Processing math: 100%

Identifier
Values
[1] => [1,0,1,0] => {{1},{2}} => 2
[2] => [1,1,0,0,1,0] => {{1,2},{3}} => 2
[1,1] => [1,0,1,1,0,0] => {{1},{2,3}} => 1
[3] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => 2
[2,1] => [1,0,1,0,1,0] => {{1},{2},{3}} => 3
[1,1,1] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => 1
[4] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => 2
[3,1] => [1,1,0,1,0,0,1,0] => {{1,3},{2},{4}} => 3
[2,2] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => 1
[2,1,1] => [1,0,1,1,0,1,0,0] => {{1},{2,4},{3}} => 2
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => 1
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => 2
[4,1] => [1,1,1,0,1,0,0,0,1,0] => {{1,2,4},{3},{5}} => 3
[3,2] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => 3
[3,1,1] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => 2
[2,2,1] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => 1
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => {{1},{2,3,5},{4}} => 2
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => 1
[6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 2
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => {{1,2,3,5},{4},{6}} => 3
[4,2] => [1,1,1,0,0,1,0,0,1,0] => {{1,4},{2,3},{5}} => 3
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => {{1,3,4},{2},{5}} => 2
[3,3] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 1
[3,2,1] => [1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => 4
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => {{1},{2,5},{3,4}} => 2
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => 1
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => {{1},{2,4,5},{3}} => 1
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2,3,4,6},{5}} => 2
[1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => 1
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}} => 2
[6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,6},{5},{7}} => 3
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => {{1,2,5},{3,4},{6}} => 3
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => {{1,2,4,5},{3},{6}} => 2
[4,3] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => 3
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => {{1,4},{2},{3},{5}} => 4
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 2
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => {{1,3},{2},{4,5}} => 1
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,5},{4}} => 2
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => {{1},{2,5},{3},{4}} => 3
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2,3,6},{4,5}} => 2
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => 1
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2,3,5,6},{4}} => 1
[2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,7},{6}} => 2
[1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => 1
[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8},{9}} => 2
[7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7},{6},{8}} => 3
[6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4,5},{7}} => 3
[6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => {{1,2,3,5,6},{4},{7}} => 2
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => {{1,5},{2,3,4},{6}} => 3
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => {{1,2,5},{3},{4},{6}} => 4
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => {{1,3,4,5},{2},{6}} => 2
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 1
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => {{1,3},{2},{4},{5}} => 4
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 2
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => {{1},{2,4},{3},{5}} => 3
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2,6},{3,4,5}} => 2
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 1
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 1
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3,5},{4}} => 2
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2,3,6},{4},{5}} => 3
[3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => {{1},{2,3,4,7},{5,6}} => 2
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 1
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2,4,5,6},{3}} => 1
[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => {{1},{2,3,4,6,7},{5}} => 1
[2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,8},{7}} => 2
[1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9}} => 1
[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9},{10}} => 2
[8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,8},{7},{9}} => 3
[7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5,6},{8}} => 3
[7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,6,7},{5},{8}} => 2
[6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => {{1,2,6},{3,4,5},{7}} => 3
[6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => {{1,2,3,6},{4},{5},{7}} => 4
[6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => {{1,2,4,5,6},{3},{7}} => 2
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => {{1,5},{2,4},{3},{6}} => 4
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => {{1,4,5},{2,3},{6}} => 2
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => {{1,3,5},{2},{4},{6}} => 3
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 2
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => {{1,2,4},{3},{5,6}} => 1
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 4
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 3
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 2
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2,6},{3,5},{4}} => 3
[4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => {{1},{2,3,7},{4,5,6}} => 2
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 1
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => 1
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2,5,6},{3,4}} => 1
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => {{1,2},{3,4,6},{5}} => 2
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2,4,6},{3},{5}} => 2
[3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => {{1},{2,3,4,7},{5},{6}} => 3
[3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6,7}} => 2
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => 1
[2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => {{1},{2,3,5,6,7},{4}} => 1
[2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,7,8},{6}} => 1
[2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,9},{8}} => 2
[1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10}} => 1
[10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,8,9,10},{11}} => 2
[9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7,9},{8},{10}} => 3
[8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,8},{6,7},{9}} => 3
[8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,7,8},{6},{9}} => 2
[7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => {{1,2,3,7},{4,5,6},{8}} => 3
>>> Load all 462 entries. <<<
[7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => {{1,2,3,4,7},{5},{6},{8}} => 4
[7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,5,6,7},{4},{8}} => 2
[6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => {{1,6},{2,3,4,5},{7}} => 3
[6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3,5},{4},{7}} => 4
[6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3,4},{7}} => 2
[6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => {{1,2,4,6},{3},{5},{7}} => 3
[6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => {{1,3,4,5,6},{2},{7}} => 2
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 1
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => {{1,2,4},{3},{5},{6}} => 4
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => {{1,5},{2,3},{4},{6}} => 4
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => {{1,5},{2},{3,4},{6}} => 3
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => {{1,4,5},{2},{3},{6}} => 2
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2,3,5},{4},{6}} => 3
[5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => {{1},{2,7},{3,4,5,6}} => 2
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => {{1,4},{2,3},{5,6}} => 1
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => {{1,3,4},{2},{5,6}} => 1
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => {{1,2,3},{4,6},{5}} => 2
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => 5
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2,6},{3,4},{5}} => 3
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => {{1,2},{3,6},{4,5}} => 2
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2,6},{3},{4,5}} => 2
[4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => {{1},{2,3,7},{4,6},{5}} => 3
[4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => {{1},{2,3,4,8},{5,6,7}} => 2
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => {{1,3},{2},{4,5,6}} => 1
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => {{1,2},{3,5,6},{4}} => 1
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2,5,6},{3},{4}} => 1
[3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4,5}} => 1
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3,4,6},{5}} => 2
[3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => {{1},{2,3,5,7},{4},{6}} => 2
[3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => {{1},{2,3,4,5,8},{6},{7}} => 3
[3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,9},{7,8}} => 2
[2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 1
[2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => {{1},{2,4,5,6,7},{3}} => 1
[2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,6,7,8},{5}} => 1
[2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,8,9},{7}} => 1
[2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,10},{9}} => 2
[1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8,9,10,11}} => 1
[6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => 3
[6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => {{1,6},{2,3,5},{4},{7}} => 4
[6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3,4},{5},{7}} => 4
[6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => {{1,2,6},{3},{4,5},{7}} => 3
[6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => {{1,2,5,6},{3},{4},{7}} => 2
[6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => {{1,3,4,6},{2},{5},{7}} => 3
[6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 2
[5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => {{1,2,3,5},{4},{6,7}} => 1
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => {{1,4},{2,3},{5},{6}} => 4
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => {{1,3,4},{2},{5},{6}} => 3
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 2
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => {{1,5},{2},{3},{4},{6}} => 5
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2,5},{3,4},{6}} => 3
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 2
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2,4,5},{3},{6}} => 2
[5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => {{1},{2,7},{3,4,6},{5}} => 3
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 1
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => {{1,4},{2},{3},{5,6}} => 1
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 1
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => {{1,3},{2},{4,6},{5}} => 2
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => {{1,2},{3,6},{4},{5}} => 3
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2,6},{3},{4},{5}} => 4
[4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => {{1},{2,3,7},{4,5},{6}} => 3
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3,6},{4,5}} => 2
[4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => {{1},{2,3,7},{4},{5,6}} => 2
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 1
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 1
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3,5,6},{4}} => 1
[3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => {{1},{2,3,6,7},{4},{5}} => 1
[3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => {{1,2},{3,4,5,7},{6}} => 2
[3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => {{1},{2,4,5,7},{3},{6}} => 2
[2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 1
[2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,5,6,7,8},{4}} => 1
[6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 1
[6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => {{1,2,3,5},{4},{6},{7}} => 4
[6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3,4},{7}} => 4
[6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2,4,5},{3},{7}} => 3
[6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3,4},{7}} => 2
[6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => {{1,2,6},{3},{4},{5},{7}} => 5
[6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => {{1,3,6},{2},{4,5},{7}} => 3
[6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2,3},{7}} => 2
[6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => {{1,3,5,6},{2},{4},{7}} => 2
[6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => {{1},{2,3,4,6},{5},{7}} => 3
[5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3,4},{6,7}} => 1
[5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => {{1,2,4,5},{3},{6,7}} => 1
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => 4
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => {{1,4},{2},{3},{5},{6}} => 5
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 3
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => {{1,3},{2},{4,5},{6}} => 2
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => {{1,2},{3,5},{4},{6}} => 3
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2,5},{3},{4},{6}} => 4
[5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4,5}} => 3
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 2
[5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => {{1},{2,7},{3,5,6},{4}} => 2
[4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 1
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5,6}} => 1
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 1
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2,4},{3},{5,6}} => 1
[4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,4,5}} => 1
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4,6},{5}} => 2
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2,3},{4,6},{5}} => 2
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3,6},{4},{5}} => 3
[4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => {{1},{2,3,7},{4},{5},{6}} => 4
[4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => {{1,2},{3,4,7},{5,6}} => 2
[4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => {{1},{2,4,7},{3},{5,6}} => 2
[3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 1
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => 1
[3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3,4}} => 1
[3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => {{1,2},{3,4,6,7},{5}} => 1
[3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => {{1},{2,4,6,7},{3},{5}} => 1
[3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => {{1},{2},{3,4,5,7},{6}} => 2
[2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 1
[2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,4,5,6,7,8},{3}} => 1
[7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 2
[6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3,4},{6},{7}} => 4
[6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => {{1,2,4,5},{3},{6},{7}} => 3
[6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => {{1,6},{2,3,4},{5},{7}} => 4
[6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2,5},{3},{4},{7}} => 5
[6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => {{1,6},{2},{3,4,5},{7}} => 3
[6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2,4},{3},{7}} => 2
[6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2,3},{5},{7}} => 3
[6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => {{1,3,6},{2},{4},{5},{7}} => 4
[6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => {{1},{2,3,6},{4,5},{7}} => 3
[6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => {{1,4,5,6},{2},{3},{7}} => 2
[6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => {{1},{2,3,5,6},{4},{7}} => 2
[5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => {{1,5},{2,3,4},{6,7}} => 1
[5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => {{1,2,5},{3},{4},{6,7}} => 1
[5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => {{1,3,4,5},{2},{6,7}} => 1
[5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => {{1,2,3,4},{5,7},{6}} => 2
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6}} => 5
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 3
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2,4},{3},{5},{6}} => 4
[5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => {{1},{2,7},{3,4,5},{6}} => 3
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 2
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 2
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3,5},{4},{6}} => 3
[5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => {{1},{2,7},{3,6},{4},{5}} => 4
[5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => {{1,2},{3,7},{4,5,6}} => 2
[5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => {{1},{2,7},{3},{4,5,6}} => 2
[4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => {{1,2,4},{3},{5,6,7}} => 1
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 1
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 1
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 1
[4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3,5},{4}} => 1
[4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => {{1,2,3},{4,5,7},{6}} => 2
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4,6},{5}} => 2
[4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3,4},{6}} => 2
[4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => {{1,2},{3,4,7},{5},{6}} => 3
[4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => {{1},{2,4,7},{3},{5},{6}} => 3
[4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => {{1},{2},{3,4,7},{5,6}} => 2
[3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => {{1,3},{2},{4,5,6,7}} => 1
[3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => {{1,2},{3,5,6,7},{4}} => 1
[3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => {{1},{2,5,6,7},{3},{4}} => 1
[3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => {{1},{2},{3,4,6,7},{5}} => 1
[2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 1
[6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => {{1,5},{2,3,4},{6},{7}} => 4
[6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => {{1,2,5},{3},{4},{6},{7}} => 5
[6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => {{1,3,4,5},{2},{6},{7}} => 3
[6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 2
[6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2,4},{3},{5},{7}} => 5
[6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2,3},{4,5},{7}} => 3
[6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => {{1,6},{2},{3,5},{4},{7}} => 4
[6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => {{1},{2,6},{3,4,5},{7}} => 3
[6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2,3},{4},{7}} => 2
[6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3,4},{7}} => 2
[6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => {{1,4,6},{2},{3},{5},{7}} => 3
[6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => {{1},{2,3,6},{4},{5},{7}} => 4
[6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 2
[6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => {{1},{2,4,5,6},{3},{7}} => 2
[5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 1
[5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2,4},{3},{6,7}} => 1
[5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2,3},{6,7}} => 1
[5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => {{1,3,5},{2},{4},{6,7}} => 1
[5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 1
[5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => {{1,2,4},{3},{5,7},{6}} => 2
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}} => 5
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => 4
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 3
[5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => {{1},{2,7},{3,5},{4},{6}} => 4
[5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => {{1,2,3},{4,7},{5,6}} => 2
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => 2
[5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => {{1},{2,7},{3,4},{5,6}} => 2
[5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => {{1,2},{3,7},{4,6},{5}} => 3
[5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => {{1},{2,7},{3},{4,6},{5}} => 3
[5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => {{1},{2},{3,7},{4,5,6}} => 2
[4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2,3},{5,6,7}} => 1
[4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => {{1,3,4},{2},{5,6,7}} => 1
[4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => {{1,2,3},{4,6,7},{5}} => 1
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => 1
[4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3,4},{5}} => 1
[4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => {{1,2},{3,6,7},{4,5}} => 1
[4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4,5}} => 1
[4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => {{1,3},{2},{4,5,7},{6}} => 2
[4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => {{1,2},{3,5,7},{4},{6}} => 2
[4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => {{1},{2,5,7},{3},{4},{6}} => 2
[4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => {{1},{2},{3,4,7},{5},{6}} => 3
[3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 1
[3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 1
[3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => {{1},{2},{3,5,6,7},{4}} => 1
[6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 4
[6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2,4},{3},{6},{7}} => 5
[6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2,3},{6},{7}} => 3
[6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => {{1,3,5},{2},{4},{6},{7}} => 4
[6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 3
[6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => {{1,2,4},{3},{5,6},{7}} => 2
[6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2,3},{4},{5},{7}} => 5
[6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => {{1,6},{2},{3,4},{5},{7}} => 4
[6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => {{1,6},{2},{3},{4,5},{7}} => 3
[6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => {{1},{2,6},{3,5},{4},{7}} => 4
[6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 2
[6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => {{1,5,6},{2},{3},{4},{7}} => 2
[6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3,4},{7}} => 2
[6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => {{1,2},{3,4,6},{5},{7}} => 3
[6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => {{1},{2,4,6},{3},{5},{7}} => 3
[6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 2
[5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => {{1,2,4},{3},{5},{6,7}} => 1
[5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2,3},{4},{6,7}} => 1
[5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => {{1,5},{2},{3,4},{6,7}} => 1
[5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => {{1,4,5},{2},{3},{6,7}} => 1
[5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => {{1},{2,3,5},{4},{6,7}} => 1
[5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2,3},{5,7},{6}} => 2
[5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => {{1,3,4},{2},{5,7},{6}} => 2
[5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => {{1,2,3},{4,7},{5},{6}} => 3
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6}} => 6
[5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => {{1},{2,7},{3,4},{5},{6}} => 4
[5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => {{1,2},{3,7},{4,5},{6}} => 3
[5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => {{1},{2,7},{3},{4,5},{6}} => 3
[5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => {{1,3},{2},{4,7},{5,6}} => 2
[5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => {{1,2},{3,7},{4},{5,6}} => 2
[5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => {{1},{2,7},{3},{4},{5,6}} => 2
[5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => {{1},{2},{3,7},{4,6},{5}} => 3
[4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 1
[4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => {{1,4},{2},{3},{5,6,7}} => 1
[4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 1
[4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => {{1,3},{2},{4,6,7},{5}} => 1
[4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => {{1,2},{3,6,7},{4},{5}} => 1
[4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => {{1},{2,6,7},{3},{4},{5}} => 1
[4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4,5}} => 1
[4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => {{1,2},{3},{4,5,7},{6}} => 2
[4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => {{1},{2,3},{4,5,7},{6}} => 2
[4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => {{1},{2},{3,5,7},{4},{6}} => 2
[3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 1
[6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => {{1,2,4},{3},{5},{6},{7}} => 5
[6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2,3},{4},{6},{7}} => 5
[6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => {{1,5},{2},{3,4},{6},{7}} => 4
[6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => {{1,4,5},{2},{3},{6},{7}} => 3
[6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => {{1},{2,3,5},{4},{6},{7}} => 4
[6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2,3},{5,6},{7}} => 2
[6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => {{1,3,4},{2},{5,6},{7}} => 2
[6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => {{1,2,3},{4,6},{5},{7}} => 3
[6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => {{1,6},{2},{3},{4},{5},{7}} => 6
[6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => {{1},{2,6},{3,4},{5},{7}} => 4
[6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => {{1,2},{3,6},{4,5},{7}} => 3
[6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => {{1},{2,6},{3},{4,5},{7}} => 3
[6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => {{1,3},{2},{4,5,6},{7}} => 2
[6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => {{1,2},{3,5,6},{4},{7}} => 2
[6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => {{1},{2,5,6},{3},{4},{7}} => 2
[6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => {{1},{2},{3,4,6},{5},{7}} => 3
[5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2,3},{5},{6,7}} => 1
[5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => {{1,3,4},{2},{5},{6,7}} => 1
[5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 1
[5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => {{1,5},{2},{3},{4},{6,7}} => 1
[5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => {{1},{2,5},{3,4},{6,7}} => 1
[5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 1
[5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => {{1},{2,4,5},{3},{6,7}} => 1
[5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => {{1,2,3},{4},{5,7},{6}} => 2
[5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => {{1,4},{2},{3},{5,7},{6}} => 2
[5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => {{1},{2,3,4},{5,7},{6}} => 2
[5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => {{1,3},{2},{4,7},{5},{6}} => 3
[5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => {{1,2},{3,7},{4},{5},{6}} => 4
[5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => {{1},{2,7},{3},{4},{5},{6}} => 5
[5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => {{1},{2},{3,7},{4,5},{6}} => 3
[5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => {{1,2},{3},{4,7},{5,6}} => 2
[5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => {{1},{2,3},{4,7},{5,6}} => 2
[5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => {{1},{2},{3,7},{4},{5,6}} => 2
[4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => {{1,3},{2},{4},{5,6,7}} => 1
[4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 1
[4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => {{1},{2,4},{3},{5,6,7}} => 1
[4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => {{1,2},{3},{4,6,7},{5}} => 1
[4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => {{1},{2,3},{4,6,7},{5}} => 1
[4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => {{1},{2},{3,6,7},{4},{5}} => 1
[4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => {{1},{2},{3},{4,5,7},{6}} => 2
[6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2,3},{5},{6},{7}} => 5
[6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => {{1,3,4},{2},{5},{6},{7}} => 4
[6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 3
[6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => {{1,5},{2},{3},{4},{6},{7}} => 6
[6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => {{1},{2,5},{3,4},{6},{7}} => 4
[6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 3
[6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => {{1},{2,4,5},{3},{6},{7}} => 3
[6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 2
[6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => {{1,4},{2},{3},{5,6},{7}} => 2
[6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 2
[6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => {{1,3},{2},{4,6},{5},{7}} => 3
[6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => {{1,2},{3,6},{4},{5},{7}} => 4
[6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => {{1},{2,6},{3},{4},{5},{7}} => 5
[6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => {{1},{2},{3,6},{4,5},{7}} => 3
[6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 2
[6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 2
[6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => {{1},{2},{3,5,6},{4},{7}} => 2
[5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 1
[5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => {{1,4},{2},{3},{5},{6,7}} => 1
[5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 1
[5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => {{1,3},{2},{4,5},{6,7}} => 1
[5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => {{1,2},{3,5},{4},{6,7}} => 1
[5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => {{1},{2,5},{3},{4},{6,7}} => 1
[5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 1
[5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => {{1,3},{2},{4},{5,7},{6}} => 2
[5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => {{1,2},{3,4},{5,7},{6}} => 2
[5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => {{1},{2,4},{3},{5,7},{6}} => 2
[5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => {{1,2},{3},{4,7},{5},{6}} => 3
[5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => {{1},{2,3},{4,7},{5},{6}} => 3
[5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => {{1},{2},{3,7},{4},{5},{6}} => 4
[5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => {{1},{2},{3},{4,7},{5,6}} => 2
[4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 1
[4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 1
[4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 1
[4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => {{1},{2},{3},{4,6,7},{5}} => 1
[6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7}} => 7
[5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => 1
[6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 2
[5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => {{1},{2},{3},{4},{5,7},{6}} => 2
[4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 1
[6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 3
[5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 1
[6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => {{1},{2},{3},{4,6},{5},{7}} => 3
[5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => {{1},{2},{3},{4,7},{5},{6}} => 3
[6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 2
[6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 4
[5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 1
[6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 2
[5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => {{1},{2},{3,4},{5,7},{6}} => 2
[6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => {{1},{2},{3,5},{4},{6},{7}} => 4
[5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => {{1},{2},{3,5},{4},{6,7}} => 1
[6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => {{1},{2},{3,6},{4},{5},{7}} => 4
[6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 3
[6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 5
[5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 1
[6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 2
[5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => {{1},{2,3},{4},{5,7},{6}} => 2
[6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 3
[5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 1
[6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => {{1},{2,3},{4,6},{5},{7}} => 3
[6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => {{1},{2,4},{3},{5},{6},{7}} => 5
[5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => {{1},{2,4},{3},{5},{6,7}} => 1
[6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => {{1},{2,4},{3},{5,6},{7}} => 2
[6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => {{1},{2,5},{3},{4},{6},{7}} => 5
[6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 4
[6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}} => 6
[5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 1
[6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 2
[5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => {{1,2},{3},{4},{5,7},{6}} => 2
[6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 3
[5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 1
[6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => {{1,2},{3},{4,6},{5},{7}} => 3
[6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 4
[5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 1
[6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 2
[6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => {{1,2},{3,5},{4},{6},{7}} => 4
[6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => {{1,3},{2},{4},{5},{6},{7}} => 6
[5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => {{1,3},{2},{4},{5},{6,7}} => 1
[6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => {{1,3},{2},{4},{5,6},{7}} => 2
[6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => {{1,3},{2},{4,5},{6},{7}} => 3
[6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => {{1,4},{2},{3},{5},{6},{7}} => 6
[6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 5
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Description
The number of terminal closers of a set partition.
A closer of a set partition is a number that is maximal in its block. In particular, a singleton is a closer. This statistic counts the number of terminal closers. In other words, this is the number of closers such that all larger elements are also closers.
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.