Identifier
Values
[1,0] => [2,1] => {{1,2}} => [2] => 1
[1,0,1,0] => [3,1,2] => {{1,3},{2}} => [2,1] => 1
[1,1,0,0] => [2,3,1] => {{1,2,3}} => [3] => 2
[1,0,1,0,1,0] => [4,1,2,3] => {{1,4},{2},{3}} => [2,1,1] => 1
[1,0,1,1,0,0] => [3,1,4,2] => {{1,3,4},{2}} => [3,1] => 2
[1,1,0,0,1,0] => [2,4,1,3] => {{1,2,4},{3}} => [3,1] => 2
[1,1,0,1,0,0] => [4,3,1,2] => {{1,4},{2,3}} => [2,2] => 1
[1,1,1,0,0,0] => [2,3,4,1] => {{1,2,3,4}} => [4] => 3
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => {{1,5},{2},{3},{4}} => [2,1,1,1] => 1
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => {{1,4,5},{2},{3}} => [3,1,1] => 2
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => {{1,3,5},{2},{4}} => [3,1,1] => 2
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => {{1,5},{2},{3,4}} => [2,2,1] => 1
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => {{1,3,4,5},{2}} => [4,1] => 3
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => {{1,2,5},{3},{4}} => [3,1,1] => 2
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => {{1,2,4,5},{3}} => [4,1] => 3
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => {{1,5},{2,3},{4}} => [2,2,1] => 1
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => {{1,5},{2,4},{3}} => [2,2,1] => 1
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => {{1,4,5},{2,3}} => [3,2] => 2
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => {{1,2,3,5},{4}} => [4,1] => 3
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => {{1,2,5},{3,4}} => [3,2] => 2
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => {{1,5},{2,3,4}} => [3,2] => 2
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => {{1,2,3,4,5}} => [5] => 4
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => {{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => {{1,5,6},{2},{3},{4}} => [3,1,1,1] => 2
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => {{1,4,6},{2},{3},{5}} => [3,1,1,1] => 2
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => {{1,6},{2},{3},{4,5}} => [2,2,1,1] => 1
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => {{1,4,5,6},{2},{3}} => [4,1,1] => 3
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => {{1,3,6},{2},{4},{5}} => [3,1,1,1] => 2
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => {{1,3,5,6},{2},{4}} => [4,1,1] => 3
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => {{1,6},{2},{3,4},{5}} => [2,2,1,1] => 1
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => {{1,6},{2},{3,5},{4}} => [2,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => {{1,5,6},{2},{3,4}} => [3,2,1] => 2
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => {{1,3,4,6},{2},{5}} => [4,1,1] => 3
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => {{1,3,6},{2},{4,5}} => [3,2,1] => 2
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => {{1,6},{2},{3,4,5}} => [3,2,1] => 2
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => {{1,3,4,5,6},{2}} => [5,1] => 4
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => {{1,2,6},{3},{4},{5}} => [3,1,1,1] => 2
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => {{1,2,5,6},{3},{4}} => [4,1,1] => 3
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => {{1,2,4,6},{3},{5}} => [4,1,1] => 3
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => {{1,2,6},{3},{4,5}} => [3,2,1] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => {{1,2,4,5,6},{3}} => [5,1] => 4
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => {{1,6},{2,3},{4},{5}} => [2,2,1,1] => 1
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => {{1,5,6},{2,3},{4}} => [3,2,1] => 2
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => {{1,6},{2,4},{3},{5}} => [2,2,1,1] => 1
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => {{1,5},{2,6},{3},{4}} => [2,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => {{1,5,6},{2,4},{3}} => [3,2,1] => 2
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => {{1,4,6},{2,3},{5}} => [3,2,1] => 2
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => {{1,6},{2,3},{4,5}} => [2,2,2] => 1
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => {{1,6},{2,4,5},{3}} => [3,2,1] => 2
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => {{1,4,5,6},{2,3}} => [4,2] => 3
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => {{1,2,3,6},{4},{5}} => [4,1,1] => 3
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => {{1,2,3,5,6},{4}} => [5,1] => 4
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => {{1,2,6},{3,4},{5}} => [3,2,1] => 2
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => {{1,2,6},{3,5},{4}} => [3,2,1] => 2
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => {{1,2,5,6},{3,4}} => [4,2] => 3
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => {{1,6},{2,3,4},{5}} => [3,2,1] => 2
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => {{1,6},{2,3,5},{4}} => [3,2,1] => 2
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => {{1,6},{2,5},{3,4}} => [2,2,2] => 1
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => {{1,5,6},{2,3,4}} => [3,3] => 3
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => {{1,2,3,4,6},{5}} => [5,1] => 4
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => {{1,2,3,6},{4,5}} => [4,2] => 3
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => {{1,2,6},{3,4,5}} => [3,3] => 3
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => {{1,6},{2,3,4,5}} => [4,2] => 3
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => {{1,2,3,4,5,6}} => [6] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => {{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => {{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => {{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5] => {{1,7},{2},{3},{4},{5,6}} => [2,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => {{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => {{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => {{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => 3
[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6] => {{1,7},{2},{3},{4,5},{6}} => [2,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => {{1,7},{2},{3},{4,6},{5}} => [2,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [6,1,2,5,3,7,4] => {{1,6,7},{2},{3},{4,5}} => [3,2,1,1] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => {{1,4,5,7},{2},{3},{6}} => [4,1,1,1] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,1,2,7,6,3,5] => {{1,4,7},{2},{3},{5,6}} => [3,2,1,1] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => {{1,7},{2},{3},{4,5,6}} => [3,2,1,1] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => {{1,4,5,6,7},{2},{3}} => [5,1,1] => 4
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => {{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => {{1,3,6,7},{2},{4},{5}} => [4,1,1,1] => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => {{1,3,5,7},{2},{4},{6}} => [4,1,1,1] => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => {{1,3,7},{2},{4},{5,6}} => [3,2,1,1] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => {{1,3,5,6,7},{2},{4}} => [5,1,1] => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6] => {{1,7},{2},{3,4},{5},{6}} => [2,2,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5] => {{1,6,7},{2},{3,4},{5}} => [3,2,1,1] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => {{1,7},{2},{3,5},{4},{6}} => [2,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => {{1,6},{2},{3,7},{4},{5}} => [2,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => {{1,6,7},{2},{3,5},{4}} => [3,2,1,1] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => {{1,5,7},{2},{3,4},{6}} => [3,2,1,1] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5] => {{1,7},{2},{3,4},{5,6}} => [2,2,2,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => {{1,7},{2},{3,5,6},{4}} => [3,2,1,1] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [5,1,4,2,6,7,3] => {{1,5,6,7},{2},{3,4}} => [4,2,1] => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => {{1,3,4,7},{2},{5},{6}} => [4,1,1,1] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => {{1,3,4,6,7},{2},{5}} => [5,1,1] => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => {{1,3,7},{2},{4,5},{6}} => [3,2,1,1] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => {{1,3,7},{2},{4,6},{5}} => [3,2,1,1] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => {{1,3,6,7},{2},{4,5}} => [4,2,1] => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => {{1,7},{2},{3,4,5},{6}} => [3,2,1,1] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => {{1,7},{2},{3,4,6},{5}} => [3,2,1,1] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => {{1,7},{2},{3,6},{4,5}} => [2,2,2,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [6,1,4,5,2,7,3] => {{1,6,7},{2},{3,4,5}} => [3,3,1] => 3
>>> Load all 370 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => {{1,3,4,5,7},{2},{6}} => [5,1,1] => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => {{1,3,4,7},{2},{5,6}} => [4,2,1] => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => {{1,3,7},{2},{4,5,6}} => [3,3,1] => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => [7,1,4,5,6,2,3] => {{1,7},{2},{3,4,5,6}} => [4,2,1] => 3
[1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => {{1,3,4,5,6,7},{2}} => [6,1] => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => {{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => {{1,2,6,7},{3},{4},{5}} => [4,1,1,1] => 3
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => {{1,2,5,7},{3},{4},{6}} => [4,1,1,1] => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,7,1,3,6,4,5] => {{1,2,7},{3},{4},{5,6}} => [3,2,1,1] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => {{1,2,5,6,7},{3},{4}} => [5,1,1] => 4
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => {{1,2,4,7},{3},{5},{6}} => [4,1,1,1] => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => {{1,2,4,6,7},{3},{5}} => [5,1,1] => 4
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,7,1,5,3,4,6] => {{1,2,7},{3},{4,5},{6}} => [3,2,1,1] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5] => {{1,2,7},{3},{4,6},{5}} => [3,2,1,1] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,6,1,5,3,7,4] => {{1,2,6,7},{3},{4,5}} => [4,2,1] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => {{1,2,4,5,7},{3},{6}} => [5,1,1] => 4
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,6,3,5] => {{1,2,4,7},{3},{5,6}} => [4,2,1] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4] => {{1,2,7},{3},{4,5,6}} => [3,3,1] => 3
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => {{1,2,4,5,6,7},{3}} => [6,1] => 5
[1,1,0,1,0,0,1,0,1,0,1,0] => [7,3,1,2,4,5,6] => {{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [6,3,1,2,4,7,5] => {{1,6,7},{2,3},{4},{5}} => [3,2,1,1] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,1,2,7,4,6] => {{1,5,7},{2,3},{4},{6}} => [3,2,1,1] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [7,3,1,2,6,4,5] => {{1,7},{2,3},{4},{5,6}} => [2,2,2,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [5,3,1,2,6,7,4] => {{1,5,6,7},{2,3},{4}} => [4,2,1] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [7,4,1,2,3,5,6] => {{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [6,4,1,2,3,7,5] => {{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,7,1,2,3,4,6] => {{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5] => {{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,1,2,3,7,4] => {{1,5},{2,6,7},{3},{4}} => [3,2,1,1] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,4,1,2,7,3,6] => {{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [7,4,1,2,6,3,5] => {{1,7},{2,4},{3},{5,6}} => [2,2,2,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4] => {{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [5,4,1,2,6,7,3] => {{1,5,6,7},{2,4},{3}} => [4,2,1] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,3,1,7,2,5,6] => {{1,4,7},{2,3},{5},{6}} => [3,2,1,1] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,3,1,6,2,7,5] => {{1,4,6,7},{2,3},{5}} => [4,2,1] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [7,3,1,5,2,4,6] => {{1,7},{2,3},{4,5},{6}} => [2,2,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [7,3,1,6,2,4,5] => {{1,7},{2,3},{4,6},{5}} => [2,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [6,3,1,5,2,7,4] => {{1,6,7},{2,3},{4,5}} => [3,2,2] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6] => {{1,7},{2,4,5},{3},{6}} => [3,2,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [7,4,1,6,2,3,5] => {{1,7},{2,4,6},{3},{5}} => [3,2,1,1] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4] => {{1,6},{2,7},{3},{4,5}} => [2,2,2,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [6,4,1,5,2,7,3] => {{1,6,7},{2,4,5},{3}} => [3,3,1] => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => {{1,4,5,7},{2,3},{6}} => [4,2,1] => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => {{1,4,7},{2,3},{5,6}} => [3,2,2] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [7,3,1,5,6,2,4] => {{1,7},{2,3},{4,5,6}} => [3,2,2] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3] => {{1,7},{2,4,5,6},{3}} => [4,2,1] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => {{1,4,5,6,7},{2,3}} => [5,2] => 4
[1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => {{1,2,3,7},{4},{5},{6}} => [4,1,1,1] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => {{1,2,3,6,7},{4},{5}} => [5,1,1] => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => {{1,2,3,5,7},{4},{6}} => [5,1,1] => 4
[1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,7,1,6,4,5] => {{1,2,3,7},{4},{5,6}} => [4,2,1] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => {{1,2,3,5,6,7},{4}} => [6,1] => 5
[1,1,1,0,0,1,0,0,1,0,1,0] => [2,7,4,1,3,5,6] => {{1,2,7},{3,4},{5},{6}} => [3,2,1,1] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,4,1,3,7,5] => {{1,2,6,7},{3,4},{5}} => [4,2,1] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [2,7,5,1,3,4,6] => {{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5] => {{1,2,6},{3,7},{4},{5}} => [3,2,1,1] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [2,6,5,1,3,7,4] => {{1,2,6,7},{3,5},{4}} => [4,2,1] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,4,1,7,3,6] => {{1,2,5,7},{3,4},{6}} => [4,2,1] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [2,7,4,1,6,3,5] => {{1,2,7},{3,4},{5,6}} => [3,2,2] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [2,7,5,1,6,3,4] => {{1,2,7},{3,5,6},{4}} => [3,3,1] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,5,4,1,6,7,3] => {{1,2,5,6,7},{3,4}} => [5,2] => 4
[1,1,1,0,1,0,0,0,1,0,1,0] => [7,3,4,1,2,5,6] => {{1,7},{2,3,4},{5},{6}} => [3,2,1,1] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [6,3,4,1,2,7,5] => {{1,6,7},{2,3,4},{5}} => [3,3,1] => 3
[1,1,1,0,1,0,0,1,0,0,1,0] => [7,3,5,1,2,4,6] => {{1,7},{2,3,5},{4},{6}} => [3,2,1,1] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [6,3,7,1,2,4,5] => {{1,6},{2,3,7},{4},{5}} => [3,2,1,1] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4] => {{1,6,7},{2,3,5},{4}} => [3,3,1] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [7,5,4,1,2,3,6] => {{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5] => {{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,7,5,1,2,3,4] => {{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,5,4,1,2,7,3] => {{1,6,7},{2,5},{3,4}} => [3,2,2] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,3,4,1,7,2,6] => {{1,5,7},{2,3,4},{6}} => [3,3,1] => 3
[1,1,1,0,1,1,0,0,0,1,0,0] => [7,3,4,1,6,2,5] => {{1,7},{2,3,4},{5,6}} => [3,2,2] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [7,3,5,1,6,2,4] => {{1,7},{2,3,5,6},{4}} => [4,2,1] => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => [7,5,4,1,6,2,3] => {{1,7},{2,5,6},{3,4}} => [3,2,2] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [5,3,4,1,6,7,2] => {{1,5,6,7},{2,3,4}} => [4,3] => 4
[1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => {{1,2,3,4,7},{5},{6}} => [5,1,1] => 4
[1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => {{1,2,3,4,6,7},{5}} => [6,1] => 5
[1,1,1,1,0,0,0,1,0,0,1,0] => [2,3,7,5,1,4,6] => {{1,2,3,7},{4,5},{6}} => [4,2,1] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,7,6,1,4,5] => {{1,2,3,7},{4,6},{5}} => [4,2,1] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,5,1,7,4] => {{1,2,3,6,7},{4,5}} => [5,2] => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => [2,7,4,5,1,3,6] => {{1,2,7},{3,4,5},{6}} => [3,3,1] => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [2,7,4,6,1,3,5] => {{1,2,7},{3,4,6},{5}} => [3,3,1] => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [2,7,6,5,1,3,4] => {{1,2,7},{3,6},{4,5}} => [3,2,2] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,6,4,5,1,7,3] => {{1,2,6,7},{3,4,5}} => [4,3] => 4
[1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => {{1,7},{2,3,4,5},{6}} => [4,2,1] => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [7,3,4,6,1,2,5] => {{1,7},{2,3,4,6},{5}} => [4,2,1] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [7,3,6,5,1,2,4] => {{1,7},{2,3,6},{4,5}} => [3,2,2] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [7,6,4,5,1,2,3] => {{1,7},{2,6},{3,4,5}} => [3,2,2] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,4,5,1,7,2] => {{1,6,7},{2,3,4,5}} => [4,3] => 4
[1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => {{1,2,3,4,5,7},{6}} => [6,1] => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,4,7,6,1,5] => {{1,2,3,4,7},{5,6}} => [5,2] => 4
[1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,5,6,1,4] => {{1,2,3,7},{4,5,6}} => [4,3] => 4
[1,1,1,1,1,0,0,1,0,0,0,0] => [2,7,4,5,6,1,3] => {{1,2,7},{3,4,5,6}} => [4,3] => 4
[1,1,1,1,1,0,1,0,0,0,0,0] => [7,3,4,5,6,1,2] => {{1,7},{2,3,4,5,6}} => [5,2] => 4
[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}} => [7] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,1,2,3,4,5,6,7] => {{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => {{1,7,8},{2},{3},{4},{5},{6}} => [3,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,1,2,3,4,7,5,6] => {{1,8},{2},{3},{4},{5},{6,7}} => [2,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,1,2,3,4,7,8,5] => {{1,6,7,8},{2},{3},{4},{5}} => [4,1,1,1,1] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,1,2,3,7,4,5,6] => {{1,8},{2},{3},{4},{5,7},{6}} => [2,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [8,1,2,3,6,7,4,5] => {{1,8},{2},{3},{4},{5,6,7}} => [3,2,1,1,1] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,1,2,3,6,7,8,4] => {{1,5,6,7,8},{2},{3},{4}} => [5,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => {{1,4,6,8},{2},{3},{5},{7}} => [4,1,1,1,1] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [4,1,2,7,6,3,8,5] => {{1,4,7,8},{2},{3},{5,6}} => [4,2,1,1] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,8,7,3,6] => {{1,4,5,8},{2},{3},{6,7}} => [4,2,1,1] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => {{1,3,8},{2},{4},{5},{6},{7}} => [3,1,1,1,1,1] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => {{1,3,5,8},{2},{4},{6},{7}} => [4,1,1,1,1] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => {{1,3,5,7,8},{2},{4},{6}} => [5,1,1,1] => 4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,1,8,2,6,7,4,5] => {{1,3,8},{2},{4},{5,6,7}} => [3,3,1,1] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,1,8,2,3,4,5,7] => {{1,6},{2},{3,8},{4},{5},{7}} => [2,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,1,5,2,3,8,4,7] => {{1,6,8},{2},{3,5},{4},{7}} => [3,2,1,1,1] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [5,1,4,2,7,3,8,6] => {{1,5,7,8},{2},{3,4},{6}} => [4,2,1,1] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [7,1,4,2,6,3,8,5] => {{1,7,8},{2},{3,4},{5,6}} => [3,2,2,1] => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [7,1,5,2,6,3,8,4] => {{1,7,8},{2},{3,5,6},{4}} => [3,3,1,1] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [5,1,4,2,8,7,3,6] => {{1,5,8},{2},{3,4},{6,7}} => [3,2,2,1] => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,8,6,2,7,4,5] => {{1,3,8},{2},{4,6,7},{5}} => [3,3,1,1] => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,1,4,5,2,3,6,7] => {{1,8},{2},{3,4,5},{6},{7}} => [3,2,1,1,1] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [8,1,4,5,2,7,3,6] => {{1,8},{2},{3,4,5},{6,7}} => [3,2,2,1] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [8,1,6,5,2,7,3,4] => {{1,8},{2},{3,6,7},{4,5}} => [3,2,2,1] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [3,1,4,8,7,2,5,6] => {{1,3,4,8},{2},{5,7},{6}} => [4,2,1,1] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [8,1,4,5,7,2,3,6] => {{1,8},{2},{3,4,5,7},{6}} => [4,2,1,1] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [8,1,4,7,6,2,3,5] => {{1,8},{2},{3,4,7},{5,6}} => [3,2,2,1] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,1,4,5,8,7,2,6] => {{1,3,4,5,8},{2},{6,7}} => [5,2,1] => 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => {{1,3,4,5,6,7,8},{2}} => [7,1] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,8,1,3,4,5,6,7] => {{1,2,8},{3},{4},{5},{6},{7}} => [3,1,1,1,1,1] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => {{1,2,4,6,8},{3},{5},{7}} => [5,1,1,1] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,4,1,6,3,7,8,5] => {{1,2,4,6,7,8},{3},{5}} => [6,1,1] => 5
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1,8,6,3,5,7] => {{1,2,4,8},{3},{5,6},{7}} => [4,2,1,1] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => {{1,2,4,5,6,7,8},{3}} => [7,1] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,3,1,2,4,5,6,7] => {{1,8},{2,3},{4},{5},{6},{7}} => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,4,1,2,3,5,6,7] => {{1,8},{2,4},{3},{5},{6},{7}} => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,1,2,3,4,5,6] => {{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,6,1,2,3,4,8,5] => {{1,7,8},{2,6},{3},{4},{5}} => [3,2,1,1,1] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,1,2,3,7,8,4] => {{1,5},{2,6,7,8},{3},{4}} => [4,2,1,1] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8,4,1,2,7,3,5,6] => {{1,8},{2,4},{3},{5,7},{6}} => [2,2,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7,4,1,2,6,3,8,5] => {{1,7,8},{2,4},{3},{5,6}} => [3,2,2,1] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,7,1,2,6,3,8,4] => {{1,5,6},{2,7,8},{3},{4}} => [3,3,1,1] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,4,1,2,8,7,3,6] => {{1,5,8},{2,4},{3},{6,7}} => [3,2,2,1] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [8,4,1,2,6,7,3,5] => {{1,8},{2,4},{3},{5,6,7}} => [3,2,2,1] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,8,1,2,6,7,3,4] => {{1,5,6,7},{2,8},{3},{4}} => [4,2,1,1] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,3,1,6,2,8,5,7] => {{1,4,6,8},{2,3},{5},{7}} => [4,2,1,1] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,3,1,6,2,7,8,5] => {{1,4,6,7,8},{2,3},{5}} => [5,2,1] => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,3,1,8,2,4,5,6] => {{1,7},{2,3},{4,8},{5},{6}} => [2,2,2,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7,3,1,6,2,4,8,5] => {{1,7,8},{2,3},{4,6},{5}} => [3,2,2,1] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [8,3,1,5,2,7,4,6] => {{1,8},{2,3},{4,5},{6,7}} => [2,2,2,2] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [8,3,1,6,2,7,4,5] => {{1,8},{2,3},{4,6,7},{5}} => [3,2,2,1] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [6,3,1,5,2,7,8,4] => {{1,6,7,8},{2,3},{4,5}} => [4,2,2] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,4,1,5,2,3,8,6] => {{1,7,8},{2,4,5},{3},{6}} => [3,3,1,1] => 3
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7,4,1,6,2,3,8,5] => {{1,7,8},{2,4,6},{3},{5}} => [3,3,1,1] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [6,7,1,5,2,3,8,4] => {{1,6},{2,7,8},{3},{4,5}} => [3,2,2,1] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,4,1,5,2,8,3,7] => {{1,6,8},{2,4,5},{3},{7}} => [3,3,1,1] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [8,4,1,5,2,7,3,6] => {{1,8},{2,4,5},{3},{6,7}} => [3,2,2,1] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [8,4,1,6,2,7,3,5] => {{1,8},{2,4,6,7},{3},{5}} => [4,2,1,1] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [6,8,1,5,2,7,3,4] => {{1,6,7},{2,8},{3},{4,5}} => [3,2,2,1] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [4,3,1,8,7,2,5,6] => {{1,4,8},{2,3},{5,7},{6}} => [3,2,2,1] => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [8,3,1,5,7,2,4,6] => {{1,8},{2,3},{4,5,7},{6}} => [3,2,2,1] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [8,3,1,7,6,2,4,5] => {{1,8},{2,3},{4,7},{5,6}} => [2,2,2,2] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [8,4,1,5,7,2,3,6] => {{1,8},{2,4,5,7},{3},{6}} => [4,2,1,1] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [8,4,1,7,6,2,3,5] => {{1,8},{2,4,7},{3},{5,6}} => [3,2,2,1] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,8,1,5,6,2,3,4] => {{1,7},{2,8},{3},{4,5,6}} => [3,2,2,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [4,3,1,5,6,8,2,7] => {{1,4,5,6,8},{2,3},{7}} => [5,2,1] => 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [4,3,1,5,8,7,2,6] => {{1,4,5,8},{2,3},{6,7}} => [4,2,2] => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,3,1,8,6,7,2,5] => {{1,4,8},{2,3},{5,6,7}} => [3,3,2] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => {{1,4,5,6,7,8},{2,3}} => [6,2] => 5
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => {{1,2,3,5,7,8},{4},{6}} => [6,1,1] => 5
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => {{1,2,3,5,6,7,8},{4}} => [7,1] => 6
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,6,4,1,3,8,5,7] => {{1,2,6,8},{3,4},{5},{7}} => [4,2,1,1] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,7,5,1,3,4,8,6] => {{1,2,7,8},{3,5},{4},{6}} => [4,2,1,1] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,6,7,1,3,4,8,5] => {{1,2,6},{3,7,8},{4},{5}} => [3,3,1,1] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,8,5,1,3,7,4,6] => {{1,2,8},{3,5},{4},{6,7}} => [3,2,2,1] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,6,8,1,3,7,4,5] => {{1,2,6,7},{3,8},{4},{5}} => [4,2,1,1] => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,8,4,1,6,3,5,7] => {{1,2,8},{3,4},{5,6},{7}} => [3,2,2,1] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,8,4,1,7,3,5,6] => {{1,2,8},{3,4},{5,7},{6}} => [3,2,2,1] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,8,5,1,7,3,4,6] => {{1,2,8},{3,5,7},{4},{6}} => [3,3,1,1] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,7,8,1,6,3,4,5] => {{1,2,7},{3,8},{4},{5,6}} => [3,2,2,1] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,3,5,1,2,4,6,7] => {{1,8},{2,3,5},{4},{6},{7}} => [3,2,1,1,1] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [7,3,5,1,2,4,8,6] => {{1,7,8},{2,3,5},{4},{6}} => [3,3,1,1] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8,3,7,1,2,4,5,6] => {{1,8},{2,3,7},{4},{5},{6}} => [3,2,1,1,1] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,3,7,1,2,4,8,5] => {{1,6},{2,3,7,8},{4},{5}} => [4,2,1,1] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [8,3,5,1,2,7,4,6] => {{1,8},{2,3,5},{4},{6,7}} => [3,2,2,1] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,3,8,1,2,7,4,5] => {{1,6,7},{2,3,8},{4},{5}} => [3,3,1,1] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,5,4,1,2,3,8,6] => {{1,7,8},{2,5},{3,4},{6}} => [3,2,2,1] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,4,1,2,3,5,6] => {{1,8},{2,7},{3,4},{5},{6}} => [2,2,2,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,1,2,3,8,5] => {{1,6},{2,7,8},{3,4},{5}} => [3,2,2,1] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,1,2,3,8,4] => {{1,6},{2,7,8},{3,5},{4}} => [3,2,2,1] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [8,5,4,1,2,7,3,6] => {{1,8},{2,5},{3,4},{6,7}} => [2,2,2,2] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [6,8,4,1,2,7,3,5] => {{1,6,7},{2,8},{3,4},{5}} => [3,2,2,1] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [6,8,5,1,2,7,3,4] => {{1,6,7},{2,8},{3,5},{4}} => [3,2,2,1] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [6,5,4,1,2,7,8,3] => {{1,6,7,8},{2,5},{3,4}} => [4,2,2] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8,3,4,1,7,2,5,6] => {{1,8},{2,3,4},{5,7},{6}} => [3,2,2,1] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,3,5,1,6,2,4,7] => {{1,8},{2,3,5,6},{4},{7}} => [4,2,1,1] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [8,3,5,1,7,2,4,6] => {{1,8},{2,3,5,7},{4},{6}} => [4,2,1,1] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,3,8,1,6,2,4,5] => {{1,7},{2,3,8},{4},{5,6}} => [3,2,2,1] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,5,4,1,6,2,3,7] => {{1,8},{2,5,6},{3,4},{7}} => [3,2,2,1] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [8,5,4,1,7,2,3,6] => {{1,8},{2,5,7},{3,4},{6}} => [3,2,2,1] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,8,4,1,6,2,3,5] => {{1,7},{2,8},{3,4},{5,6}} => [2,2,2,2] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,8,5,1,6,2,3,4] => {{1,7},{2,8},{3,5,6},{4}} => [3,2,2,1] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,5,4,1,6,2,8,3] => {{1,7,8},{2,5,6},{3,4}} => [3,3,2] => 3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [5,3,4,1,6,8,2,7] => {{1,5,6,8},{2,3,4},{7}} => [4,3,1] => 4
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,3,4,1,8,7,2,6] => {{1,5,8},{2,3,4},{6,7}} => [3,3,2] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [8,3,5,1,6,7,2,4] => {{1,8},{2,3,5,6,7},{4}} => [5,2,1] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [5,3,4,1,6,7,8,2] => {{1,5,6,7,8},{2,3,4}} => [5,3] => 5
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,4,8,1,5,6,7] => {{1,2,3,4,8},{5},{6},{7}} => [5,1,1,1] => 4
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,7,6,1,4,8,5] => {{1,2,3,7,8},{4,6},{5}} => [5,2,1] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,8,5,1,7,4,6] => {{1,2,3,8},{4,5},{6,7}} => [4,2,2] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,6,5,1,7,8,4] => {{1,2,3,6,7,8},{4,5}} => [6,2] => 5
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,8,4,6,1,3,5,7] => {{1,2,8},{3,4,6},{5},{7}} => [3,3,1,1] => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,7,4,8,1,3,5,6] => {{1,2,7},{3,4,8},{5},{6}} => [3,3,1,1] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,7,4,6,1,3,8,5] => {{1,2,7,8},{3,4,6},{5}} => [4,3,1] => 4
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,8,6,5,1,3,4,7] => {{1,2,8},{3,6},{4,5},{7}} => [3,2,2,1] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,8,5,1,3,4,6] => {{1,2,7},{3,8},{4,5},{6}} => [3,2,2,1] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,7,8,6,1,3,4,5] => {{1,2,7},{3,8},{4,6},{5}} => [3,2,2,1] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => {{1,2,8},{3,4,5},{6,7}} => [3,3,2] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,6,4,5,1,7,8,3] => {{1,2,6,7,8},{3,4,5}} => [5,3] => 5
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,3,4,8,1,2,5,6] => {{1,7},{2,3,4,8},{5},{6}} => [4,2,1,1] => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,3,6,5,1,2,4,7] => {{1,8},{2,3,6},{4,5},{7}} => [3,2,2,1] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,3,8,5,1,2,4,6] => {{1,7},{2,3,8},{4,5},{6}} => [3,2,2,1] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,8,6,1,2,4,5] => {{1,7},{2,3,8},{4,6},{5}} => [3,2,2,1] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,6,4,5,1,2,3,7] => {{1,8},{2,6},{3,4,5},{7}} => [3,2,2,1] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,8,4,5,1,2,3,6] => {{1,7},{2,8},{3,4,5},{6}} => [3,2,2,1] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,8,4,6,1,2,3,5] => {{1,7},{2,8},{3,4,6},{5}} => [3,2,2,1] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,8,6,5,1,2,3,4] => {{1,7},{2,8},{3,6},{4,5}} => [2,2,2,2] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,6,4,5,1,2,8,3] => {{1,7,8},{2,6},{3,4,5}} => [3,3,2] => 3
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [8,3,4,6,1,7,2,5] => {{1,8},{2,3,4,6,7},{5}} => [5,2,1] => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [8,3,6,5,1,7,2,4] => {{1,8},{2,3,6,7},{4,5}} => [4,2,2] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [6,3,4,5,1,7,8,2] => {{1,6,7,8},{2,3,4,5}} => [4,4] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => {{1,2,3,4,5,7,8},{6}} => [7,1] => 6
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,3,4,8,6,1,5,7] => {{1,2,3,4,8},{5,6},{7}} => [5,2,1] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,4,8,7,1,5,6] => {{1,2,3,4,8},{5,7},{6}} => [5,2,1] => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,3,8,5,6,1,4,7] => {{1,2,3,8},{4,5,6},{7}} => [4,3,1] => 4
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,3,8,5,7,1,4,6] => {{1,2,3,8},{4,5,7},{6}} => [4,3,1] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,8,7,6,1,4,5] => {{1,2,3,8},{4,7},{5,6}} => [4,2,2] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,3,7,5,6,1,8,4] => {{1,2,3,7,8},{4,5,6}} => [5,3] => 5
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,8,4,5,7,1,3,6] => {{1,2,8},{3,4,5,7},{6}} => [4,3,1] => 4
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,8,4,7,6,1,3,5] => {{1,2,8},{3,4,7},{5,6}} => [3,3,2] => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => {{1,2,8},{3,7},{4,5,6}} => [3,3,2] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,7,4,5,6,1,8,3] => {{1,2,7,8},{3,4,5,6}} => [4,4] => 5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => {{1,8},{2,3,4,5,6},{7}} => [5,2,1] => 4
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [8,3,4,5,7,1,2,6] => {{1,8},{2,3,4,5,7},{6}} => [5,2,1] => 4
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [8,3,4,7,6,1,2,5] => {{1,8},{2,3,4,7},{5,6}} => [4,2,2] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [8,3,7,5,6,1,2,4] => {{1,8},{2,3,7},{4,5,6}} => [3,3,2] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => {{1,2,3,4,5,6,8},{7}} => [7,1] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,4,5,8,7,1,6] => {{1,2,3,4,5,8},{6,7}} => [6,2] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,8,6,7,1,5] => {{1,2,3,4,8},{5,6,7}} => [5,3] => 5
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,3,8,5,6,7,1,4] => {{1,2,3,8},{4,5,6,7}} => [4,4] => 5
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,4,5,6,7,1,3] => {{1,2,8},{3,4,5,6,7}} => [5,3] => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [8,3,4,5,6,7,1,2] => {{1,8},{2,3,4,5,6,7}} => [6,2] => 5
[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}} => [8] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,1,2,3,4,5,6,7,8] => {{1,9},{2},{3},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,1,2,3,4,5,6,9,7] => {{1,8,9},{2},{3},{4},{5},{6},{7}} => [3,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,1,2,3,4,5,8,6,7] => {{1,9},{2},{3},{4},{5},{6},{7,8}} => [2,2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,1,2,3,4,5,8,9,6] => {{1,7,8,9},{2},{3},{4},{5},{6}} => [4,1,1,1,1,1] => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,1,2,3,4,8,5,6,7] => {{1,9},{2},{3},{4},{5},{6,8},{7}} => [2,2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [9,1,2,3,4,7,8,5,6] => {{1,9},{2},{3},{4},{5},{6,7,8}} => [3,2,1,1,1,1] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => {{1,3,4,5,6,7,8,9},{2}} => [8,1] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,9,1,3,4,5,6,7,8] => {{1,2,9},{3},{4},{5},{6},{7},{8}} => [3,1,1,1,1,1,1] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,3,1,2,4,5,6,7,8] => {{1,9},{2,3},{4},{5},{6},{7},{8}} => [2,2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,9,1,2,3,4,5,6,7] => {{1,8},{2,9},{3},{4},{5},{6},{7}} => [2,2,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,9,1,8] => {{1,2,3,4,5,6,7,9},{8}} => [8,1] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => {{1,2,3,4,5,6,7,8,9}} => [9] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,10,1,9] => {{1,2,3,4,5,6,7,8,10},{9}} => [9,1] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => {{1,3,4,5,6,7,8,9,10},{2}} => [9,1] => 8
[] => [1] => {{1}} => [1] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,1,2,3,4,5,6,7,8] => {{1,10},{2,9},{3},{4},{5},{6},{7},{8}} => [2,2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => {{1,2,3,4,5,6,7,8,9,10}} => [10] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,1,2,3,4,5,6,7,10,8] => {{1,9,10},{2},{3},{4},{5},{6},{7},{8}} => [3,1,1,1,1,1,1,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,1,2,3,4,5,6,9,10,7] => {{1,8,9,10},{2},{3},{4},{5},{6},{7}} => [4,1,1,1,1,1,1] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => {{1,2,4,6,8,10},{3},{5},{7},{9}} => [6,1,1,1,1] => 5
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The spin of an integer partition.
The Ferrers shape of an integer partition $\lambda$ can be decomposed into border strips. The spin is then defined to be the total number of crossings of border strips of $\lambda$ with the vertical lines in the Ferrers shape.
The following example is taken from Appendix B in [1]: Let $\lambda = (5,5,4,4,2,1)$. Removing the border strips successively yields the sequence of partitions
$$(5,5,4,4,2,1), (4,3,3,1), (2,2), (1), ().$$
The first strip $(5,5,4,4,2,1) \setminus (4,3,3,1)$ crosses $4$ times, the second strip $(4,3,3,1) \setminus (2,2)$ crosses $3$ times, the strip $(2,2) \setminus (1)$ crosses $1$ time, and the remaining strip $(1) \setminus ()$ does not cross.
This yields the spin of $(5,5,4,4,2,1)$ to be $4+3+1 = 8$.
Map
shape
Description
Sends a set partition to the integer partition obtained by the sizes of the blocks.
Map
weak exceedance partition
Description
The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.