3,6,7,8},{4,5}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [7,8,6,5,4,3,2,1] => {{1,2,7,8},{3,6},{4,5}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1] => {{1,8},{2,7},{3,6},{4,5}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => [1,9,8,7,6,5,4,3,2] => {{1},{2,9},{3,8},{4,7},{5,6}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [8,7,6,5,4,3,2,1,9] => {{1,8},{2,7},{3,6},{4,5},{9}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [1,10,9,8,7,6,5,4,3,2] => {{1},{2,10},{3,9},{4,8},{5,7},{6}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1,3,4,5,6,7,8] => [1,8,9,7,6,5,4,3,2] => {{1},{2,3,8,9},{4,7},{5,6}}
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,1] => [7,8,6,5,4,3,2,1,9] => {{1,2,7,8},{3,6},{4,5},{9}}
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [9,8,7,6,5,4,3,2,1,10] => {{1,9},{2,8},{3,7},{4,6},{5},{10}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => [1,11,10,9,8,7,6,5,4,3,2] => {{1},{2,11},{3,10},{4,9},{5,8},{6,7}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2,1,3,4,5,6,7,8,9] => [1,9,10,8,7,6,5,4,3,2] => {{1},{2,3,9,10},{4,8},{5,7},{6}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [9,3,1,2,4,5,6,7,8] => [1,7,9,8,6,5,4,3,2] => {{1},{2,3,4,7,8,9},{5,6}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,1,4,5,6,7,8] => [1,8,7,9,6,5,4,3,2] => {{1},{2,3,4,7,8,9},{5,6}}
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,1] => [6,8,7,5,4,3,2,1,9] => {{1,2,3,6,7,8},{4,5},{9}}
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,1] => [7,6,8,5,4,3,2,1,9] => {{1,2,3,6,7,8},{4,5},{9}}
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,1] => [8,9,7,6,5,4,3,2,1,10] => {{1,2,8,9},{3,7},{4,6},{5},{10}}
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [10,9,8,7,6,5,4,3,2,1,11] => {{1,10},{2,9},{3,8},{4,7},{5,6},{11}}
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [12,1,2,3,4,5,6,7,8,9,10,11] => [1,12,11,10,9,8,7,6,5,4,3,2] => {{1},{2,12},{3,11},{4,10},{5,9},{6,8},{7}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,1,4,5,6,7,8,9] => [1,9,8,10,7,6,5,4,3,2] => {{1},{2,3,4,8,9,10},{5,7},{6}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2,1,4,5,6,7,8] => [1,7,8,9,6,5,4,3,2] => {{1},{2,4,7,9},{3,8},{5,6}}
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,1] => [6,7,8,5,4,3,2,1,9] => {{1,3,6,8},{2,7},{4,5},{9}}
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [3,4,5,2,6,7,8,9,1] => [7,6,5,8,4,3,2,1,9] => {{1,2,3,4,5,6,7,8},{9}}
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,10,1] => [8,7,9,6,5,4,3,2,1,10] => {{1,2,3,7,8,9},{4,6},{5},{10}}
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [10,3,2,1,4,5,6,7,8,9] => [1,8,9,10,7,6,5,4,3,2] => {{1},{2,4,8,10},{3,9},{5,7},{6}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [6,2,3,4,5,7,8,9,1] => [4,8,7,6,5,3,2,1,9] => {{1,2,3,4,6,7,8},{5},{9}}
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [4,5,2,3,6,7,8,9,1] => [6,5,8,7,4,3,2,1,9] => {{1,3,6,8},{2,4,5,7},{9}}
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,10,1] => [7,8,9,6,5,4,3,2,1,10] => {{1,3,7,9},{2,8},{4,6},{5},{10}}
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,2,6,7,8,9,10,1] => [8,7,6,9,5,4,3,2,1,10] => {{1,2,3,4,6,7,8,9},{5},{10}}
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,10,11,1] => [9,8,10,7,6,5,4,3,2,1,11] => {{1,2,3,8,9,10},{4,7},{5,6},{11}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [6,2,3,4,5,7,8,9,10,1] => [5,9,8,7,6,4,3,2,1,10] => {{1,2,3,4,5,6,7,8,9},{10}}
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [4,5,3,2,6,7,8,9,1] => [6,5,7,8,4,3,2,1,9] => {{1,2,3,4,5,6,7,8},{9}}
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,2,8,9,1] => [7,6,5,4,3,8,2,1,9] => {{1,2,6,7,8},{3,5},{4},{9}}
[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,2,6,7,8,9,10,11,1] => [9,8,7,10,6,5,4,3,2,1,11] => {{1,2,3,4,7,8,9,10},{5,6},{11}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [9,7,1,2,3,4,5,6,8] => [1,3,9,8,7,6,5,4,2] => {{1},{2,3,9},{4,8},{5,7},{6}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [9,4,3,2,1,5,6,7,8] => [1,6,7,8,9,5,4,3,2] => {{1},{2,5,6,9},{3,4,7,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => [2,1,9,8,7,6,5,4,3] => {{1,2},{3,9},{4,8},{5,7},{6}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => [2,8,7,6,5,4,3,1,9] => {{1,2,8},{3,7},{4,6},{5},{9}}
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [5,6,2,3,4,7,8,9,1] => [5,4,8,7,6,3,2,1,9] => {{1,3,5,6,8},{2,4,7},{9}}
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => [7,6,5,4,3,2,1,9,8] => {{1,7},{2,6},{3,5},{4},{8,9}}
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,9,1] => [7,6,5,4,3,2,8,1,9] => {{1,7,8},{2,6},{3,5},{4},{9}}
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,2,8,9,10,1] => [8,7,6,5,4,9,3,2,1,10] => {{1,2,3,6,7,8,9},{4,5},{10}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [10,4,3,2,1,5,6,7,8,9] => [1,7,8,9,10,6,5,4,3,2] => {{1},{2,5,7,10},{3,4,8,9},{6}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [9,8,1,2,3,4,5,6,7] => [1,2,9,8,7,6,5,4,3] => {{1},{2},{3,9},{4,8},{5,7},{6}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,8,1] => [1,8,7,6,5,4,3,2,9] => {{1},{2,8},{3,7},{4,6},{5},{9}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,1,3,4,5,6,7] => [2,1,8,9,7,6,5,4,3] => {{1,2},{3,4,8,9},{5,7},{6}}
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,3,5,6,7,8,9,1,2] => [6,7,5,4,3,2,1,9,8] => {{1,2,6,7},{3,5},{4},{8,9}}
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,1] => [7,6,5,4,3,2,1,8,9] => {{1,7},{2,6},{3,5},{4},{8},{9}}
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,9,10,1] => [8,7,6,5,4,3,9,2,1,10] => {{1,2,7,8,9},{3,6},{4,5},{10}}
[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,2,8,9,10,11,1] => [9,8,7,6,5,10,4,3,2,1,11] => {{1,2,3,4,6,7,8,9,10},{5},{11}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [10,8,1,2,3,4,5,6,7,9] => [1,3,10,9,8,7,6,5,4,2] => {{1},{2,3,10},{4,9},{5,8},{6,7}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => [2,1,10,9,8,7,6,5,4,3] => {{1,2},{3,10},{4,9},{5,8},{6,7}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2,4,5,6,7,8,1] => [1,7,8,6,5,4,3,2,9] => {{1},{2,3,7,8},{4,6},{5},{9}}
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,3,5,6,7,8,9,2,1] => [6,7,5,4,3,2,1,8,9] => {{1,2,6,7},{3,5},{4},{8},{9}}
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [8,7,6,5,4,3,2,1,10,9] => {{1,8},{2,7},{3,6},{4,5},{9,10}}
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,10,1] => [8,7,6,5,4,3,2,9,1,10] => {{1,8,9},{2,7},{3,6},{4,5},{10}}
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,9,10,11,1] => [9,8,7,6,5,4,10,3,2,1,11] => {{1,2,3,7,8,9,10},{4,6},{5},{11}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [10,9,1,2,3,4,5,6,7,8] => [1,2,10,9,8,7,6,5,4,3] => {{1},{2},{3,10},{4,9},{5,8},{6,7}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,8,9,1] => [1,9,8,7,6,5,4,3,2,10] => {{1},{2,9},{3,8},{4,7},{5,6},{10}}
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [8,7,6,5,4,3,2,1,9,10] => {{1,8},{2,7},{3,6},{4,5},{9},{10}}
[] => [] => [] => {}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,9] => [2,3,4,5,6,7,8,9,1] => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,1,9] => [3,2,4,5,6,7,8,9,1] => {{1,3,4,5,6,7,8,9},{2}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [8,6,7,5,4,3,2,1,9] => [2,4,3,5,6,7,8,9,1] => {{1,2,4,5,6,7,8,9},{3}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7,6,8,5,4,3,2,1,9] => [3,4,2,5,6,7,8,9,1] => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [6,7,8,5,4,3,2,1,9] => [4,3,2,5,6,7,8,9,1] => {{1,4,5,6,7,8,9},{2,3}}
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1,9] => [5,4,3,2,6,7,8,9,1] => {{1,5,6,7,8,9},{2,4},{3}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,3,2,1,9] => [2,3,4,6,5,7,8,9,1] => {{1,2,3,4,6,7,8,9},{5}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,6,3,2,1,9] => [2,3,5,6,4,7,8,9,1] => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,3,2,1,9] => [6,5,4,3,2,7,8,9,1] => {{1,6,7,8,9},{2,5},{3,4}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,4,2,1,9] => [2,3,4,5,7,6,8,9,1] => {{1,2,3,4,5,7,8,9},{6}}
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1,9] => [7,6,5,4,3,2,8,9,1] => {{1,7,8,9},{2,6},{3,5},{4}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,1,9] => [2,3,4,5,6,8,7,9,1] => {{1,2,3,4,5,6,8,9},{7}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,2,4,1,9] => [2,3,4,5,7,8,6,9,1] => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,8,1,9] => [3,4,5,6,7,8,2,9,1] => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [5,4,6,3,7,2,8,1,9] => [5,6,4,7,3,8,2,9,1] => {{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,1,9] => [2,8,7,6,5,4,3,9,1] => {{1,2,8,9},{3,7},{4,6},{5}}
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,1,9] => [6,8,7,5,4,3,2,9,1] => {{1,2,3,6,7,8,9},{4,5}}
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1,9] => [7,8,6,5,4,3,2,9,1] => {{1,2,7,8,9},{3,6},{4,5}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => [8,7,6,5,4,3,2,9,1] => {{1,8,9},{2,7},{3,6},{4,5}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,1,2,9] => [2,3,4,5,6,7,9,8,1] => {{1,2,3,4,5,6,7,9},{8}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7,8,5,6,3,4,1,2,9] => [3,2,5,4,7,6,9,8,1] => {{1,3,5,7,9},{2},{4},{6},{8}}
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9] => [7,6,5,4,3,2,9,8,1] => {{1,7,9},{2,6},{3,5},{4},{8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,1,3,9] => [2,3,4,5,6,8,9,7,1] => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,2,1,4,9] => [2,3,4,5,7,8,9,6,1] => {{1,2,3,4,5,7,9},{6,8}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,6,5,4,3,2,1,7,9] => [2,4,5,6,7,8,9,3,1] => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1,8,9] => [3,4,5,6,7,8,9,2,1] => {{1,3,5,7,9},{2,4,6,8}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,2,3,4,5,6,1,8,9] => [3,8,7,6,5,4,9,2,1] => {{1,3,7,9},{2,8},{4,6},{5}}
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => [8,7,6,5,4,3,9,2,1] => {{1,2,7,8,9},{3,6},{4,5}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,1,2,3,9] => [2,3,4,5,6,9,8,7,1] => {{1,2,3,4,5,6,9},{7,8}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,2,1,3,4,9] => [2,3,4,5,8,9,7,6,1] => {{1,2,3,4,5,6,8,9},{7}}
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [6,7,4,3,2,1,5,8,9] => [4,3,6,7,8,9,5,2,1] => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [7,5,4,3,2,1,6,8,9] => [3,5,6,7,8,9,4,2,1] => {{1,3,6,9},{2,5,8},{4,7}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,7,8,9] => [4,5,6,7,8,9,3,2,1] => {{1,3,4,6,7,9},{2,5,8}}
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,6,4,3,2,1,7,8,9] => [5,4,6,7,8,9,3,2,1] => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [6,2,3,4,5,1,7,8,9] => [4,8,7,6,5,9,3,2,1] => {{1,4,6,9},{2,8},{3,7},{5}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [8,7,6,5,4,9,3,2,1] => {{1,2,3,6,7,8,9},{4,5}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => [5,4,3,2,9,8,7,6,1] => {{1,5,9},{2,4},{3},{6,8},{7}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,1,2,7,8,9] => [4,5,6,7,9,8,3,2,1] => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [5,6,3,4,1,2,7,8,9] => [5,4,7,6,9,8,3,2,1] => {{1,5,9},{2,4,6,8},{3,7}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9] => [5,6,7,8,9,4,3,2,1] => {{1,5,9},{2,4,6,8},{3,7}}
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,5,3,2,1,6,7,8,9] => [6,5,7,8,9,4,3,2,1] => {{1,2,4,5,6,8,9},{3,7}}
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8,9] => [7,6,8,5,9,4,3,2,1] => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [5,2,3,4,1,6,7,8,9] => [5,8,7,6,9,4,3,2,1] => {{1,5,9},{2,8},{3,7},{4,6}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [8,7,6,5,9,4,3,2,1] => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9] => [6,5,4,9,8,7,3,2,1] => {{1,3,4,6,7,9},{2,5,8}}
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,1,2,6,7,8,9] => [5,6,7,9,8,4,3,2,1] => {{1,2,4,5,6,8,9},{3,7}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9] => [6,7,8,9,5,4,3,2,1] => {{1,4,6,9},{2,3,7,8},{5}}
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8,9] => [7,6,8,9,5,4,3,2,1] => {{1,2,3,4,6,7,8,9},{5}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,1,4,5,6,7,9] => [2,8,7,9,6,5,4,3,1] => {{1,2,3,4,7,8,9},{5,6}}
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,1,5,6,7,8,9] => [6,8,7,9,5,4,3,2,1] => {{1,4,6,9},{2,8},{3,7},{5}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => [8,7,6,9,5,4,3,2,1] => {{1,2,3,4,6,7,8,9},{5}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [8,7,1,2,3,4,5,6,9] => [2,3,9,8,7,6,5,4,1] => {{1,2,3,9},{4,8},{5,7},{6}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,8,1,2,3,4,5,6,9] => [3,2,9,8,7,6,5,4,1] => {{1,3,9},{2},{4,8},{5,7},{6}}
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1,2,4,6,7,8,9] => [5,7,9,8,6,4,3,2,1] => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9] => [6,7,9,8,5,4,3,2,1] => {{1,2,3,4,6,7,8,9},{5}}
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9] => [7,6,9,8,5,4,3,2,1] => {{1,3,7,9},{2,4,6,8},{5}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1,3,4,5,6,7,9] => [2,8,9,7,6,5,4,3,1] => {{1,2,3,8,9},{4,7},{5,6}}
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9] => [7,8,9,6,5,4,3,2,1] => {{1,3,7,9},{2,8},{4,6},{5}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9] => [8,7,9,6,5,4,3,2,1] => {{1,2,3,7,8,9},{4,6},{5}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,7,9] => [2,9,8,7,6,5,4,3,1] => {{1,2,9},{3,8},{4,7},{5,6}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,5,6,8,9] => [3,9,8,7,6,5,4,2,1] => {{1,2,3,8,9},{4,7},{5,6}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => [4,9,8,7,6,5,3,2,1] => {{1,2,3,4,7,8,9},{5,6}}
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => [5,9,8,7,6,4,3,2,1] => {{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => [6,9,8,7,5,4,3,2,1] => {{1,2,3,4,6,7,8,9},{5}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => [7,9,8,6,5,4,3,2,1] => {{1,2,3,7,8,9},{4,6},{5}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [8,9,7,6,5,4,3,2,1] => {{1,2,8,9},{3,7},{4,6},{5}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [9,8,7,6,5,4,3,2,1] => {{1,9},{2,8},{3,7},{4,6},{5}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1] => [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] => [8,9,7,6,5,4,3,2,1] => [2,1,3,4,5,6,7,8,9] => {{1,2},{3},{4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,2,1] => [2,3,1,4,5,6,7,8,9] => {{1,2,3},{4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,7,6,9,5,4,3,2,1] => [2,3,4,1,5,6,7,8,9] => {{1,2,3,4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,9,4,3,2,1] => [2,3,4,5,1,6,7,8,9] => {{1,2,3,4,5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,9,3,2,1] => [2,3,4,5,6,1,7,8,9] => {{1,2,3,4,5,6},{7},{8},{9}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,9,2,1] => [2,3,4,5,6,7,1,8,9] => {{1,2,3,4,5,6,7},{8},{9}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [2,3,4,5,6,7,8,1,9] => {{1,2,3,4,5,6,7,8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,2,1] => [2,1,3,4,5,6,7,8,9,10] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,8,9,6,5,4,3,2,1] => [3,2,1,4,5,6,7,8,9] => {{1,3},{2},{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] => [9,8,10,7,6,5,4,3,2,1] => [2,3,1,4,5,6,7,8,9,10] => {{1,2,3},{4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [8,6,7,9,5,4,3,2,1] => [2,4,3,1,5,6,7,8,9] => {{1,2,4},{3},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,8,7,10,6,5,4,3,2,1] => [2,3,4,1,5,6,7,8,9,10] => {{1,2,3,4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [8,7,5,6,9,4,3,2,1] => [2,3,5,4,1,6,7,8,9] => {{1,2,3,5},{4},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,8,7,6,10,5,4,3,2,1] => [2,3,4,5,1,6,7,8,9,10] => {{1,2,3,4,5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,9,3,2,1] => [2,3,4,6,5,1,7,8,9] => {{1,2,3,4,6},{5},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,10,4,3,2,1] => [2,3,4,5,6,1,7,8,9,10] => {{1,2,3,4,5,6},{7},{8},{9},{10}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,4,9,2,1] => [2,3,4,5,7,6,1,8,9] => {{1,2,3,4,5,7},{6},{8},{9}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,10,3,2,1] => [2,3,4,5,6,7,1,8,9,10] => {{1,2,3,4,5,6,7},{8},{9},{10}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,9,1] => [2,3,4,5,6,8,7,1,9] => {{1,2,3,4,5,6,8},{7},{9}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,10,2,1] => [2,3,4,5,6,7,8,1,9,10] => {{1,2,3,4,5,6,7,8},{9},{10}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [2,3,4,5,6,7,8,9,1,10] => {{1,2,3,4,5,6,7,8,9},{10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,8,9,10,1] => {{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,3,2,1] => [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] => [10,11,9,8,7,6,5,4,3,2,1] => [2,1,3,4,5,6,7,8,9,10,11] => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => [3,2,1,4,5,6,7,8,9,10] => {{1,3},{2},{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] => [10,9,11,8,7,6,5,4,3,2,1] => [2,3,1,4,5,6,7,8,9,10,11] => {{1,2,3},{4},{5},{6},{7},{8},{9},{10},{11}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [7,6,8,9,5,4,3,2,1] => [3,4,2,1,5,6,7,8,9] => {{1,2,3,4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [4,3,2,1,5,6,7,8,9] => {{1,4},{2,3},{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] => [9,8,7,6,5,4,3,1,2,10] => [2,3,4,5,6,7,8,10,9,1] => {{1,2,3,4,5,6,7,8,10},{9}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [2,3,4,5,6,7,8,9,10,1,11] => {{1,2,3,4,5,6,7,8,9,10},{11}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,1,11] => [2,3,4,5,6,7,8,9,10,11,1] => {{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => [4,3,2,1,5,6,7,8,9,10] => {{1,4},{2,3},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [6,5,7,8,9,4,3,2,1] => [4,5,3,2,1,6,7,8,9] => {{1,2,4,5},{3},{6},{7},{8},{9}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,1,2,3,10] => [2,3,4,5,6,7,10,9,8,1] => {{1,2,3,4,5,6,7,10},{8,9}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,1,2,11] => [2,3,4,5,6,7,8,9,11,10,1] => {{1,2,3,4,5,6,7,8,9,11},{10}}
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,8,9,3,2,1] => [3,4,5,6,2,1,7,8,9] => {{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] => [5,6,7,8,9,4,3,2,1] => [5,4,3,2,1,6,7,8,9] => {{1,5},{2,4},{3},{6},{7},{8},{9}}
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,8,9,2,1] => [3,4,5,6,7,2,1,8,9] => {{1,3,5,7},{2,4,6},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [5,4,3,2,1,6,7,8,9,10] => {{1,5},{2,4},{3},{6},{7},{8},{9},{10}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,6,5,4,3,2,7,9,1] => [2,4,5,6,7,8,3,1,9] => {{1,2,4,6,8},{3,5,7},{9}}
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,8,9,1] => [3,4,5,6,7,8,2,1,9] => {{1,2,3,4,5,6,7,8},{9}}
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [5,4,6,7,8,9,3,2,1] => [5,6,4,3,2,1,7,8,9] => {{1,2,5,6},{3,4},{7},{8},{9}}
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [6,5,4,3,2,1,7,8,9] => {{1,6},{2,5},{3,4},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => [6,5,4,3,2,1,7,8,9,10] => {{1,6},{2,5},{3,4},{7},{8},{9},{10}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9,7,6,5,4,3,2,1,8,10] => [2,4,5,6,7,8,9,10,3,1] => {{1,2,4,6,8,10},{3,5,7,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [9,7,8,6,5,4,3,2,1] => [1,3,2,4,5,6,7,8,9] => {{1},{2,3},{4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [9,8,6,7,5,4,3,2,1] => [1,2,4,3,5,6,7,8,9] => {{1},{2},{3,4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [8,9,6,7,5,4,3,2,1] => [2,1,4,3,5,6,7,8,9] => {{1,2},{3,4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [9,6,7,8,5,4,3,2,1] => [1,4,3,2,5,6,7,8,9] => {{1},{2,4},{3},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,4,3,2,1] => [1,2,3,5,4,6,7,8,9] => {{1},{2},{3},{4,5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,4,3,2,1] => [1,3,2,5,4,6,7,8,9] => {{1},{2,3},{4,5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [7,8,9,5,6,4,3,2,1] => [3,2,1,5,4,6,7,8,9] => {{1,3},{2},{4,5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,3,2,1] => [1,2,3,4,6,5,7,8,9] => {{1},{2},{3},{4},{5,6},{7},{8},{9}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,3,2,1] => [2,1,4,3,6,5,7,8,9] => {{1,2},{3,4},{5,6},{7},{8},{9}}
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,4,5,3,2,1] => [4,3,2,1,6,5,7,8,9] => {{1,4},{2,3},{5,6},{7},{8},{9}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,4,2,1] => [1,2,3,4,5,7,6,8,9] => {{1},{2},{3},{4},{5},{6,7},{8},{9}}
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,3,4,2,1] => [5,4,3,2,1,7,6,8,9] => {{1,5},{2,4},{3},{6,7},{8},{9}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,2,3,1] => [1,2,3,4,5,6,8,7,9] => {{1},{2},{3},{4},{5},{6},{7,8},{9}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,2,3,1] => [2,1,3,4,5,6,8,7,9] => {{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] => [9,8,7,6,4,5,2,3,1] => [1,2,3,4,6,5,8,7,9] => {{1},{2},{3},{4},{5,6},{7,8},{9}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [9,8,6,7,4,5,2,3,1] => [1,2,4,3,6,5,8,7,9] => {{1},{2},{3,4},{5,6},{7,8},{9}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,2,3,1] => [2,1,4,3,6,5,8,7,9] => {{1,2},{3,4},{5,6},{7,8},{9}}
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,3,1] => [6,5,4,3,2,1,8,7,9] => {{1,6},{2,5},{3,4},{7,8},{9}}
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,2,3,4,1] => [5,4,3,2,1,8,7,6,9] => {{1,5},{2,4},{3},{6,8},{7},{9}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,3,4,5,1] => [4,3,2,1,8,7,6,5,9] => {{1,4},{2,3},{5,8},{6,7},{9}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,3,4,5,6,7,1] => [2,1,8,7,6,5,4,3,9] => {{1,2},{3,8},{4,7},{5,6},{9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,7,9,8] => {{1},{2},{3},{4},{5},{6},{7},{8,9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,3,1,2] => [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] => [9,7,8,6,5,4,3,1,2] => [1,3,2,4,5,6,7,9,8] => {{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] => [9,8,7,6,5,3,4,1,2] => [1,2,3,4,5,7,6,9,8] => {{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] => [9,8,7,5,6,3,4,1,2] => [1,2,3,5,4,7,6,9,8] => {{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] => [9,7,8,5,6,3,4,1,2] => [1,3,2,5,4,7,6,9,8] => {{1},{2,3},{4,5},{6,7},{8,9}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [7,8,9,5,6,3,4,1,2] => [3,2,1,5,4,7,6,9,8] => {{1,3},{2},{4,5},{6,7},{8,9}}
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,3,4,1,2] => [5,4,3,2,1,7,6,9,8] => {{1,5},{2,4},{3},{6,7},{8,9}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,1,2] => [1,7,6,5,4,3,2,9,8] => {{1},{2,7},{3,6},{4,5},{8,9}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,1,2,3] => [1,2,3,4,5,6,9,8,7] => {{1},{2},{3},{4},{5},{6},{7,9},{8}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,1,2,3] => [1,2,3,4,6,5,9,8,7] => {{1},{2},{3},{4},{5,6},{7,9},{8}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [8,9,6,7,4,5,1,2,3] => [2,1,4,3,6,5,9,8,7] => {{1,2},{3,4},{5,6},{7,9},{8}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,6,1,2,3] => [1,2,3,6,5,4,9,8,7] => {{1},{2},{3},{4,6},{5},{7,9},{8}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [7,8,9,4,5,6,1,2,3] => [3,2,1,6,5,4,9,8,7] => {{1,3},{2},{4,6},{5},{7,9},{8}}
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,1,2,3] => [6,5,4,3,2,1,9,8,7] => {{1,6},{2,5},{3,4},{7,9},{8}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,1,2,3,4] => [1,2,3,4,5,9,8,7,6] => {{1},{2},{3},{4},{5},{6,9},{7,8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,1,2,3,4] => [1,2,3,5,4,9,8,7,6] => {{1},{2},{3},{4,5},{6,9},{7,8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [9,7,8,5,6,1,2,3,4] => [1,3,2,5,4,9,8,7,6] => {{1},{2,3},{4,5},{6,9},{7,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [9,8,5,6,7,1,2,3,4] => [1,2,5,4,3,9,8,7,6] => {{1},{2},{3,5},{4},{6,9},{7,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [8,9,5,6,7,1,2,3,4] => [2,1,5,4,3,9,8,7,6] => {{1,2},{3,5},{4},{6,9},{7,8}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [9,5,6,7,8,1,2,3,4] => [1,5,4,3,2,9,8,7,6] => {{1},{2,5},{3,4},{6,9},{7,8}}
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => [5,4,3,2,1,9,8,7,6] => {{1,5},{2,4},{3},{6,9},{7,8}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,1,2,3,4,5] => [1,2,3,4,9,8,7,6,5] => {{1},{2},{3},{4},{5,9},{6,8},{7}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [9,8,6,7,1,2,3,4,5] => [1,2,4,3,9,8,7,6,5] => {{1},{2},{3,4},{5,9},{6,8},{7}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [9,6,7,8,1,2,3,4,5] => [1,4,3,2,9,8,7,6,5] => {{1},{2,4},{3},{5,9},{6,8},{7}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [4,3,2,1,9,8,7,6,5] => {{1,4},{2,3},{5,9},{6,8},{7}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,1,2,3,4,5,6] => [1,2,3,9,8,7,6,5,4] => {{1},{2},{3},{4,9},{5,8},{6,7}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [9,7,8,1,2,3,4,5,6] => [1,3,2,9,8,7,6,5,4] => {{1},{2,3},{4,9},{5,8},{6,7}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => [3,2,1,9,8,7,6,5,4] => {{1,3},{2},{4,9},{5,8},{6,7}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [10,8,9,7,6,5,4,3,2,1] => [1,3,2,4,5,6,7,8,9,10] => {{1},{2,3},{4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [10,9,7,8,6,5,4,3,2,1] => [1,2,4,3,5,6,7,8,9,10] => {{1},{2},{3,4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [9,10,7,8,6,5,4,3,2,1] => [2,1,4,3,5,6,7,8,9,10] => {{1,2},{3,4},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [10,9,8,6,7,5,4,3,2,1] => [1,2,3,5,4,6,7,8,9,10] => {{1},{2},{3},{4,5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,4,3,2,1] => [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] => [9,10,7,8,5,6,4,3,2,1] => [2,1,4,3,6,5,7,8,9,10] => {{1,2},{3,4},{5,6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,5,3,2,1] => [1,2,3,4,5,7,6,8,9,10] => {{1},{2},{3},{4},{5},{6,7},{8},{9},{10}}
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [7,6,5,4,3,2,1,8,9,10] => {{1,7},{2,6},{3,5},{4},{8},{9},{10}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,4,2,1] => [1,2,3,4,5,6,8,7,9,10] => {{1},{2},{3},{4},{5},{6},{7,8},{9},{10}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,4,2,1] => [2,1,4,3,6,5,8,7,9,10] => {{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] => [10,9,8,7,6,5,4,2,3,1] => [1,2,3,4,5,6,7,9,8,10] => {{1},{2},{3},{4},{5},{6},{7},{8,9},{10}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [10,9,8,6,7,4,5,2,3,1] => [1,2,3,5,4,7,6,9,8,10] => {{1},{2},{3},{4,5},{6,7},{8,9},{10}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,2,3,1] => [1,3,2,5,4,7,6,9,8,10] => {{1},{2,3},{4,5},{6,7},{8,9},{10}}
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,2,3,1] => [7,6,5,4,3,2,1,9,8,10] => {{1,7},{2,6},{3,5},{4},{8,9},{10}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,2,3,4,1] => [3,2,1,6,5,4,9,8,7,10] => {{1,3},{2},{4,6},{5},{7,9},{8},{10}}
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,2,3,4,1] => [6,5,4,3,2,1,9,8,7,10] => {{1,6},{2,5},{3,4},{7,9},{8},{10}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,2,3,4,5,1] => [5,4,3,2,1,9,8,7,6,10] => {{1,5},{2,4},{3},{6,9},{7,8},{10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8,10,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,1,2] => [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] => [10,9,8,7,6,5,3,4,1,2] => [1,2,3,4,5,6,8,7,10,9] => {{1},{2},{3},{4},{5},{6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,3,4,1,2] => [1,2,3,4,6,5,8,7,10,9] => {{1},{2},{3},{4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [10,9,7,8,5,6,3,4,1,2] => [1,2,4,3,6,5,8,7,10,9] => {{1},{2},{3,4},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7,10,9] => {{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] => [10,9,8,7,6,5,4,1,2,3] => [1,2,3,4,5,6,7,10,9,8] => {{1},{2},{3},{4},{5},{6},{7},{8,10},{9}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,5,1,2,3] => [1,2,3,4,5,7,6,10,9,8] => {{1},{2},{3},{4},{5},{6,7},{8,10},{9}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,1,2,3] => [1,3,2,5,4,7,6,10,9,8] => {{1},{2,3},{4,5},{6,7},{8,10},{9}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,6,1,2,3] => [2,1,4,3,7,6,5,10,9,8] => {{1,2},{3,4},{5,7},{6},{8,10},{9}}
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => [7,6,5,4,3,2,1,10,9,8] => {{1,7},{2,6},{3,5},{4},{8,10},{9}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,1,2,3,4] => [1,2,3,4,5,6,10,9,8,7] => {{1},{2},{3},{4},{5},{6},{7,10},{8,9}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,1,2,3,4] => [2,1,4,3,6,5,10,9,8,7] => {{1,2},{3,4},{5,6},{7,10},{8,9}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [8,9,10,5,6,7,1,2,3,4] => [3,2,1,6,5,4,10,9,8,7] => {{1,3},{2},{4,6},{5},{7,10},{8,9}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [10,9,5,6,7,8,1,2,3,4] => [1,2,6,5,4,3,10,9,8,7] => {{1},{2},{3,6},{4,5},{7,10},{8,9}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [9,10,5,6,7,8,1,2,3,4] => [2,1,6,5,4,3,10,9,8,7] => {{1,2},{3,6},{4,5},{7,10},{8,9}}
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [6,5,4,3,2,1,10,9,8,7] => {{1,6},{2,5},{3,4},{7,10},{8,9}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,1,2,3,4,5] => [1,2,3,4,5,10,9,8,7,6] => {{1},{2},{3},{4},{5},{6,10},{7,9},{8}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,1,2,3,4,5] => [1,3,2,5,4,10,9,8,7,6] => {{1},{2,3},{4,5},{6,10},{7,9},{8}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [10,6,7,8,9,1,2,3,4,5] => [1,5,4,3,2,10,9,8,7,6] => {{1},{2,5},{3,4},{6,10},{7,9},{8}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [5,4,3,2,1,10,9,8,7,6] => {{1,5},{2,4},{3},{6,10},{7,9},{8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,1,2,3,4,5,6] => [1,2,3,4,10,9,8,7,6,5] => {{1},{2},{3},{4},{5,10},{6,9},{7,8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [10,7,8,9,1,2,3,4,5,6] => [1,4,3,2,10,9,8,7,6,5] => {{1},{2,4},{3},{5,10},{6,9},{7,8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [4,3,2,1,10,9,8,7,6,5] => {{1,4},{2,3},{5,10},{6,9},{7,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [10,9,8,1,2,3,4,5,6,7] => [1,2,3,10,9,8,7,6,5,4] => {{1},{2},{3},{4,10},{5,9},{6,8},{7}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [10,8,9,1,2,3,4,5,6,7] => [1,3,2,10,9,8,7,6,5,4] => {{1},{2,3},{4,10},{5,9},{6,8},{7}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [3,2,1,10,9,8,7,6,5,4] => {{1,3},{2},{4,10},{5,9},{6,8},{7}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,3,2,1] => {{1,10},{2,9},{3,8},{4,7},{5,6}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,2,1,3] => [1,2,3,4,5,6,8,9,7] => {{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,2,1,4] => [1,2,3,4,5,7,8,9,6] => {{1},{2},{3},{4},{5},{6,7,8,9}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,2,1,5] => [1,2,3,4,6,7,8,9,5] => {{1},{2},{3},{4},{5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [9,8,7,5,4,3,2,1,6] => [1,2,3,5,6,7,8,9,4] => {{1},{2},{3},{4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,4,3,2,1,7] => [1,2,4,5,6,7,8,9,3] => {{1},{2},{3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,2,1,8] => [1,3,4,5,6,7,8,9,2] => {{1},{2,3,4,5,6,7,8,9}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,2,1,3] => [1,2,3,4,5,6,7,9,10,8] => {{1},{2},{3},{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] => [9,8,7,6,5,2,3,1,4] => [1,2,3,4,5,8,7,9,6] => {{1},{2},{3},{4},{5},{6,8,9},{7}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,2,1,4] => [1,2,3,4,5,6,8,9,10,7] => {{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,3,4,2,1,5] => [1,2,3,4,7,6,8,9,5] => {{1},{2},{3},{4},{5,7,8,9},{6}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,3,2,1,5] => [1,2,3,4,5,7,8,9,10,6] => {{1},{2},{3},{4},{5},{6,7,8,9,10}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,5,3,2,1,6] => [1,2,3,6,5,7,8,9,4] => {{1},{2},{3},{4,6,7,8,9},{5}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,4,3,2,1,6] => [1,2,3,4,6,7,8,9,10,5] => {{1},{2},{3},{4},{5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [9,8,5,6,4,3,2,1,7] => [1,2,5,4,6,7,8,9,3] => {{1},{2},{3,5,6,7,8,9},{4}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [10,9,8,6,5,4,3,2,1,7] => [1,2,3,5,6,7,8,9,10,4] => {{1},{2},{3},{4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [9,6,7,5,4,3,2,1,8] => [1,4,3,5,6,7,8,9,2] => {{1},{2,4,5,6,7,8,9},{3}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [10,9,7,6,5,4,3,2,1,8] => [1,2,4,5,6,7,8,9,10,3] => {{1},{2},{3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,2,1,9] => [1,3,4,5,6,7,8,9,10,2] => {{1},{2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,1,2,7,8,9,10] => [5,6,7,8,10,9,4,3,2,1] => {{1,5,10},{2,6,9},{3,4,7,8}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,1,2,8,9,10] => [4,5,6,7,8,10,9,3,2,1] => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,3,1,2] => [1,2,3,4,5,6,7,8,9,11,10] => {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,1,2] => [2,3,1,4,5,6,7,9,8] => {{1,2,3},{4},{5},{6},{7},{8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,1,10] => [3,2,4,5,6,7,8,9,10,1] => {{1,3,4,5,6,7,8,9,10},{2}}
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => [9,8,10,7,6,5,4,3,2,1] => {{1,2,3,8,9,10},{4,7},{5,6}}
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => [8,10,9,7,6,5,4,3,2,1] => {{1,2,3,8,9,10},{4,7},{5,6}}
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10,11] => [10,9,11,8,7,6,5,4,3,2,1] => {{1,2,3,9,10,11},{4,8},{5,7},{6}}
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9,10] => [7,8,10,9,6,5,4,3,2,1] => {{1,2,3,4,7,8,9,10},{5,6}}
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11] => [9,11,10,8,7,6,5,4,3,2,1] => {{1,2,3,9,10,11},{4,8},{5,7},{6}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,2,1,3] => [2,3,1,4,5,6,8,9,7] => {{1,2,3},{4},{5},{6},{7,8,9}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,2,1,3] => [2,1,3,4,5,6,8,9,7] => {{1,2},{3},{4},{5},{6},{7,8,9}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,6,5,4,3,2,1,7,8] => [1,4,5,6,7,8,9,3,2] => {{1},{2,3,4,5,6,7,8,9}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,1,3,4] => [1,2,3,4,5,8,9,7,6] => {{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] => [2,3,4,5,6,7,8,9,1,10] => [9,8,7,6,5,4,3,2,10,1] => {{1,9,10},{2,8},{3,7},{4,6},{5}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,8,10] => [2,10,9,8,7,6,5,4,3,1] => {{1,2,10},{3,9},{4,8},{5,7},{6}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => [2,11,10,9,8,7,6,5,4,3,1] => {{1,2,11},{3,10},{4,9},{5,8},{6,7}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [9,8,6,1,2,3,4,5,7] => [1,2,4,9,8,7,6,5,3] => {{1},{2},{3,4,9},{5,8},{6,7}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [9,8,7,5,1,2,3,4,6] => [1,2,3,5,9,8,7,6,4] => {{1},{2},{3},{4,5,9},{6,8},{7}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,1,2,3,5] => [1,2,3,4,6,9,8,7,5] => {{1},{2},{3},{4},{5,6,9},{7,8}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,1,2,4] => [1,2,3,4,5,7,9,8,6] => {{1},{2},{3},{4},{5},{6,7,9},{8}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [9,10,8,7,6,5,4,3,2,1] => {{1,2,9,10},{3,8},{4,7},{5,6}}
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9,10] => [9,8,7,10,6,5,4,3,2,1] => {{1,2,3,4,7,8,9,10},{5,6}}
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9,10] => [9,8,7,6,10,5,4,3,2,1] => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10] => [9,8,7,6,5,10,4,3,2,1] => {{1,2,3,4,6,7,8,9,10},{5}}
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9,10] => [9,8,7,6,5,4,10,3,2,1] => {{1,2,3,7,8,9,10},{4,6},{5}}
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9,10] => [9,8,7,6,5,4,3,10,2,1] => {{1,2,8,9,10},{3,7},{4,6},{5}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,6,5,4,3,2,7,1,8] => [1,4,5,6,7,8,3,9,2] => {{1},{2,4,6,8,9},{3,5,7}}
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,9,1,10] => [3,4,5,6,7,8,9,2,10,1] => {{1,3,5,7,9,10},{2,4,6,8}}
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => [10,11,9,8,7,6,5,4,3,2,1] => {{1,2,10,11},{3,9},{4,8},{5,7},{6}}
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,1,3] => [6,5,4,3,2,1,8,9,7] => {{1,6},{2,5},{3,4},{7,8,9}}
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,2,1,3,4] => [5,4,3,2,1,8,9,7,6] => {{1,5},{2,4},{3},{6,7,8,9}}
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,1,3,4,5] => [4,3,2,1,8,9,7,6,5] => {{1,4},{2,3},{5,6,8,9},{7}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,2,1,3,4,5,6] => [3,2,1,8,9,7,6,5,4] => {{1,3},{2},{4,5,8,9},{6,7}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,1,2,8] => [1,3,4,5,6,7,9,8,2] => {{1},{2,3,4,5,6,7,9},{8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,9,1] => [3,2,4,5,6,7,8,1,9] => {{1,3,4,5,6,7,8},{2},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [8,9,6,5,4,3,2,1,7] => [2,1,4,5,6,7,8,9,3] => {{1,2},{3,4,5,6,7,8,9}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,9,1,2] => [2,3,4,5,6,7,1,9,8] => {{1,2,3,4,5,6,7},{8,9}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [7,8,9,5,4,3,2,1,6] => [3,2,1,5,6,7,8,9,4] => {{1,3},{2},{4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7,8,9,6,5,4,3,2,1,10] => [4,3,2,5,6,7,8,9,10,1] => {{1,4,5,6,7,8,9,10},{2,3}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,4,3,2,1,5] => [4,3,2,1,6,7,8,9,5] => {{1,4},{2,3},{5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,1,8,9,10] => [4,5,6,7,8,9,10,3,2,1] => {{1,4,7,10},{2,3,5,6,8,9}}
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [6,5,7,8,9,1,2,3,4] => [4,5,3,2,1,9,8,7,6] => {{1,2,4,5},{3},{6,9},{7,8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [8,7,9,1,2,3,4,5,6] => [2,3,1,9,8,7,6,5,4] => {{1,2,3},{4,9},{5,8},{6,7}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => [3,10,9,8,7,6,5,4,2,1] => {{1,2,3,9,10},{4,8},{5,7},{6}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [7,6,8,9,1,2,3,4,5] => [3,4,2,1,9,8,7,6,5] => {{1,2,3,4},{5,9},{6,8},{7}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => [4,10,9,8,7,6,5,3,2,1] => {{1,2,3,4,8,9,10},{5,7},{6}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => [5,10,9,8,7,6,4,3,2,1] => {{1,2,3,4,5,7,8,9,10},{6}}
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [5,4,6,7,8,9,1,2,3] => [5,6,4,3,2,1,9,8,7] => {{1,2,5,6},{3,4},{7,9},{8}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => [6,10,9,8,7,5,4,3,2,1] => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => [7,10,9,8,6,5,4,3,2,1] => {{1,2,3,4,7,8,9,10},{5,6}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [9,8,6,5,7,4,3,2,1] => [1,2,4,5,3,6,7,8,9] => {{1},{2},{3,4,5},{6},{7},{8},{9}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,3,2,5,1] => [1,2,3,4,5,7,8,9,6,10] => {{1},{2},{3},{4},{5},{6,7,8,9},{10}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,9,4,3,1,2] => [2,3,4,5,1,6,7,9,8] => {{1,2,3,4,5},{6},{7},{8,9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [8,9,6,5,7,4,3,2,1] => [2,1,4,5,3,6,7,8,9] => {{1,2},{3,4,5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,6,4,3,2,1,10] => [2,3,4,6,5,7,8,9,10,1] => {{1,2,3,4,6,7,8,9,10},{5}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [9,6,7,4,5,2,3,1,8] => [1,4,3,6,5,8,7,9,2] => {{1},{2,4,6,8,9},{3},{5},{7}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,2,3,1,4] => [2,1,4,3,6,5,9,8,10,7] => {{1,2},{3,4},{5,6},{7,9,10},{8}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,2,3,1,6] => [2,1,4,3,7,6,9,8,10,5] => {{1,2},{3,4},{5,7,9,10},{6},{8}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [9,10,6,7,4,5,2,3,1,8] => [2,1,5,4,7,6,9,8,10,3] => {{1,2},{3,5,7,9,10},{4},{6},{8}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8,9,6,7,4,5,2,3,1,10] => [3,2,5,4,7,6,9,8,10,1] => {{1,3,5,7,9,10},{2},{4},{6},{8}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [10,8,9,6,7,4,5,2,1,3] => [1,3,2,5,4,7,6,9,10,8] => {{1},{2,3},{4,5},{6,7},{8,9,10}}
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,1,10] => [8,7,6,5,4,3,2,9,10,1] => {{1,8,9,10},{2,7},{3,6},{4,5}}
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,3,2,1,10] => [7,6,5,4,3,2,8,9,10,1] => {{1,7,8,9,10},{2,6},{3,5},{4}}
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1,10] => [6,5,4,3,2,7,8,9,10,1] => {{1,6,7,8,9,10},{2,5},{3,4}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [6,7,8,9,5,4,3,2,1,10] => [5,4,3,2,6,7,8,9,10,1] => {{1,5,6,7,8,9,10},{2,4},{3}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,1,9,10] => [3,4,5,6,7,8,9,10,2,1] => {{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [9,10,8,7,6,5,4,3,2,1,11] => [3,2,4,5,6,7,8,9,10,11,1] => {{1,3,4,5,6,7,8,9,10,11},{2}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,4,3,2,1,10,11] => [3,4,5,6,7,8,9,10,11,2,1] => {{1,3,5,7,9,11},{2,4,6,8,10}}
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9,10] => [8,7,10,9,6,5,4,3,2,1] => {{1,3,8,10},{2,4,7,9},{5,6}}
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => [7,6,5,10,9,8,4,3,2,1] => {{1,4,7,10},{2,3,5,6,8,9}}
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => [6,5,4,3,10,9,8,7,2,1] => {{1,2,5,6,9,10},{3,4},{7,8}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [6,5,7,4,8,3,9,2,10,1] => [5,6,4,7,3,8,2,9,1,10] => {{1,2,3,4,5,6,7,8,9},{10}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [10,8,6,4,2,1,3,5,7,9] => [1,3,5,7,9,10,8,6,4,2] => {{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] => [1,2,3,4,5,6,7,8,9,10,11] => [11,10,9,8,7,6,5,4,3,2,1] => {{1,11},{2,10},{3,9},{4,8},{5,7},{6}}
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,11,1,2] => [9,8,7,6,5,4,3,2,1,11,10] => {{1,9},{2,8},{3,7},{4,6},{5},{10,11}}
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [10,7,6,5,4,3,2,1,8,9] => [1,4,5,6,7,8,9,10,3,2] => {{1},{2,4,6,8,10},{3,5,7,9}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [9,5,4,3,2,1,6,7,8] => [1,5,6,7,8,9,4,3,2] => {{1},{2,3,5,6,8,9},{4,7}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [10,5,4,3,2,1,6,7,8,9] => [1,6,7,8,9,10,5,4,3,2] => {{1},{2,6,10},{3,5,7,9},{4,8}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [10,6,5,4,3,2,1,7,8,9] => [1,5,6,7,8,9,10,4,3,2] => {{1},{2,4,5,7,8,10},{3,6,9}}
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1,11] => [10,9,8,7,6,5,4,3,2,11,1] => {{1,10,11},{2,9},{3,8},{4,7},{5,6}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,2,1,3] => [1,2,3,4,5,6,7,8,10,11,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10,11}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,2,1,3] => [2,1,3,4,5,6,7,9,10,8] => {{1,2},{3},{4},{5},{6},{7},{8,9,10}}
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,3,9,2,1] => [6,5,4,3,2,7,1,8,9] => {{1,6,7},{2,5},{3,4},{8},{9}}
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,4,9,3,2,1] => [5,4,3,2,6,1,7,8,9] => {{1,5,6},{2,4},{3},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [6,7,8,5,9,4,3,2,1] => [4,3,2,5,1,6,7,8,9] => {{1,4,5},{2,3},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [7,8,6,9,5,4,3,2,1] => [3,2,4,1,5,6,7,8,9] => {{1,3,4},{2},{5},{6},{7},{8},{9}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,9,1,2,3] => [2,3,4,5,6,1,9,8,7] => {{1,2,3,4,5,6},{7,9},{8}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,9,1,2,3,4] => [2,3,4,5,1,9,8,7,6] => {{1,2,3,4,5},{6,9},{7,8}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [10,11,1,2,3,4,5,6,7,8,9] => [2,1,11,10,9,8,7,6,5,4,3] => {{1,2},{3,11},{4,10},{5,9},{6,8},{7}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1,7,8,9,10] => [5,6,7,8,9,10,4,3,2,1] => {{1,2,5,6,9,10},{3,4,7,8}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,2,4,1] => [1,2,3,4,5,7,8,6,9] => {{1},{2},{3},{4},{5},{6,7,8},{9}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,10,1,2] => [2,3,4,5,6,7,8,1,10,9] => {{1,2,3,4,5,6,7,8},{9,10}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,9,2,1,3] => [2,3,4,5,6,1,8,9,7] => {{1,2,3,4,5,6},{7,8,9}}
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9,10] => [8,9,10,7,6,5,4,3,2,1] => {{1,3,8,10},{2,9},{4,7},{5,6}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [9,8,7,10,5,4,3,2,1,6] => [2,3,4,1,6,7,8,9,10,5] => {{1,2,3,4},{5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [9,7,6,8,5,4,3,2,1] => [1,3,4,2,5,6,7,8,9] => {{1},{2,3,4},{5},{6},{7},{8},{9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [10,8,7,9,6,5,4,3,2,1] => [1,3,4,2,5,6,7,8,9,10] => {{1},{2,3,4},{5},{6},{7},{8},{9},{10}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,4,3,2,1,5] => [2,1,3,4,5,7,8,9,10,6] => {{1,2},{3},{4},{5},{6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9,10] => [6,7,8,9,10,5,4,3,2,1] => {{1,5,6,10},{2,4,7,9},{3,8}}
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9,10] => [7,8,9,10,6,5,4,3,2,1] => {{1,4,7,10},{2,3,8,9},{5,6}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [11,9,8,7,6,5,4,3,2,1,10] => [1,3,4,5,6,7,8,9,10,11,2] => {{1},{2,3,4,5,6,7,8,9,10,11}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,2,8,1] => [1,3,4,5,6,7,8,2,9] => {{1},{2,3,4,5,6,7,8},{9}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,2,3,1] => [1,2,3,4,5,6,7,8,10,9,11] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10},{11}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => [3,2,10,9,8,7,6,5,4,1] => {{1,3,10},{2},{4,9},{5,8},{6,7}}
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2,10] => [8,7,6,5,4,3,2,10,9,1] => {{1,8,10},{2,7},{3,6},{4,5},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [7,6,8,5,9,4,3,2,1] => [3,4,2,5,1,6,7,8,9] => {{1,2,3,4,5},{6},{7},{8},{9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [9,10,7,6,5,4,3,2,1,8] => [2,1,4,5,6,7,8,9,10,3] => {{1,2},{3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [8,7,9,5,4,3,2,1,6] => [2,3,1,5,6,7,8,9,4] => {{1,2,3},{4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,1,2,3,4,7] => [1,2,4,5,9,8,7,6,3] => {{1},{2},{3,4,5,9},{6,8},{7}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [8,7,9,5,6,3,4,1,2] => [2,3,1,5,4,7,6,9,8] => {{1,2,3},{4,5},{6,7},{8,9}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [10,8,7,9,5,6,3,4,1,2] => [1,3,4,2,6,5,8,7,10,9] => {{1},{2,3,4},{5,6},{7,8},{9,10}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,2,1,3,4] => [2,1,4,3,6,5,9,10,8,7] => {{1,2},{3,4},{5,6},{7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [11,10,1,2,3,4,5,6,7,8,9] => [1,2,11,10,9,8,7,6,5,4,3] => {{1},{2},{3,11},{4,10},{5,9},{6,8},{7}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,2,4,1] => [1,2,3,4,5,6,8,9,7,10] => {{1},{2},{3},{4},{5},{6},{7,8,9},{10}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,2,9,1] => [1,3,4,5,6,7,8,9,2,10] => {{1},{2,3,4,5,6,7,8,9},{10}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,9,3,2,1,4] => [2,3,4,5,1,7,8,9,6] => {{1,2,3,4,5},{6,7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [8,9,7,10,6,5,4,3,2,1] => [3,2,4,1,5,6,7,8,9,10] => {{1,3,4},{2},{5},{6},{7},{8},{9},{10}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,4,7,3,2,1] => [1,2,4,5,6,3,7,8,9] => {{1},{2},{3,4,5,6},{7},{8},{9}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,1,2,4] => [2,1,4,3,6,5,8,10,9,7] => {{1,2},{3,4},{5,6},{7,8,10},{9}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [9,7,8,5,6,3,4,1,2,10] => [2,4,3,6,5,8,7,10,9,1] => {{1,2,4,6,8,10},{3},{5},{7},{9}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [10,7,8,5,6,3,4,1,2,9] => [1,4,3,6,5,8,7,10,9,2] => {{1},{2,4,6,8,10},{3},{5},{7},{9}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,1,2,9] => [1,3,4,5,6,7,8,10,9,2] => {{1},{2,3,4,5,6,7,8,10},{9}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,8,2,1] => [1,3,4,5,6,7,2,8,9] => {{1},{2,3,4,5,6,7},{8},{9}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,1,2,8] => [1,7,6,5,4,3,9,8,2] => {{1},{2,7,9},{3,6},{4,5},{8}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,8,1,2] => [1,3,4,5,6,7,2,9,8] => {{1},{2,3,4,5,6,7},{8,9}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [9,8,10,6,7,4,5,2,3,1] => [2,3,1,5,4,7,6,9,8,10] => {{1,2,3},{4,5},{6,7},{8,9},{10}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,9,2,3,1] => [2,3,4,5,6,1,8,7,9] => {{1,2,3,4,5,6},{7,8},{9}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,1,2,4] => [1,2,3,4,5,6,8,10,9,7] => {{1},{2},{3},{4},{5},{6},{7,8,10},{9}}
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1] => [5,4,6,3,7,2,8,1,9] => {{1,5,7,8},{2,3,4,6},{9}}
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [6,7,5,8,4,9,3,10,1,2] => [5,4,6,3,7,2,8,1,10,9] => {{1,5,7,8},{2,3,4,6},{9,10}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [8,9,7,10,4,5,2,3,1,6] => [3,2,4,1,7,6,9,8,10,5] => {{1,3,4},{2},{5,7,9,10},{6},{8}}
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8,9,6,7,4,5,2,3,10,1] => [3,2,5,4,7,6,9,8,1,10] => {{1,3,5,7,9},{2},{4},{6},{8},{10}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,1,2,3] => [1,2,3,4,5,6,7,8,11,10,9] => {{1},{2},{3},{4},{5},{6},{7},{8},{9,11},{10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7,10,9,12,11] => {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [11,9,10,7,8,5,6,3,4,1,2,12] => [2,4,3,6,5,8,7,10,9,12,11,1] => {{1,2,4,6,8,10,12},{3},{5},{7},{9},{11}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [7,8,5,6,3,4,1,2,9,10] => [4,3,6,5,8,7,10,9,2,1] => {{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,11,2,1] => [9,8,7,6,5,4,3,2,1,10,11] => {{1,9},{2,8},{3,7},{4,6},{5},{10},{11}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => [9,7,5,4,3,2,1,6,8,10] => [2,4,6,7,8,9,10,5,3,1] => {{1,2,4,7,10},{3,6,9},{5,8}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [8,7,6,9,4,3,2,1,5] => [2,3,4,1,6,7,8,9,5] => {{1,2,3,4},{5,6,7,8,9}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,1,2,10] => [3,2,4,5,6,7,8,10,9,1] => {{1,3,4,5,6,7,8,10},{2},{9}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,3,6,1,2] => [2,1,4,3,7,6,8,5,10,9] => {{1,2},{3,4},{5,7,8},{6},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [9,10,6,7,5,8,3,4,1,2] => [2,1,5,4,6,3,8,7,10,9] => {{1,2},{3,5,6},{4},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [8,9,7,10,5,6,3,4,1,2] => [3,2,4,1,6,5,8,7,10,9] => {{1,3,4},{2},{5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [8,9,6,7,5,10,3,4,1,2] => [3,2,5,4,6,1,8,7,10,9] => {{1,3,5,6},{2},{4},{7,8},{9,10}}
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8,9,6,7,4,5,3,10,1,2] => [3,2,5,4,7,6,8,1,10,9] => {{1,3,5,7,8},{2},{4},{6},{9,10}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [9,10,7,8,6,4,3,5,1,2] => [2,1,4,3,5,7,8,6,10,9] => {{1,2},{3,4},{5},{6,7,8},{9,10}}
[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,2,11,1] => [9,8,7,6,5,4,3,2,10,1,11] => {{1,9,10},{2,8},{3,7},{4,6},{5},{11}}
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1,10] => [6,5,7,4,8,3,9,2,10,1] => {{1,3,6,7,9,10},{2,5,8},{4}}
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [6,7,5,8,4,9,3,10,2,11,1,12] => [7,6,8,5,9,4,10,3,11,2,12,1] => {{1,2,4,5,6,7,9,10,11,12},{3,8}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7,8,9,4,5,6,1,2,3,10] => [4,3,2,7,6,5,10,9,8,1] => {{1,4,7,10},{2,3},{5,6},{8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [9,8,10,6,5,4,3,2,1,7] => [2,3,1,5,6,7,8,9,10,4] => {{1,2,3},{4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [9,8,7,10,5,6,3,2,1,4] => [2,3,4,1,6,5,8,9,10,7] => {{1,2,3,4},{5,6},{7,8,9,10}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,7,5,3,1,2,4,6,8] => [1,3,5,7,9,8,6,4,2] => {{1},{2,3,5,9},{4,6,7,8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,10,3,4,1,2] => [2,3,4,5,6,1,8,7,10,9] => {{1,2,3,4,5,6},{7,8},{9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [9,8,7,10,5,6,3,4,1,2] => [2,3,4,1,6,5,8,7,10,9] => {{1,2,3,4},{5,6},{7,8},{9,10}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [9,8,6,4,2,1,3,5,7] => [1,2,4,6,8,9,7,5,3] => {{1},{2},{3,4,6,9},{5,8},{7}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [8,7,9,6,10,5,4,3,2,1] => [3,4,2,5,1,6,7,8,9,10] => {{1,2,3,4,5},{6},{7},{8},{9},{10}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,4,3,2,1,6] => [2,1,4,3,6,7,8,9,10,5] => {{1,2},{3,4},{5,6,7,8,9,10}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,2,1,4] => [2,1,4,3,6,5,8,9,10,7] => {{1,2},{3,4},{5,6},{7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [12,10,9,8,7,6,5,4,3,2,1,11] => [1,3,4,5,6,7,8,9,10,11,12,2] => {{1},{2,3,4,5,6,7,8,9,10,11,12}}
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [6,5,4,7,3,8,2,9,1] => [4,5,6,3,7,2,8,1,9] => {{1,2,3,4,5,6,7,8},{9}}
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
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].
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
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