Identifier
Values
[1,0,1,0] => [2,1] => {{1,2}} => 1
[1,1,0,0] => [1,2] => {{1},{2}} => 0
[1,0,1,0,1,0] => [3,2,1] => {{1,3},{2}} => 1
[1,0,1,1,0,0] => [2,3,1] => {{1,2,3}} => 1
[1,1,0,0,1,0] => [3,1,2] => {{1,3},{2}} => 1
[1,1,0,1,0,0] => [2,1,3] => {{1,2},{3}} => 1
[1,1,1,0,0,0] => [1,2,3] => {{1},{2},{3}} => 0
[1,0,1,0,1,0,1,0] => [4,3,2,1] => {{1,4},{2,3}} => 2
[1,0,1,0,1,1,0,0] => [3,4,2,1] => {{1,3},{2,4}} => 1
[1,0,1,1,0,0,1,0] => [4,2,3,1] => {{1,4},{2},{3}} => 1
[1,0,1,1,0,1,0,0] => [3,2,4,1] => {{1,3,4},{2}} => 1
[1,0,1,1,1,0,0,0] => [2,3,4,1] => {{1,2,3,4}} => 1
[1,1,0,0,1,0,1,0] => [4,3,1,2] => {{1,4},{2,3}} => 2
[1,1,0,0,1,1,0,0] => [3,4,1,2] => {{1,3},{2,4}} => 1
[1,1,0,1,0,0,1,0] => [4,2,1,3] => {{1,4},{2},{3}} => 1
[1,1,0,1,0,1,0,0] => [3,2,1,4] => {{1,3},{2},{4}} => 1
[1,1,0,1,1,0,0,0] => [2,3,1,4] => {{1,2,3},{4}} => 1
[1,1,1,0,0,0,1,0] => [4,1,2,3] => {{1,4},{2},{3}} => 1
[1,1,1,0,0,1,0,0] => [3,1,2,4] => {{1,3},{2},{4}} => 1
[1,1,1,0,1,0,0,0] => [2,1,3,4] => {{1,2},{3},{4}} => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => {{1},{2},{3},{4}} => 0
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => {{1,5},{2,4},{3}} => 2
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => {{1,4},{2,5},{3}} => 1
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => {{1,5},{2,3,4}} => 2
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => {{1,4},{2,3,5}} => 2
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => {{1,3,5},{2,4}} => 1
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => {{1,5},{2,4},{3}} => 2
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => {{1,4},{2,5},{3}} => 1
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => {{1,5},{2,3},{4}} => 2
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => {{1,4,5},{2,3}} => 2
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => {{1,3},{2,4,5}} => 1
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => {{1,5},{2},{3},{4}} => 1
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => {{1,4,5},{2},{3}} => 1
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => {{1,3,4,5},{2}} => 1
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => {{1,2,3,4,5}} => 1
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => {{1,5},{2,4},{3}} => 2
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => {{1,4},{2,5},{3}} => 1
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => {{1,5},{2,3,4}} => 2
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => {{1,4},{2,3,5}} => 2
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => {{1,3,5},{2,4}} => 1
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => {{1,5},{2,4},{3}} => 2
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => {{1,4},{2,5},{3}} => 1
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => {{1,5},{2,3},{4}} => 2
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => {{1,4},{2,3},{5}} => 2
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => {{1,3},{2,4},{5}} => 1
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => {{1,5},{2},{3},{4}} => 1
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => {{1,4},{2},{3},{5}} => 1
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => {{1,3,4},{2},{5}} => 1
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => {{1,2,3,4},{5}} => 1
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => {{1,5},{2,4},{3}} => 2
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => {{1,4},{2,5},{3}} => 1
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => {{1,5},{2,3},{4}} => 2
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => {{1,4},{2,3},{5}} => 2
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => {{1,3},{2,4},{5}} => 1
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => {{1,5},{2},{3},{4}} => 1
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => {{1,4},{2},{3},{5}} => 1
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => {{1,3},{2},{4},{5}} => 1
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => {{1,2,3},{4},{5}} => 1
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => {{1,5},{2},{3},{4}} => 1
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => {{1,4},{2},{3},{5}} => 1
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => {{1,3},{2},{4},{5}} => 1
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => {{1,2},{3},{4},{5}} => 1
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => {{1},{2},{3},{4},{5}} => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => {{1,6},{2,5},{3,4}} => 3
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => {{1,5},{2,6},{3,4}} => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => {{1,6},{2,4},{3,5}} => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => {{1,5},{2,4},{3,6}} => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => {{1,4},{2,5},{3,6}} => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => {{1,6},{2,5},{3},{4}} => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => {{1,5},{2,6},{3},{4}} => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => {{1,6},{2,4,5},{3}} => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => {{1,5},{2,4,6},{3}} => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => {{1,4,6},{2,5},{3}} => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => {{1,6},{2,3,4,5}} => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => {{1,5},{2,3,4,6}} => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => {{1,4,6},{2,3,5}} => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => {{1,3,5},{2,4,6}} => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => {{1,6},{2,5},{3,4}} => 3
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => {{1,5},{2,6},{3,4}} => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => {{1,6},{2,4},{3,5}} => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => {{1,5},{2,4},{3,6}} => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => {{1,4},{2,5},{3,6}} => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => {{1,6},{2,5},{3},{4}} => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => {{1,5},{2,6},{3},{4}} => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => {{1,6},{2,4},{3},{5}} => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => {{1,5,6},{2,4},{3}} => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => {{1,4},{2,5,6},{3}} => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => {{1,6},{2,3,4},{5}} => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => {{1,5,6},{2,3,4}} => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => {{1,4},{2,3,5,6}} => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => {{1,3,5,6},{2,4}} => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => {{1,6},{2,5},{3},{4}} => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => {{1,5},{2,6},{3},{4}} => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => {{1,6},{2,4},{3},{5}} => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => {{1,5,6},{2,4},{3}} => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => {{1,4},{2,5,6},{3}} => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => {{1,6},{2,3},{4},{5}} => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => {{1,5,6},{2,3},{4}} => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => {{1,4,5,6},{2,3}} => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => {{1,3},{2,4,5,6}} => 1
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => {{1,6},{2},{3},{4},{5}} => 1
>>> Load all 632 entries. <<<
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => {{1,5,6},{2},{3},{4}} => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => {{1,4,5,6},{2},{3}} => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => {{1,3,4,5,6},{2}} => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => {{1,2,3,4,5,6}} => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => {{1,6},{2,5},{3,4}} => 3
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => {{1,5},{2,6},{3,4}} => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => {{1,6},{2,4},{3,5}} => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => {{1,5},{2,4},{3,6}} => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => {{1,4},{2,5},{3,6}} => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => {{1,6},{2,5},{3},{4}} => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => {{1,5},{2,6},{3},{4}} => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => {{1,6},{2,4,5},{3}} => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => {{1,5},{2,4,6},{3}} => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => {{1,4,6},{2,5},{3}} => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => {{1,6},{2,3,4,5}} => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => {{1,5},{2,3,4,6}} => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => {{1,4,6},{2,3,5}} => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => {{1,3,5},{2,4,6}} => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => {{1,6},{2,5},{3,4}} => 3
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => {{1,5},{2,6},{3,4}} => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => {{1,6},{2,4},{3,5}} => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => {{1,5},{2,4},{3,6}} => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => {{1,4},{2,5},{3,6}} => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => {{1,6},{2,5},{3},{4}} => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => {{1,5},{2,6},{3},{4}} => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => {{1,6},{2,4},{3},{5}} => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => {{1,5},{2,4},{3},{6}} => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => {{1,4},{2,5},{3},{6}} => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => {{1,6},{2,3,4},{5}} => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => {{1,5},{2,3,4},{6}} => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => {{1,4},{2,3,5},{6}} => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => {{1,3,5},{2,4},{6}} => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => {{1,6},{2,5},{3},{4}} => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => {{1,5},{2,6},{3},{4}} => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => {{1,6},{2,4},{3},{5}} => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => {{1,5},{2,4},{3},{6}} => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => {{1,4},{2,5},{3},{6}} => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => {{1,6},{2,3},{4},{5}} => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => {{1,5},{2,3},{4},{6}} => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => {{1,4,5},{2,3},{6}} => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => {{1,3},{2,4,5},{6}} => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => {{1,6},{2},{3},{4},{5}} => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => {{1,5},{2},{3},{4},{6}} => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => {{1,4,5},{2},{3},{6}} => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => {{1,3,4,5},{2},{6}} => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => {{1,2,3,4,5},{6}} => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => {{1,6},{2,5},{3,4}} => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => {{1,5},{2,6},{3,4}} => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => {{1,6},{2,4},{3,5}} => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => {{1,5},{2,4},{3,6}} => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => {{1,4},{2,5},{3,6}} => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => {{1,6},{2,5},{3},{4}} => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => {{1,5},{2,6},{3},{4}} => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => {{1,6},{2,4},{3},{5}} => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => {{1,5},{2,4},{3},{6}} => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => {{1,4},{2,5},{3},{6}} => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => {{1,6},{2,3,4},{5}} => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => {{1,5},{2,3,4},{6}} => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => {{1,4},{2,3,5},{6}} => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => {{1,3,5},{2,4},{6}} => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => {{1,6},{2,5},{3},{4}} => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => {{1,5},{2,6},{3},{4}} => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => {{1,6},{2,4},{3},{5}} => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => {{1,5},{2,4},{3},{6}} => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => {{1,4},{2,5},{3},{6}} => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => {{1,6},{2,3},{4},{5}} => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => {{1,5},{2,3},{4},{6}} => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => {{1,4},{2,3},{5},{6}} => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => {{1,3},{2,4},{5},{6}} => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => {{1,6},{2},{3},{4},{5}} => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => {{1,5},{2},{3},{4},{6}} => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => {{1,4},{2},{3},{5},{6}} => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => {{1,3,4},{2},{5},{6}} => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => {{1,2,3,4},{5},{6}} => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => {{1,6},{2,5},{3},{4}} => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => {{1,5},{2,6},{3},{4}} => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => {{1,6},{2,4},{3},{5}} => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => {{1,5},{2,4},{3},{6}} => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => {{1,4},{2,5},{3},{6}} => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => {{1,6},{2,3},{4},{5}} => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => {{1,5},{2,3},{4},{6}} => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => {{1,4},{2,3},{5},{6}} => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => {{1,3},{2,4},{5},{6}} => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => {{1,6},{2},{3},{4},{5}} => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => {{1,5},{2},{3},{4},{6}} => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => {{1,4},{2},{3},{5},{6}} => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => {{1,3},{2},{4},{5},{6}} => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => {{1,2,3},{4},{5},{6}} => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => {{1,6},{2},{3},{4},{5}} => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => {{1,5},{2},{3},{4},{6}} => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => {{1,4},{2},{3},{5},{6}} => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => {{1,3},{2},{4},{5},{6}} => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => {{1,2},{3},{4},{5},{6}} => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => {{1},{2},{3},{4},{5},{6}} => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => {{1,7},{2,6},{3,5},{4}} => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => {{1,6},{2,7},{3,5},{4}} => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => {{1,7},{2,5},{3,6},{4}} => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => {{1,6},{2,5},{3,7},{4}} => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => {{1,5},{2,6},{3,7},{4}} => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => {{1,7},{2,6},{3,4,5}} => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => {{1,6},{2,7},{3,4,5}} => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => {{1,7},{2,5},{3,4,6}} => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => {{1,6},{2,5},{3,4,7}} => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => {{1,5},{2,6},{3,4,7}} => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => {{1,7},{2,4,6},{3,5}} => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => {{1,6},{2,4,7},{3,5}} => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => {{1,5},{2,4,7},{3,6}} => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => {{1,4,7},{2,5},{3,6}} => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => {{1,7},{2,6},{3,5},{4}} => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => {{1,6},{2,7},{3,5},{4}} => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => {{1,7},{2,5},{3,6},{4}} => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => {{1,6},{2,5},{3,7},{4}} => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => {{1,5},{2,6},{3,7},{4}} => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => {{1,7},{2,6},{3,4},{5}} => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => {{1,6},{2,7},{3,4},{5}} => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => {{1,7},{2,5,6},{3,4}} => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => {{1,6},{2,5,7},{3,4}} => 3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => {{1,5,7},{2,6},{3,4}} => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => {{1,7},{2,4},{3,5,6}} => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => {{1,6},{2,4},{3,5,7}} => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => {{1,5,7},{2,4},{3,6}} => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => {{1,4},{2,5,7},{3,6}} => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => {{1,7},{2,6},{3},{4},{5}} => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => {{1,6},{2,7},{3},{4},{5}} => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => {{1,7},{2,5,6},{3},{4}} => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => {{1,6},{2,5,7},{3},{4}} => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => {{1,5,7},{2,6},{3},{4}} => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => {{1,7},{2,4,5,6},{3}} => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => {{1,6},{2,4,5,7},{3}} => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => {{1,5,7},{2,4,6},{3}} => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => {{1,4,6},{2,5,7},{3}} => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => {{1,7},{2,3,4,5,6}} => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => {{1,6},{2,3,4,5,7}} => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => {{1,5,7},{2,3,4,6}} => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => {{1,4,6},{2,3,5,7}} => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => {{1,3,5,7},{2,4,6}} => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => {{1,7},{2,6},{3,5},{4}} => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => {{1,6},{2,7},{3,5},{4}} => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => {{1,7},{2,5},{3,6},{4}} => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => {{1,6},{2,5},{3,7},{4}} => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => {{1,5},{2,6},{3,7},{4}} => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => {{1,7},{2,6},{3,4,5}} => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => {{1,6},{2,7},{3,4,5}} => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => {{1,7},{2,5},{3,4,6}} => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => {{1,6},{2,5},{3,4,7}} => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => {{1,5},{2,6},{3,4,7}} => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => {{1,7},{2,4,6},{3,5}} => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => {{1,6},{2,4,7},{3,5}} => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => {{1,5},{2,4,7},{3,6}} => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => {{1,4,7},{2,5},{3,6}} => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => {{1,7},{2,6},{3,5},{4}} => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => {{1,6},{2,7},{3,5},{4}} => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => {{1,7},{2,5},{3,6},{4}} => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => {{1,6},{2,5},{3,7},{4}} => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => {{1,5},{2,6},{3,7},{4}} => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => {{1,7},{2,6},{3,4},{5}} => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => {{1,6},{2,7},{3,4},{5}} => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => {{1,7},{2,5},{3,4},{6}} => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => {{1,6,7},{2,5},{3,4}} => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => {{1,5},{2,6,7},{3,4}} => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => {{1,7},{2,4},{3,5},{6}} => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => {{1,6,7},{2,4},{3,5}} => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => {{1,5},{2,4},{3,6,7}} => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => {{1,4},{2,5},{3,6,7}} => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => {{1,7},{2,6},{3},{4},{5}} => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => {{1,6},{2,7},{3},{4},{5}} => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => {{1,7},{2,5},{3},{4},{6}} => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => {{1,6,7},{2,5},{3},{4}} => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => {{1,5},{2,6,7},{3},{4}} => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => {{1,7},{2,4,5},{3},{6}} => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => {{1,6,7},{2,4,5},{3}} => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => {{1,5},{2,4,6,7},{3}} => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => {{1,4,6,7},{2,5},{3}} => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => {{1,7},{2,3,4,5},{6}} => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => {{1,6,7},{2,3,4,5}} => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => {{1,5},{2,3,4,6,7}} => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => {{1,4,6,7},{2,3,5}} => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => {{1,3,5},{2,4,6,7}} => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => {{1,7},{2,6},{3,5},{4}} => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => {{1,6},{2,7},{3,5},{4}} => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => {{1,7},{2,5},{3,6},{4}} => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => {{1,6},{2,5},{3,7},{4}} => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => {{1,5},{2,6},{3,7},{4}} => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => {{1,7},{2,6},{3,4},{5}} => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => {{1,6},{2,7},{3,4},{5}} => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => {{1,7},{2,5},{3,4},{6}} => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => {{1,6,7},{2,5},{3,4}} => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => {{1,5},{2,6,7},{3,4}} => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => {{1,7},{2,4},{3,5},{6}} => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => {{1,6,7},{2,4},{3,5}} => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => {{1,5},{2,4},{3,6,7}} => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => {{1,4},{2,5},{3,6,7}} => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => {{1,7},{2,6},{3},{4},{5}} => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => {{1,6},{2,7},{3},{4},{5}} => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => {{1,7},{2,5},{3},{4},{6}} => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => {{1,6,7},{2,5},{3},{4}} => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => {{1,5},{2,6,7},{3},{4}} => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => {{1,7},{2,4},{3},{5},{6}} => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => {{1,6,7},{2,4},{3},{5}} => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => {{1,5,6,7},{2,4},{3}} => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => {{1,4},{2,5,6,7},{3}} => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => {{1,7},{2,3,4},{5},{6}} => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => {{1,6,7},{2,3,4},{5}} => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => {{1,5,6,7},{2,3,4}} => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => {{1,4},{2,3,5,6,7}} => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => {{1,3,5,6,7},{2,4}} => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => {{1,7},{2,6},{3},{4},{5}} => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => {{1,6},{2,7},{3},{4},{5}} => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => {{1,7},{2,5},{3},{4},{6}} => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => {{1,6,7},{2,5},{3},{4}} => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => {{1,5},{2,6,7},{3},{4}} => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => {{1,7},{2,4},{3},{5},{6}} => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => {{1,6,7},{2,4},{3},{5}} => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => {{1,5,6,7},{2,4},{3}} => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => {{1,4},{2,5,6,7},{3}} => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => {{1,7},{2,3},{4},{5},{6}} => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => {{1,6,7},{2,3},{4},{5}} => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => {{1,5,6,7},{2,3},{4}} => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => {{1,4,5,6,7},{2,3}} => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => {{1,3},{2,4,5,6,7}} => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => {{1,7},{2},{3},{4},{5},{6}} => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => {{1,6,7},{2},{3},{4},{5}} => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => {{1,5,6,7},{2},{3},{4}} => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => {{1,4,5,6,7},{2},{3}} => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => {{1,3,4,5,6,7},{2}} => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => {{1,2,3,4,5,6,7}} => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => {{1,7},{2,6},{3,5},{4}} => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => {{1,6},{2,7},{3,5},{4}} => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => {{1,7},{2,5},{3,6},{4}} => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => {{1,6},{2,5},{3,7},{4}} => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => {{1,5},{2,6},{3,7},{4}} => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => {{1,7},{2,6},{3,4,5}} => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => {{1,6},{2,7},{3,4,5}} => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => {{1,7},{2,5},{3,4,6}} => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => {{1,6},{2,5},{3,4,7}} => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => {{1,5},{2,6},{3,4,7}} => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => {{1,7},{2,4,6},{3,5}} => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => {{1,6},{2,4,7},{3,5}} => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => {{1,5},{2,4,7},{3,6}} => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => {{1,4,7},{2,5},{3,6}} => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => {{1,7},{2,6},{3,5},{4}} => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => {{1,6},{2,7},{3,5},{4}} => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => {{1,7},{2,5},{3,6},{4}} => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => {{1,6},{2,5},{3,7},{4}} => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => {{1,5},{2,6},{3,7},{4}} => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => {{1,7},{2,6},{3,4},{5}} => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => {{1,6},{2,7},{3,4},{5}} => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => {{1,7},{2,5,6},{3,4}} => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => {{1,6},{2,5,7},{3,4}} => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => {{1,5,7},{2,6},{3,4}} => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => {{1,7},{2,4},{3,5,6}} => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => {{1,6},{2,4},{3,5,7}} => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => {{1,5,7},{2,4},{3,6}} => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => {{1,4},{2,5,7},{3,6}} => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => {{1,7},{2,6},{3},{4},{5}} => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => {{1,6},{2,7},{3},{4},{5}} => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => {{1,7},{2,5,6},{3},{4}} => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => {{1,6},{2,5,7},{3},{4}} => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => {{1,5,7},{2,6},{3},{4}} => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => {{1,7},{2,4,5,6},{3}} => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => {{1,6},{2,4,5,7},{3}} => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => {{1,5,7},{2,4,6},{3}} => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => {{1,4,6},{2,5,7},{3}} => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => {{1,7},{2,3,4,5,6}} => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => {{1,6},{2,3,4,5,7}} => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => {{1,5,7},{2,3,4,6}} => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => {{1,4,6},{2,3,5,7}} => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => {{1,3,5,7},{2,4,6}} => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => {{1,7},{2,6},{3,5},{4}} => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => {{1,6},{2,7},{3,5},{4}} => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => {{1,7},{2,5},{3,6},{4}} => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => {{1,6},{2,5},{3,7},{4}} => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => {{1,5},{2,6},{3,7},{4}} => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => {{1,7},{2,6},{3,4,5}} => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => {{1,6},{2,7},{3,4,5}} => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => {{1,7},{2,5},{3,4,6}} => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => {{1,6},{2,5},{3,4,7}} => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => {{1,5},{2,6},{3,4,7}} => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => {{1,7},{2,4,6},{3,5}} => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => {{1,6},{2,4,7},{3,5}} => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => {{1,5},{2,4,7},{3,6}} => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => {{1,4,7},{2,5},{3,6}} => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => {{1,7},{2,6},{3,5},{4}} => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => {{1,6},{2,7},{3,5},{4}} => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => {{1,7},{2,5},{3,6},{4}} => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => {{1,6},{2,5},{3,7},{4}} => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => {{1,5},{2,6},{3,7},{4}} => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => {{1,7},{2,6},{3,4},{5}} => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => {{1,6},{2,7},{3,4},{5}} => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => {{1,7},{2,5},{3,4},{6}} => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => {{1,6},{2,5},{3,4},{7}} => 3
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => {{1,5},{2,6},{3,4},{7}} => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => {{1,7},{2,4},{3,5},{6}} => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => {{1,6},{2,4},{3,5},{7}} => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => {{1,5},{2,4},{3,6},{7}} => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => {{1,4},{2,5},{3,6},{7}} => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => {{1,7},{2,6},{3},{4},{5}} => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => {{1,6},{2,7},{3},{4},{5}} => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => {{1,7},{2,5},{3},{4},{6}} => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => {{1,6},{2,5},{3},{4},{7}} => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => {{1,5},{2,6},{3},{4},{7}} => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => {{1,7},{2,4,5},{3},{6}} => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => {{1,6},{2,4,5},{3},{7}} => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => {{1,5},{2,4,6},{3},{7}} => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => {{1,4,6},{2,5},{3},{7}} => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => {{1,7},{2,3,4,5},{6}} => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => {{1,6},{2,3,4,5},{7}} => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => {{1,5},{2,3,4,6},{7}} => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => {{1,4,6},{2,3,5},{7}} => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => {{1,3,5},{2,4,6},{7}} => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => {{1,7},{2,6},{3,5},{4}} => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => {{1,6},{2,7},{3,5},{4}} => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => {{1,7},{2,5},{3,6},{4}} => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => {{1,6},{2,5},{3,7},{4}} => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => {{1,5},{2,6},{3,7},{4}} => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => {{1,7},{2,6},{3,4},{5}} => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => {{1,6},{2,7},{3,4},{5}} => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => {{1,7},{2,5},{3,4},{6}} => 3
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => {{1,6},{2,5},{3,4},{7}} => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => {{1,5},{2,6},{3,4},{7}} => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => {{1,7},{2,4},{3,5},{6}} => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => {{1,6},{2,4},{3,5},{7}} => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => {{1,5},{2,4},{3,6},{7}} => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => {{1,4},{2,5},{3,6},{7}} => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => {{1,7},{2,6},{3},{4},{5}} => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => {{1,6},{2,7},{3},{4},{5}} => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => {{1,7},{2,5},{3},{4},{6}} => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => {{1,6},{2,5},{3},{4},{7}} => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => {{1,5},{2,6},{3},{4},{7}} => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => {{1,7},{2,4},{3},{5},{6}} => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => {{1,6},{2,4},{3},{5},{7}} => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => {{1,5,6},{2,4},{3},{7}} => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => {{1,4},{2,5,6},{3},{7}} => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => {{1,7},{2,3,4},{5},{6}} => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => {{1,6},{2,3,4},{5},{7}} => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => {{1,5,6},{2,3,4},{7}} => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => {{1,4},{2,3,5,6},{7}} => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => {{1,3,5,6},{2,4},{7}} => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => {{1,7},{2,6},{3},{4},{5}} => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => {{1,6},{2,7},{3},{4},{5}} => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => {{1,7},{2,5},{3},{4},{6}} => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => {{1,6},{2,5},{3},{4},{7}} => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => {{1,5},{2,6},{3},{4},{7}} => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => {{1,7},{2,4},{3},{5},{6}} => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => {{1,6},{2,4},{3},{5},{7}} => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => {{1,5,6},{2,4},{3},{7}} => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => {{1,4},{2,5,6},{3},{7}} => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => {{1,7},{2,3},{4},{5},{6}} => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => {{1,6},{2,3},{4},{5},{7}} => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => {{1,5,6},{2,3},{4},{7}} => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => {{1,4,5,6},{2,3},{7}} => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => {{1,3},{2,4,5,6},{7}} => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => {{1,7},{2},{3},{4},{5},{6}} => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => {{1,6},{2},{3},{4},{5},{7}} => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => {{1,5,6},{2},{3},{4},{7}} => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => {{1,4,5,6},{2},{3},{7}} => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => {{1,3,4,5,6},{2},{7}} => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => {{1,2,3,4,5,6},{7}} => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => {{1,7},{2,6},{3,5},{4}} => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => {{1,6},{2,7},{3,5},{4}} => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => {{1,7},{2,5},{3,6},{4}} => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => {{1,6},{2,5},{3,7},{4}} => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => {{1,5},{2,6},{3,7},{4}} => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => {{1,7},{2,6},{3,4,5}} => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => {{1,6},{2,7},{3,4,5}} => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => {{1,7},{2,5},{3,4,6}} => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => {{1,6},{2,5},{3,4,7}} => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => {{1,5},{2,6},{3,4,7}} => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => {{1,7},{2,4,6},{3,5}} => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => {{1,6},{2,4,7},{3,5}} => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => {{1,5},{2,4,7},{3,6}} => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => {{1,4,7},{2,5},{3,6}} => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => {{1,7},{2,6},{3,5},{4}} => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => {{1,6},{2,7},{3,5},{4}} => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => {{1,7},{2,5},{3,6},{4}} => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => {{1,6},{2,5},{3,7},{4}} => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => {{1,5},{2,6},{3,7},{4}} => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => {{1,7},{2,6},{3,4},{5}} => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => {{1,6},{2,7},{3,4},{5}} => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => {{1,7},{2,5},{3,4},{6}} => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => {{1,6},{2,5},{3,4},{7}} => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => {{1,5},{2,6},{3,4},{7}} => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => {{1,7},{2,4},{3,5},{6}} => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => {{1,6},{2,4},{3,5},{7}} => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => {{1,5},{2,4},{3,6},{7}} => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => {{1,4},{2,5},{3,6},{7}} => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => {{1,7},{2,6},{3},{4},{5}} => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => {{1,6},{2,7},{3},{4},{5}} => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => {{1,7},{2,5},{3},{4},{6}} => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => {{1,6},{2,5},{3},{4},{7}} => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => {{1,5},{2,6},{3},{4},{7}} => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => {{1,7},{2,4,5},{3},{6}} => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => {{1,6},{2,4,5},{3},{7}} => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => {{1,5},{2,4,6},{3},{7}} => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => {{1,4,6},{2,5},{3},{7}} => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => {{1,7},{2,3,4,5},{6}} => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => {{1,6},{2,3,4,5},{7}} => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => {{1,5},{2,3,4,6},{7}} => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => {{1,4,6},{2,3,5},{7}} => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => {{1,3,5},{2,4,6},{7}} => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => {{1,7},{2,6},{3,5},{4}} => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => {{1,6},{2,7},{3,5},{4}} => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => {{1,7},{2,5},{3,6},{4}} => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => {{1,6},{2,5},{3,7},{4}} => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => {{1,5},{2,6},{3,7},{4}} => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => {{1,7},{2,6},{3,4},{5}} => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => {{1,6},{2,7},{3,4},{5}} => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => {{1,7},{2,5},{3,4},{6}} => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => {{1,6},{2,5},{3,4},{7}} => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => {{1,5},{2,6},{3,4},{7}} => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => {{1,7},{2,4},{3,5},{6}} => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => {{1,6},{2,4},{3,5},{7}} => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => {{1,5},{2,4},{3,6},{7}} => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => {{1,4},{2,5},{3,6},{7}} => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => {{1,7},{2,6},{3},{4},{5}} => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => {{1,6},{2,7},{3},{4},{5}} => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => {{1,7},{2,5},{3},{4},{6}} => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => {{1,6},{2,5},{3},{4},{7}} => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => {{1,5},{2,6},{3},{4},{7}} => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => {{1,7},{2,4},{3},{5},{6}} => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => {{1,6},{2,4},{3},{5},{7}} => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => {{1,5},{2,4},{3},{6},{7}} => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => {{1,4},{2,5},{3},{6},{7}} => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => {{1,7},{2,3,4},{5},{6}} => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => {{1,6},{2,3,4},{5},{7}} => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => {{1,5},{2,3,4},{6},{7}} => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => {{1,4},{2,3,5},{6},{7}} => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => {{1,3,5},{2,4},{6},{7}} => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => {{1,7},{2,6},{3},{4},{5}} => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => {{1,6},{2,7},{3},{4},{5}} => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => {{1,7},{2,5},{3},{4},{6}} => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => {{1,6},{2,5},{3},{4},{7}} => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => {{1,5},{2,6},{3},{4},{7}} => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => {{1,7},{2,4},{3},{5},{6}} => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => {{1,6},{2,4},{3},{5},{7}} => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => {{1,5},{2,4},{3},{6},{7}} => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => {{1,4},{2,5},{3},{6},{7}} => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => {{1,7},{2,3},{4},{5},{6}} => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => {{1,6},{2,3},{4},{5},{7}} => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => {{1,5},{2,3},{4},{6},{7}} => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => {{1,4,5},{2,3},{6},{7}} => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => {{1,3},{2,4,5},{6},{7}} => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => {{1,7},{2},{3},{4},{5},{6}} => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => {{1,6},{2},{3},{4},{5},{7}} => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => {{1,5},{2},{3},{4},{6},{7}} => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => {{1,4,5},{2},{3},{6},{7}} => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => {{1,3,4,5},{2},{6},{7}} => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => {{1,2,3,4,5},{6},{7}} => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => {{1,7},{2,6},{3,5},{4}} => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => {{1,6},{2,7},{3,5},{4}} => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => {{1,7},{2,5},{3,6},{4}} => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => {{1,6},{2,5},{3,7},{4}} => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => {{1,5},{2,6},{3,7},{4}} => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => {{1,7},{2,6},{3,4},{5}} => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => {{1,6},{2,7},{3,4},{5}} => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => {{1,7},{2,5},{3,4},{6}} => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => {{1,6},{2,5},{3,4},{7}} => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => {{1,5},{2,6},{3,4},{7}} => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => {{1,7},{2,4},{3,5},{6}} => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => {{1,6},{2,4},{3,5},{7}} => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => {{1,5},{2,4},{3,6},{7}} => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => {{1,4},{2,5},{3,6},{7}} => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => {{1,7},{2,6},{3},{4},{5}} => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => {{1,6},{2,7},{3},{4},{5}} => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => {{1,7},{2,5},{3},{4},{6}} => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => {{1,6},{2,5},{3},{4},{7}} => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => {{1,5},{2,6},{3},{4},{7}} => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => {{1,7},{2,4},{3},{5},{6}} => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => {{1,6},{2,4},{3},{5},{7}} => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => {{1,5},{2,4},{3},{6},{7}} => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => {{1,4},{2,5},{3},{6},{7}} => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => {{1,7},{2,3,4},{5},{6}} => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => {{1,6},{2,3,4},{5},{7}} => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => {{1,5},{2,3,4},{6},{7}} => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => {{1,4},{2,3,5},{6},{7}} => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => {{1,3,5},{2,4},{6},{7}} => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => {{1,7},{2,6},{3},{4},{5}} => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => {{1,6},{2,7},{3},{4},{5}} => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => {{1,7},{2,5},{3},{4},{6}} => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => {{1,6},{2,5},{3},{4},{7}} => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => {{1,5},{2,6},{3},{4},{7}} => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => {{1,7},{2,4},{3},{5},{6}} => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => {{1,6},{2,4},{3},{5},{7}} => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => {{1,5},{2,4},{3},{6},{7}} => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => {{1,4},{2,5},{3},{6},{7}} => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => {{1,7},{2,3},{4},{5},{6}} => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => {{1,6},{2,3},{4},{5},{7}} => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => {{1,5},{2,3},{4},{6},{7}} => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => {{1,4},{2,3},{5},{6},{7}} => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => {{1,3},{2,4},{5},{6},{7}} => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => {{1,7},{2},{3},{4},{5},{6}} => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => {{1,6},{2},{3},{4},{5},{7}} => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => {{1,5},{2},{3},{4},{6},{7}} => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => {{1,4},{2},{3},{5},{6},{7}} => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => {{1,3,4},{2},{5},{6},{7}} => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => {{1,2,3,4},{5},{6},{7}} => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => {{1,7},{2,6},{3},{4},{5}} => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => {{1,6},{2,7},{3},{4},{5}} => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => {{1,7},{2,5},{3},{4},{6}} => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => {{1,6},{2,5},{3},{4},{7}} => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => {{1,5},{2,6},{3},{4},{7}} => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => {{1,7},{2,4},{3},{5},{6}} => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => {{1,6},{2,4},{3},{5},{7}} => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => {{1,5},{2,4},{3},{6},{7}} => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => {{1,4},{2,5},{3},{6},{7}} => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => {{1,7},{2,3},{4},{5},{6}} => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => {{1,6},{2,3},{4},{5},{7}} => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => {{1,5},{2,3},{4},{6},{7}} => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => {{1,4},{2,3},{5},{6},{7}} => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => {{1,3},{2,4},{5},{6},{7}} => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => {{1,7},{2},{3},{4},{5},{6}} => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => {{1,6},{2},{3},{4},{5},{7}} => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => {{1,5},{2},{3},{4},{6},{7}} => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => {{1,4},{2},{3},{5},{6},{7}} => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => {{1,3},{2},{4},{5},{6},{7}} => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => {{1,2,3},{4},{5},{6},{7}} => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => {{1,7},{2},{3},{4},{5},{6}} => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => {{1,6},{2},{3},{4},{5},{7}} => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => {{1,5},{2},{3},{4},{6},{7}} => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => {{1,4},{2},{3},{5},{6},{7}} => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => {{1,3},{2},{4},{5},{6},{7}} => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => {{1,2},{3},{4},{5},{6},{7}} => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => {{1},{2},{3},{4},{5},{6},{7}} => 0
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => {{1,3,5,6,7,8},{2,4}} => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => {{1,4,5,6,7,8},{2,3}} => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => {{1,3},{2,4,5,6,7,8}} => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => {{1,4,5,6,7,8},{2},{3}} => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => {{1,3,4,5,6,7,8},{2}} => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => {{1,2,3,4,5,6,7,8}} => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => {{1,8},{2,3,4,5,6,7}} => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => {{1,2,3,4,5,6,7},{8}} => 1
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Description
The nesting number of a set partition.
This is the maximal number of chords in the standard representation of a set partition that mutually nest.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
weak exceedance partition
Description
The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.