- FindStat

Identifier

Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
St000700: Ordered trees ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 2672 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

{{1,4,6,7},{2,5},{3}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[[]]]],[[]],[]] => 1

{{1,4,6},{2,5,7},{3}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[]]],[[[]]],[]] => 1

{{1,4,6},{2,5},{3,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[]]],[[]],[[]]] => 2

{{1,4,6},{2,5},{3},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[]]],[[]],[],[]] => 1

{{1,4,7},{2,5,6},{3}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[]]],[[[]]],[]] => 1

{{1,4},{2,5,6,7},{3}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[[[[]]]],[]] => 1

{{1,4},{2,5,6},{3,7}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[[[]]],[[]]] => 2

{{1,4},{2,5,6},{3},{7}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[[[]]],[],[]] => 1

{{1,4,7},{2,5},{3,6}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[]]],[[]],[[]]] => 2

{{1,4},{2,5,7},{3,6}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[[[]]],[[]]] => 2

{{1,4},{2,5},{3,6,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[[]],[[[]]]] => 2

{{1,4},{2,5},{3,6},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1,4,7},{2,5},{3},{6}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[]]],[[]],[],[]] => 1

{{1,4},{2,5,7},{3},{6}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[[[]]],[],[]] => 1

{{1,4},{2,5},{3,7},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1,4},{2,5},{3},{6,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[[]],[],[[]]] => 1

{{1,4},{2,5},{3},{6},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[]] => 1

{{1,4,6,7},{2},{3,5}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[[[]]]],[],[[]]] => 1

{{1,4,6},{2,7},{3,5}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[]]],[[]],[[]]] => 2

{{1,4,6},{2},{3,5,7}} => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[[[]]]] => 1

{{1,4,6},{2},{3,5},{7}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[[]],[]] => 1

{{1,4,7},{2,6},{3,5}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[]]],[[]],[[]]] => 2

{{1,4},{2,6,7},{3,5}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[[[]]],[[]]] => 2

{{1,4},{2,6},{3,5,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[[]],[[[]]]] => 2

{{1,4},{2,6},{3,5},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1,4,7},{2},{3,5,6}} => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[[[]]]] => 1

{{1,4},{2,7},{3,5,6}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[[]],[[[]]]] => 2

{{1,4},{2},{3,5,6,7}} => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[]],[],[[[[]]]]] => 1

{{1,4},{2},{3,5,6},{7}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[[[]]],[]] => 1

{{1,4,7},{2},{3,5},{6}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[[]],[]] => 1

{{1,4},{2,7},{3,5},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1,4},{2},{3,5,7},{6}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[[[]]],[]] => 1

{{1,4},{2},{3,5},{6,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[[]],[[]]] => 1

{{1,4},{2},{3,5},{6},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[[]],[],[]] => 1

{{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[[]]]],[],[],[]] => 1

{{1,4,6},{2,7},{3},{5}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[]]],[[]],[],[]] => 1

{{1,4,6},{2},{3,7},{5}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[[]],[]] => 1

{{1,4,6},{2},{3},{5,7}} => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[]]],[],[],[[]]] => 1

{{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[]] => 1

{{1,4,7},{2,6},{3},{5}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[]]],[[]],[],[]] => 1

{{1,4},{2,6,7},{3},{5}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[[[]]],[],[]] => 1

{{1,4},{2,6},{3,7},{5}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1,4},{2,6},{3},{5,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[[]],[],[[]]] => 1

{{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[]] => 1

{{1,4,7},{2},{3,6},{5}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[[]],[]] => 1

{{1,4},{2,7},{3,6},{5}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1,4},{2},{3,6,7},{5}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[[[]]],[]] => 1

{{1,4},{2},{3,6},{5,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[[]],[[]]] => 1

{{1,4},{2},{3,6},{5},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[[]],[],[]] => 1

{{1,4,7},{2},{3},{5,6}} => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[]]],[],[],[[]]] => 1

{{1,4},{2,7},{3},{5,6}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[[]],[],[[]]] => 1

{{1,4},{2},{3,7},{5,6}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[[]],[[]]] => 1

{{1,4},{2},{3},{5,6,7}} => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[]],[],[],[[[]]]] => 1

{{1,4},{2},{3},{5,6},{7}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[[]],[]] => 1

{{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[]] => 1

{{1,4},{2,7},{3},{5},{6}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[]] => 1

{{1,4},{2},{3,7},{5},{6}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[[]],[],[]] => 1

{{1,4},{2},{3},{5,7},{6}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[[]],[]] => 1

{{1,4},{2},{3},{5},{6,7}} => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[],[[]]] => 1

{{1,4},{2},{3},{5},{6},{7}} => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[]] => 1

{{1,5,6,7},{2,4},{3}} => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[[]]]],[[]],[]] => 1

{{1,5,6},{2,4,7},{3}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[]]],[[[]]],[]] => 1

{{1,5,6},{2,4},{3,7}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[]]],[[]],[[]]] => 2

{{1,5,6},{2,4},{3},{7}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[]]],[[]],[],[]] => 1

{{1,5,7},{2,4,6},{3}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[]]],[[[]]],[]] => 1

{{1,5},{2,4,6,7},{3}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[[[[]]]],[]] => 1

{{1,5},{2,4,6},{3,7}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[[[]]],[[]]] => 2

{{1,5},{2,4,6},{3},{7}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[[[]]],[],[]] => 1

{{1,5,7},{2,4},{3,6}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[]]],[[]],[[]]] => 2

{{1,5},{2,4,7},{3,6}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[[[]]],[[]]] => 2

{{1,5},{2,4},{3,6,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[[]],[[[]]]] => 2

{{1,5},{2,4},{3,6},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[]]],[[]],[],[]] => 1

{{1,5},{2,4,7},{3},{6}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[[[]]],[],[]] => 1

{{1,5},{2,4},{3,7},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1,5},{2,4},{3},{6,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[[]],[],[[]]] => 1

{{1,5},{2,4},{3},{6},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[]] => 1

{{1,6,7},{2,4,5},{3}} => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[]]],[[[]]],[]] => 1

{{1,6},{2,4,5,7},{3}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[[[[]]]],[]] => 1

{{1,6},{2,4,5},{3,7}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[[[]]],[[]]] => 2

{{1,6},{2,4,5},{3},{7}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[[[]]],[],[]] => 1

{{1,7},{2,4,5,6},{3}} => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[[[[]]]],[]] => 1

{{1},{2,4,5,6,7},{3}} => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[],[[[[[]]]]],[]] => 1

{{1},{2,4,5,6},{3,7}} => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[],[[[[]]]],[[]]] => 1

{{1},{2,4,5,6},{3},{7}} => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[],[[[[]]]],[],[]] => 1

{{1,7},{2,4,5},{3,6}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[[[]]],[[]]] => 2

{{1},{2,4,5,7},{3,6}} => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[],[[[[]]]],[[]]] => 1

{{1},{2,4,5},{3,6,7}} => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[],[[[]]],[[[]]]] => 1

{{1},{2,4,5},{3,6},{7}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[[[]]],[[]],[]] => 1

{{1,7},{2,4,5},{3},{6}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[[[]]],[],[]] => 1

{{1},{2,4,5,7},{3},{6}} => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[],[[[[]]]],[],[]] => 1

{{1},{2,4,5},{3,7},{6}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[[[]]],[[]],[]] => 1

{{1},{2,4,5},{3},{6,7}} => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[],[[[]]],[],[[]]] => 1

{{1},{2,4,5},{3},{6},{7}} => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[]] => 1

{{1,6,7},{2,4},{3,5}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[]]],[[]],[[]]] => 2

{{1,6},{2,4,7},{3,5}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[[[]]],[[]]] => 2

{{1,6},{2,4},{3,5,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[[]],[[[]]]] => 2

{{1,6},{2,4},{3,5},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1,7},{2,4,6},{3,5}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[[[]]],[[]]] => 2

{{1},{2,4,6,7},{3,5}} => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[],[[[[]]]],[[]]] => 1

{{1},{2,4,6},{3,5,7}} => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[],[[[]]],[[[]]]] => 1

{{1},{2,4,6},{3,5},{7}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[[[]]],[[]],[]] => 1

{{1,7},{2,4},{3,5,6}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[[]],[[[]]]] => 2

{{1},{2,4,7},{3,5,6}} => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[],[[[]]],[[[]]]] => 1

{{1},{2,4},{3,5,6,7}} => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[],[[]],[[[[]]]]] => 1

{{1},{2,4},{3,5,6},{7}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[[]],[[[]]],[]] => 1

{{1,7},{2,4},{3,5},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1},{2,4,7},{3,5},{6}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[[[]]],[[]],[]] => 1

{{1},{2,4},{3,5,7},{6}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[[]],[[[]]],[]] => 1

{{1},{2,4},{3,5},{6,7}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]],[[]]] => 1

{{1},{2,4},{3,5},{6},{7}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[[]],[[]],[],[]] => 1

{{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[]]],[[]],[],[]] => 1

{{1,6},{2,4,7},{3},{5}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[[[]]],[],[]] => 1

{{1,6},{2,4},{3,7},{5}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1,6},{2,4},{3},{5,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[[]],[],[[]]] => 1

{{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[]] => 1

{{1,7},{2,4,6},{3},{5}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[[[]]],[],[]] => 1

{{1},{2,4,6,7},{3},{5}} => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[],[[[[]]]],[],[]] => 1

{{1},{2,4,6},{3,7},{5}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[[[]]],[[]],[]] => 1

{{1},{2,4,6},{3},{5,7}} => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[],[[[]]],[],[[]]] => 1

{{1},{2,4,6},{3},{5},{7}} => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[]] => 1

{{1,7},{2,4},{3,6},{5}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1},{2,4,7},{3,6},{5}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[[[]]],[[]],[]] => 1

{{1},{2,4},{3,6,7},{5}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[[]],[[[]]],[]] => 1

{{1},{2,4},{3,6},{5,7}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]],[[]]] => 1

{{1},{2,4},{3,6},{5},{7}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[[]],[[]],[],[]] => 1

{{1,7},{2,4},{3},{5,6}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[[]],[],[[]]] => 1

{{1},{2,4,7},{3},{5,6}} => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[],[[[]]],[],[[]]] => 1

{{1},{2,4},{3,7},{5,6}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]],[[]]] => 1

{{1},{2,4},{3},{5,6,7}} => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[],[[]],[],[[[]]]] => 1

{{1},{2,4},{3},{5,6},{7}} => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[],[[]],[],[[]],[]] => 1

{{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[]] => 1

{{1},{2,4,7},{3},{5},{6}} => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[]] => 1

{{1},{2,4},{3,7},{5},{6}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[[]],[[]],[],[]] => 1

{{1},{2,4},{3},{5,7},{6}} => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[],[[]],[],[[]],[]] => 1

{{1},{2,4},{3},{5},{6,7}} => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[],[[]],[],[],[[]]] => 1

{{1},{2,4},{3},{5},{6},{7}} => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[],[[]],[],[],[],[]] => 1

{{1,5,6,7},{2},{3,4}} => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[[[]]]],[],[[]]] => 1

{{1,5,6},{2,7},{3,4}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[]]],[[]],[[]]] => 2

{{1,5,6},{2},{3,4,7}} => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[[[]]]] => 1

{{1,5,6},{2},{3,4},{7}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[[]],[]] => 1

{{1,5,7},{2,6},{3,4}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[]]],[[]],[[]]] => 2

{{1,5},{2,6,7},{3,4}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[[[]]],[[]]] => 2

{{1,5},{2,6},{3,4,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[[]],[[[]]]] => 2

{{1,5},{2,6},{3,4},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1,5,7},{2},{3,4,6}} => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[[[]]]] => 1

{{1,5},{2,7},{3,4,6}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[[]],[[[]]]] => 2

{{1,5},{2},{3,4,6,7}} => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[]],[],[[[[]]]]] => 1

{{1,5},{2},{3,4,6},{7}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[[[]]],[]] => 1

{{1,5,7},{2},{3,4},{6}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[[]],[]] => 1

{{1,5},{2,7},{3,4},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1,5},{2},{3,4,7},{6}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[[[]]],[]] => 1

{{1,5},{2},{3,4},{6,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[[]],[[]]] => 1

{{1,5},{2},{3,4},{6},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[[]],[],[]] => 1

{{1,6,7},{2,5},{3,4}} => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[]]],[[]],[[]]] => 2

{{1,6},{2,5,7},{3,4}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[[[]]],[[]]] => 2

{{1,6},{2,5},{3,4,7}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[[]],[[[]]]] => 2

{{1,6},{2,5},{3,4},{7}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1,7},{2,5,6},{3,4}} => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[[[]]],[[]]] => 2

{{1},{2,5,6,7},{3,4}} => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[],[[[[]]]],[[]]] => 1

{{1},{2,5,6},{3,4,7}} => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[],[[[]]],[[[]]]] => 1

{{1},{2,5,6},{3,4},{7}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[[[]]],[[]],[]] => 1

{{1,7},{2,5},{3,4,6}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[[]],[[[]]]] => 2

{{1},{2,5,7},{3,4,6}} => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[],[[[]]],[[[]]]] => 1

{{1},{2,5},{3,4,6,7}} => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[],[[]],[[[[]]]]] => 1

{{1},{2,5},{3,4,6},{7}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[[]],[[[]]],[]] => 1

{{1,7},{2,5},{3,4},{6}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1},{2,5,7},{3,4},{6}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[[[]]],[[]],[]] => 1

{{1},{2,5},{3,4,7},{6}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[[]],[[[]]],[]] => 1

{{1},{2,5},{3,4},{6,7}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]],[[]]] => 1

{{1},{2,5},{3,4},{6},{7}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[[]],[[]],[],[]] => 1

{{1,6,7},{2},{3,4,5}} => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[[[]]]] => 1

{{1,6},{2,7},{3,4,5}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[[]],[[[]]]] => 2

{{1,6},{2},{3,4,5,7}} => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[]],[],[[[[]]]]] => 1

{{1,6},{2},{3,4,5},{7}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[[[]]],[]] => 1

{{1,7},{2,6},{3,4,5}} => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[[]],[[[]]]] => 2

{{1},{2,6,7},{3,4,5}} => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[],[[[]]],[[[]]]] => 1

{{1},{2,6},{3,4,5,7}} => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[],[[]],[[[[]]]]] => 1

{{1},{2,6},{3,4,5},{7}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[[]],[[[]]],[]] => 1

{{1,7},{2},{3,4,5,6}} => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[]],[],[[[[]]]]] => 1

{{1},{2,7},{3,4,5,6}} => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[],[[]],[[[[]]]]] => 1

{{1},{2},{3,4,5,6,7}} => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[],[],[[[[[]]]]]] => 1

{{1},{2},{3,4,5,6},{7}} => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[],[],[[[[]]]],[]] => 1

{{1,7},{2},{3,4,5},{6}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[[[]]],[]] => 1

{{1},{2,7},{3,4,5},{6}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[[]],[[[]]],[]] => 1

{{1},{2},{3,4,5,7},{6}} => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[],[],[[[[]]]],[]] => 1

{{1},{2},{3,4,5},{6,7}} => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[],[],[[[]]],[[]]] => 1

{{1},{2},{3,4,5},{6},{7}} => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => 1

{{1,6,7},{2},{3,4},{5}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[[]],[]] => 1

{{1,6},{2,7},{3,4},{5}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1,6},{2},{3,4,7},{5}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[[[]]],[]] => 1

{{1,6},{2},{3,4},{5,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[[]],[[]]] => 1

{{1,6},{2},{3,4},{5},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[[]],[],[]] => 1

{{1,7},{2,6},{3,4},{5}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1},{2,6,7},{3,4},{5}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[[[]]],[[]],[]] => 1

{{1},{2,6},{3,4,7},{5}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[[]],[[[]]],[]] => 1

{{1},{2,6},{3,4},{5,7}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]],[[]]] => 1

{{1},{2,6},{3,4},{5},{7}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[[]],[[]],[],[]] => 1

{{1,7},{2},{3,4,6},{5}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[[[]]],[]] => 1

{{1},{2,7},{3,4,6},{5}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[[]],[[[]]],[]] => 1

{{1},{2},{3,4,6,7},{5}} => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[],[],[[[[]]]],[]] => 1

{{1},{2},{3,4,6},{5,7}} => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[],[],[[[]]],[[]]] => 1

{{1},{2},{3,4,6},{5},{7}} => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => 1

{{1,7},{2},{3,4},{5,6}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[[]],[[]]] => 1

{{1},{2,7},{3,4},{5,6}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]],[[]]] => 1

{{1},{2},{3,4,7},{5,6}} => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[],[],[[[]]],[[]]] => 1

{{1},{2},{3,4},{5,6,7}} => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[],[],[[]],[[[]]]] => 1

{{1},{2},{3,4},{5,6},{7}} => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[[]],[[]],[]] => 1

{{1,7},{2},{3,4},{5},{6}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[[]],[],[]] => 1

{{1},{2,7},{3,4},{5},{6}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[[]],[[]],[],[]] => 1

{{1},{2},{3,4,7},{5},{6}} => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => 1

{{1},{2},{3,4},{5,7},{6}} => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[[]],[[]],[]] => 1

{{1},{2},{3,4},{5},{6,7}} => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[],[],[[]],[],[[]]] => 1

{{1},{2},{3,4},{5},{6},{7}} => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[]] => 1

{{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[[]]]],[],[],[]] => 1

{{1,5,6},{2,7},{3},{4}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[]]],[[]],[],[]] => 1

{{1,5,6},{2},{3,7},{4}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[[]],[]] => 1

{{1,5,6},{2},{3},{4,7}} => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[]]],[],[],[[]]] => 1

{{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[]] => 1

{{1,5,7},{2,6},{3},{4}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[]]],[[]],[],[]] => 1

{{1,5},{2,6,7},{3},{4}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[[[]]],[],[]] => 1

{{1,5},{2,6},{3,7},{4}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[[]],[],[[]]] => 1

{{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[]] => 1

{{1,5,7},{2},{3,6},{4}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[[]],[]] => 1

{{1,5},{2,7},{3,6},{4}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1,5},{2},{3,6,7},{4}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[[[]]],[]] => 1

{{1,5},{2},{3,6},{4,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[[]],[[]]] => 1

{{1,5},{2},{3,6},{4},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[[]],[],[]] => 1

{{1,5,7},{2},{3},{4,6}} => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[]]],[],[],[[]]] => 1

{{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[[]],[],[[]]] => 1

{{1,5},{2},{3,7},{4,6}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[[]],[[]]] => 1

{{1,5},{2},{3},{4,6,7}} => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[]],[],[],[[[]]]] => 1

{{1,5},{2},{3},{4,6},{7}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[[]],[]] => 1

{{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[]] => 1

{{1,5},{2,7},{3},{4},{6}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[]] => 1

{{1,5},{2},{3,7},{4},{6}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[[]],[],[]] => 1

{{1,5},{2},{3},{4,7},{6}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[[]],[]] => 1

{{1,5},{2},{3},{4},{6,7}} => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[],[[]]] => 1

{{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[]] => 1

{{1,6,7},{2,5},{3},{4}} => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[]]],[[]],[],[]] => 1

{{1,6},{2,5,7},{3},{4}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[[[]]],[],[]] => 1

{{1,6},{2,5},{3,7},{4}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[[]],[],[[]]] => 1

{{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[]] => 1

{{1,7},{2,5,6},{3},{4}} => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[[[]]],[],[]] => 1

{{1},{2,5,6,7},{3},{4}} => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[],[[[[]]]],[],[]] => 1

{{1},{2,5,6},{3,7},{4}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[[[]]],[[]],[]] => 1

{{1},{2,5,6},{3},{4,7}} => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[],[[[]]],[],[[]]] => 1

{{1},{2,5,6},{3},{4},{7}} => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[]] => 1

{{1,7},{2,5},{3,6},{4}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1},{2,5,7},{3,6},{4}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[[[]]],[[]],[]] => 1

{{1},{2,5},{3,6,7},{4}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[[]],[[[]]],[]] => 1

{{1},{2,5},{3,6},{4,7}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]],[[]]] => 1

{{1},{2,5},{3,6},{4},{7}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[[]],[[]],[],[]] => 1

{{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[[]],[],[[]]] => 1

{{1},{2,5,7},{3},{4,6}} => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[],[[[]]],[],[[]]] => 1

{{1},{2,5},{3,7},{4,6}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]],[[]]] => 1

{{1},{2,5},{3},{4,6,7}} => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[],[[]],[],[[[]]]] => 1

{{1},{2,5},{3},{4,6},{7}} => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[],[[]],[],[[]],[]] => 1

{{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[]] => 1

{{1},{2,5,7},{3},{4},{6}} => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[]] => 1

{{1},{2,5},{3,7},{4},{6}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[[]],[[]],[],[]] => 1

{{1},{2,5},{3},{4,7},{6}} => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[],[[]],[],[[]],[]] => 1

{{1},{2,5},{3},{4},{6,7}} => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[],[[]],[],[],[[]]] => 1

{{1},{2,5},{3},{4},{6},{7}} => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[],[[]],[],[],[],[]] => 1

{{1,6,7},{2},{3,5},{4}} => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[[]],[]] => 1

{{1,6},{2,7},{3,5},{4}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1,6},{2},{3,5,7},{4}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[[[]]],[]] => 1

{{1,6},{2},{3,5},{4,7}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[[]],[[]]] => 1

{{1,6},{2},{3,5},{4},{7}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[[]],[],[]] => 1

{{1,7},{2,6},{3,5},{4}} => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 1

{{1},{2,6,7},{3,5},{4}} => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[[[]]],[[]],[]] => 1

{{1},{2,6},{3,5,7},{4}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[[]],[[[]]],[]] => 1

{{1},{2,6},{3,5},{4,7}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]],[[]]] => 1

{{1},{2,6},{3,5},{4},{7}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[[]],[[]],[],[]] => 1

{{1,7},{2},{3,5,6},{4}} => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[[[]]],[]] => 1

{{1},{2,7},{3,5,6},{4}} => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[[]],[[[]]],[]] => 1

{{1},{2},{3,5,6,7},{4}} => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[],[],[[[[]]]],[]] => 1

{{1},{2},{3,5,6},{4,7}} => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[],[],[[[]]],[[]]] => 1

{{1},{2},{3,5,6},{4},{7}} => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => 1

{{1,7},{2},{3,5},{4,6}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[[]],[[]]] => 1

{{1},{2,7},{3,5},{4,6}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]],[[]]] => 1

{{1},{2},{3,5,7},{4,6}} => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[],[],[[[]]],[[]]] => 1

{{1},{2},{3,5},{4,6,7}} => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[],[],[[]],[[[]]]] => 1

{{1},{2},{3,5},{4,6},{7}} => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[[]],[[]],[]] => 1

{{1,7},{2},{3,5},{4},{6}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[[]],[],[]] => 1

{{1},{2,7},{3,5},{4},{6}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[[]],[[]],[],[]] => 1

{{1},{2},{3,5,7},{4},{6}} => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => 1

{{1},{2},{3,5},{4,7},{6}} => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[[]],[[]],[]] => 1

{{1},{2},{3,5},{4},{6,7}} => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[],[],[[]],[],[[]]] => 1

{{1},{2},{3,5},{4},{6},{7}} => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[]] => 1

{{1,6,7},{2},{3},{4,5}} => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[]]],[],[],[[]]] => 1

{{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[[]],[],[[]]] => 1

{{1,6},{2},{3,7},{4,5}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[[]],[[]]] => 1

{{1,6},{2},{3},{4,5,7}} => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[]],[],[],[[[]]]] => 1

{{1,6},{2},{3},{4,5},{7}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[[]],[]] => 1

{{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[[]],[],[[]]] => 1

{{1},{2,6,7},{3},{4,5}} => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[],[[[]]],[],[[]]] => 1

{{1},{2,6},{3,7},{4,5}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]],[[]]] => 1

{{1},{2,6},{3},{4,5,7}} => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[],[[]],[],[[[]]]] => 1

{{1},{2,6},{3},{4,5},{7}} => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[],[[]],[],[[]],[]] => 1

{{1,7},{2},{3,6},{4,5}} => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[[]],[[]]] => 1

{{1},{2,7},{3,6},{4,5}} => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]],[[]]] => 1

{{1},{2},{3,6,7},{4,5}} => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[],[],[[[]]],[[]]] => 1

{{1},{2},{3,6},{4,5,7}} => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[],[],[[]],[[[]]]] => 1

{{1},{2},{3,6},{4,5},{7}} => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[[]],[[]],[]] => 1

{{1,7},{2},{3},{4,5,6}} => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[]],[],[],[[[]]]] => 1

{{1},{2,7},{3},{4,5,6}} => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[],[[]],[],[[[]]]] => 1

{{1},{2},{3,7},{4,5,6}} => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[],[],[[]],[[[]]]] => 1

{{1},{2},{3},{4,5,6,7}} => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[],[[[[]]]]] => 1

{{1},{2},{3},{4,5,6},{7}} => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[],[[[]]],[]] => 1

{{1,7},{2},{3},{4,5},{6}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[[]],[]] => 1

{{1},{2,7},{3},{4,5},{6}} => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[],[[]],[],[[]],[]] => 1

{{1},{2},{3,7},{4,5},{6}} => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[[]],[[]],[]] => 1

{{1},{2},{3},{4,5,7},{6}} => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[],[[[]]],[]] => 1

{{1},{2},{3},{4,5},{6,7}} => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[],[[]],[[]]] => 1

{{1},{2},{3},{4,5},{6},{7}} => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[],[[]],[],[]] => 1

{{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[]] => 1

{{1,6},{2,7},{3},{4},{5}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[]] => 1

{{1,6},{2},{3,7},{4},{5}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[[]],[],[]] => 1

{{1,6},{2},{3},{4,7},{5}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[[]],[]] => 1

{{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[],[[]]] => 1

{{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[]] => 1

{{1,7},{2,6},{3},{4},{5}} => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[]] => 1

{{1},{2,6,7},{3},{4},{5}} => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[]] => 1

{{1},{2,6},{3,7},{4},{5}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[[]],[[]],[],[]] => 1

{{1},{2,6},{3},{4,7},{5}} => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[],[[]],[],[[]],[]] => 1

{{1},{2,6},{3},{4},{5,7}} => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[],[[]],[],[],[[]]] => 1

{{1},{2,6},{3},{4},{5},{7}} => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[],[[]],[],[],[],[]] => 1

{{1,7},{2},{3,6},{4},{5}} => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[[]],[],[]] => 1

{{1},{2,7},{3,6},{4},{5}} => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[[]],[[]],[],[]] => 1

{{1},{2},{3,6,7},{4},{5}} => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => 1

{{1},{2},{3,6},{4,7},{5}} => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[[]],[[]],[]] => 1

{{1},{2},{3,6},{4},{5,7}} => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[],[],[[]],[],[[]]] => 1

{{1},{2},{3,6},{4},{5},{7}} => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[]] => 1

{{1,7},{2},{3},{4,6},{5}} => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[[]],[]] => 1

{{1},{2,7},{3},{4,6},{5}} => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[],[[]],[],[[]],[]] => 1

{{1},{2},{3,7},{4,6},{5}} => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[[]],[[]],[]] => 1

{{1},{2},{3},{4,6,7},{5}} => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[],[[[]]],[]] => 1

{{1},{2},{3},{4,6},{5,7}} => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[],[[]],[[]]] => 1

{{1},{2},{3},{4,6},{5},{7}} => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[],[[]],[],[]] => 1

{{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[],[[]]] => 1

{{1},{2,7},{3},{4},{5,6}} => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[],[[]],[],[],[[]]] => 1

{{1},{2},{3,7},{4},{5,6}} => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[],[],[[]],[],[[]]] => 1

{{1},{2},{3},{4,7},{5,6}} => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[],[[]],[[]]] => 1

{{1},{2},{3},{4},{5,6,7}} => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[],[[[]]]] => 1

{{1},{2},{3},{4},{5,6},{7}} => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[],[[]],[]] => 1

{{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[]] => 1

{{1},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[],[[]],[],[],[],[]] => 1

{{1},{2},{3,7},{4},{5},{6}} => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[]] => 1

{{1},{2},{3},{4,7},{5},{6}} => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[],[[]],[],[]] => 1

{{1},{2},{3},{4},{5,7},{6}} => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[],[[]],[]] => 1

{{1},{2},{3},{4},{5},{6,7}} => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[],[[]]] => 1

{{1},{2},{3},{4},{5},{6},{7}} => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => 1

{{1,2},{3,4},{5,6},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,3},{2,4},{5,6},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,4},{2,3},{5,6},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,5},{2,3},{4,6},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,6},{2,3},{4,5},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,7},{2,3},{4,5},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,8},{2,3},{4,5},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,8},{2,4},{3,5},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,7},{2,4},{3,5},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,6},{2,4},{3,5},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,5},{2,4},{3,6},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,4},{2,5},{3,6},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,3},{2,5},{4,6},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,2},{3,5},{4,6},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,2},{3,6},{4,5},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,3},{2,6},{4,5},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,4},{2,6},{3,5},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,5},{2,6},{3,4},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,6},{2,5},{3,4},{7,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,7},{2,5},{3,4},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,8},{2,5},{3,4},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,8},{2,6},{3,4},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,7},{2,6},{3,4},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,6},{2,7},{3,4},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,5},{2,7},{3,4},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,4},{2,7},{3,5},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,3},{2,7},{4,5},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,2},{3,7},{4,5},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,2},{3,8},{4,5},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,3},{2,8},{4,5},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,4},{2,8},{3,5},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,5},{2,8},{3,4},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,6},{2,8},{3,4},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,7},{2,8},{3,4},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,8},{2,7},{3,4},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,8},{2,7},{3,5},{4,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,7},{2,8},{3,5},{4,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,6},{2,8},{3,5},{4,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,5},{2,8},{3,6},{4,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,4},{2,8},{3,6},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,3},{2,8},{4,6},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,2},{3,8},{4,6},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,2},{3,7},{4,6},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,3},{2,7},{4,6},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,4},{2,7},{3,6},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,5},{2,7},{3,6},{4,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,6},{2,7},{3,5},{4,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,7},{2,6},{3,5},{4,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,8},{2,6},{3,5},{4,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,8},{2,5},{3,6},{4,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,7},{2,5},{3,6},{4,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,6},{2,5},{3,7},{4,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,5},{2,6},{3,7},{4,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,4},{2,6},{3,7},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,3},{2,6},{4,7},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,2},{3,6},{4,7},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,2},{3,5},{4,7},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,3},{2,5},{4,7},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,4},{2,5},{3,7},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,5},{2,4},{3,7},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,6},{2,4},{3,7},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,7},{2,4},{3,6},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,8},{2,4},{3,6},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,8},{2,3},{4,6},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,7},{2,3},{4,6},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,6},{2,3},{4,7},{5,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,5},{2,3},{4,7},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,4},{2,3},{5,7},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,3},{2,4},{5,7},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,2},{3,4},{5,7},{6,8}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,2},{3,4},{5,8},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,3},{2,4},{5,8},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,4},{2,3},{5,8},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,5},{2,3},{4,8},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,6},{2,3},{4,8},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,7},{2,3},{4,8},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,8},{2,3},{4,7},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,8},{2,4},{3,7},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,7},{2,4},{3,8},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,6},{2,4},{3,8},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,5},{2,4},{3,8},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,4},{2,5},{3,8},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,3},{2,5},{4,8},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,2},{3,5},{4,8},{6,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,2},{3,6},{4,8},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,3},{2,6},{4,8},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,4},{2,6},{3,8},{5,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,5},{2,6},{3,8},{4,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,6},{2,5},{3,8},{4,7}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,7},{2,5},{3,8},{4,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,8},{2,5},{3,7},{4,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,8},{2,6},{3,7},{4,5}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,7},{2,6},{3,8},{4,5}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,6},{2,7},{3,8},{4,5}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,5},{2,7},{3,8},{4,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,4},{2,7},{3,8},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,3},{2,7},{4,8},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,2},{3,7},{4,8},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,2},{3,8},{4,7},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,3},{2,8},{4,7},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,4},{2,8},{3,7},{5,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,5},{2,8},{3,7},{4,6}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,6},{2,8},{3,7},{4,5}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,7},{2,8},{3,6},{4,5}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1,8},{2,7},{3,6},{4,5}} => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => 2

{{1},{2},{3},{4},{5},{6},{7},{8}} => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[],[]] => 1

{{1},{2},{3},{4},{5},{6},{7,8}} => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[],[],[[]]] => 1

{{1},{2},{3},{4},{5},{6,8},{7}} => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[],[],[[]],[]] => 1

{{1},{2},{3},{4},{5},{6,7,8}} => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[],[],[[[]]]] => 1

{{1},{2},{3},{4},{5,6},{7},{8}} => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[],[],[[]],[],[]] => 1

{{1},{2},{3},{4},{5,6},{7,8}} => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[],[],[[]],[[]]] => 1

{{1},{2},{3},{4},{5,7},{6},{8}} => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[],[],[[]],[],[]] => 1

{{1},{2},{3},{4},{5,8},{6},{7}} => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[],[],[[]],[],[]] => 1

{{1},{2},{3},{4},{5,7,8},{6}} => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[],[],[[[]]],[]] => 1

{{1},{2},{3},{4},{5,6,7},{8}} => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[],[],[[[]]],[]] => 1

{{1},{2},{3},{4},{5,8},{6,7}} => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[],[],[[]],[[]]] => 1

{{1},{2},{3},{4},{5,6,8},{7}} => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[],[],[[[]]],[]] => 1

{{1},{2},{3},{4},{5,6,7,8}} => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[],[],[[[[]]]]] => 1

{{1},{2},{3},{4,5},{6},{7,8}} => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[],[],[],[[]],[],[[]]] => 1

{{1},{2},{3},{4,8},{5},{6},{7}} => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[],[[]],[],[],[]] => 1

{{1},{2},{3},{4,6,7,8},{5}} => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[],[],[],[[[[]]]],[]] => 1

{{1},{2},{3},{4,8},{5,6},{7}} => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[],[[]],[[]],[]] => 1

{{1},{2},{3},{4,7,8},{5,6}} => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[],[],[],[[[]]],[[]]] => 1

{{1},{2},{3},{4,8},{5,7},{6}} => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[],[[]],[[]],[]] => 1

{{1},{2},{3},{4,8},{5,6,7}} => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[],[],[],[[]],[[[]]]] => 1

{{1},{2},{3},{4,5,6,7,8}} => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[],[],[],[[[[[]]]]]] => 1

{{1},{2},{3,4},{5},{6},{7,8}} => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[],[],[[]],[],[],[[]]] => 1

{{1},{2},{3,4},{5},{6,8},{7}} => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[],[[]],[]] => 1

{{1},{2},{3,4},{5,6},{7},{8}} => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[[]],[],[]] => 1

{{1},{2},{3,4},{5,8},{6},{7}} => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[[]],[],[]] => 1

{{1},{2},{3,4},{5,8},{6,7}} => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[],[],[[]],[[]],[[]]] => 1

{{1},{2},{3,4},{5,6,7,8}} => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[],[],[[]],[[[[]]]]] => 1

{{1},{2},{3,5},{4},{6,7,8}} => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[],[],[[]],[],[[[]]]] => 1

{{1},{2},{3,8},{4},{5},{6},{7}} => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[],[]] => 1

{{1},{2},{3,7,8},{4},{5},{6}} => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[],[],[[[]]],[],[],[]] => 1

{{1},{2},{3,7,8},{4},{5,6}} => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[],[],[[[]]],[],[[]]] => 1

{{1},{2},{3,5,7,8},{4},{6}} => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[],[],[[[[]]]],[],[]] => 1

{{1},{2},{3,8},{4},{5,6,7}} => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[],[],[[]],[],[[[]]]] => 1

{{1},{2},{3,5,8},{4},{6,7}} => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[],[],[[[]]],[],[[]]] => 1

{{1},{2},{3,5,6,7,8},{4}} => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[],[],[[[[[]]]]],[]] => 1

{{1},{2},{3,4,5},{6},{7},{8}} => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[],[],[[[]]],[],[],[]] => 1

{{1},{2},{3,4,5},{6,7,8}} => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[],[],[[[]]],[[[]]]] => 1

{{1},{2},{3,8},{4,5},{6},{7}} => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[[]],[],[]] => 1

{{1},{2},{3,6,7,8},{4,5}} => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[],[],[[[[]]]],[[]]] => 1

{{1},{2},{3,8},{4,6},{5},{7}} => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[[]],[],[]] => 1

{{1},{2},{3,7,8},{4,6},{5}} => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[],[[[]]],[[]],[]] => 1

{{1},{2},{3,8},{4,7},{5},{6}} => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[[]],[],[]] => 1

{{1},{2},{3,8},{4,6,7},{5}} => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[],[[]],[[[]]],[]] => 1

{{1},{2},{3,4,5,6},{7,8}} => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[],[],[[[[]]]],[[]]] => 1

{{1},{2},{3,8},{4,5,6},{7}} => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[],[[]],[[[]]],[]] => 1

{{1},{2},{3,7,8},{4,5,6}} => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[],[],[[[]]],[[[]]]] => 1

{{1},{2},{3,8},{4,7},{5,6}} => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[],[],[[]],[[]],[[]]] => 1

{{1},{2},{3,4,7,8},{5,6}} => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[],[],[[[[]]]],[[]]] => 1

{{1},{2},{3,4,5,8},{6},{7}} => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[],[],[[[[]]]],[],[]] => 1

{{1},{2},{3,4,5,6,7},{8}} => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[],[],[[[[[]]]]],[]] => 1

{{1},{2},{3,8},{4,5,6,7}} => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[],[],[[]],[[[[]]]]] => 1

{{1},{2},{3,4,8},{5,6,7}} => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[],[],[[[]]],[[[]]]] => 1

{{1},{2},{3,4,5,8},{6,7}} => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[],[],[[[[]]]],[[]]] => 1

{{1},{2},{3,4,5,6,8},{7}} => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[],[],[[[[[]]]]],[]] => 1

{{1},{2},{3,4,5,6,7,8}} => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[],[],[[[[[[]]]]]]] => 1

{{1},{2,3},{4},{5},{6},{7,8}} => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[],[[]],[],[],[],[[]]] => 1

{{1},{2,3},{4},{5},{6,7},{8}} => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[],[[]],[],[],[[]],[]] => 1

{{1},{2,3},{4},{5},{6,8},{7}} => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[],[[]],[],[],[[]],[]] => 1

{{1},{2,3},{4},{5,8},{6,7}} => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[],[[]],[],[[]],[[]]] => 1

{{1},{2,3},{4},{5,6,7,8}} => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[],[[]],[],[[[[]]]]] => 1

{{1},{2,3},{4,5},{6,7},{8}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1},{2,3},{4,5},{6,8},{7}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1},{2,3},{4,5},{6,7,8}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1},{2,3},{4,6,7},{5},{8}} => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[],[[]],[[[]]],[],[]] => 1

{{1},{2,3},{4,6,8},{5},{7}} => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[],[[]],[[[]]],[],[]] => 1

{{1},{2,3},{4,6,7,8},{5}} => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 1

{{1},{2,3},{4,5,6},{7,8}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1},{2,3},{4,7},{5,6},{8}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1},{2,3},{4,8},{5,6},{7}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1},{2,3},{4,7,8},{5,6}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1},{2,3},{4,8},{5,7},{6}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1},{2,3},{4,5,8},{6},{7}} => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[],[[]],[[[]]],[],[]] => 1

{{1},{2,3},{4,8},{5,6,7}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1},{2,3},{4,5,8},{6,7}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1},{2,3},{4,5,6,8},{7}} => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 1

{{1},{2,3},{4,5,6,7,8}} => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[],[[]],[[[[[]]]]]] => 1

{{1},{2,4},{3},{5},{6},{7,8}} => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[],[[]],[],[],[],[[]]] => 1

{{1},{2,4},{3},{5},{6,8},{7}} => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[],[[]],[],[],[[]],[]] => 1

{{1},{2,4},{3},{5},{6,7,8}} => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[],[[]],[],[],[[[]]]] => 1

{{1},{2,4},{3},{5,6},{7,8}} => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[],[[]],[],[[]],[[]]] => 1

{{1},{2,4},{3},{5,7},{6},{8}} => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[[]],[],[]] => 1

{{1},{2,4},{3},{5,7,8},{6}} => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[],[[]],[],[[[]]],[]] => 1

{{1},{2,4},{3},{5,8},{6,7}} => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[],[[]],[],[[]],[[]]] => 1

{{1},{2,4},{3},{5,6,7,8}} => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[],[[]],[],[[[[]]]]] => 1

{{1},{2,5},{3},{4},{6,8},{7}} => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[],[[]],[],[],[[]],[]] => 1

{{1},{2,8},{3},{4},{5},{6},{7}} => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[],[[]],[],[],[],[],[]] => 1

{{1},{2,7,8},{3},{4},{5},{6}} => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[],[]] => 1

{{1},{2,5,8},{3},{4},{6},{7}} => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[],[]] => 1

{{1},{2,8},{3},{4},{5,6,7}} => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[],[[]],[],[],[[[]]]] => 1

{{1},{2,5,6,8},{3},{4},{7}} => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[],[[[[]]]],[],[],[]] => 1

{{1},{2,5,6,7,8},{3},{4}} => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[],[[[[[]]]]],[],[]] => 1

{{1},{2,4,5},{3},{6,7},{8}} => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[],[[[]]],[],[[]],[]] => 1

{{1},{2,4,5},{3},{6,8},{7}} => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[],[[[]]],[],[[]],[]] => 1

{{1},{2,4,5},{3},{6,7,8}} => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[],[[[]]],[],[[[]]]] => 1

{{1},{2,6},{3},{4,5},{7,8}} => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[],[[]],[],[[]],[[]]] => 1

{{1},{2,6,8},{3},{4,5},{7}} => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[],[[[]]],[],[[]],[]] => 1

{{1},{2,6,7,8},{3},{4,5}} => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[],[[[[]]]],[],[[]]] => 1

{{1},{2,4,6},{3},{5},{7,8}} => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[],[[[]]],[],[],[[]]] => 1

{{1},{2,4,6,7},{3},{5},{8}} => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[],[[[[]]]],[],[],[]] => 1

{{1},{2,8},{3},{4,6,7},{5}} => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[],[[]],[],[[[]]],[]] => 1

{{1},{2,4,8},{3},{5},{6,7}} => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[],[[[]]],[],[],[[]]] => 1

{{1},{2,4,6,8},{3},{5},{7}} => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[],[[[[]]]],[],[],[]] => 1

{{1},{2,4,6,7,8},{3},{5}} => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[],[[[[[]]]]],[],[]] => 1

{{1},{2,7,8},{3},{4,5,6}} => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[],[[[]]],[],[[[]]]] => 1

{{1},{2,4,7},{3},{5,6},{8}} => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[],[[[]]],[],[[]],[]] => 1

{{1},{2,8},{3},{4,7},{5,6}} => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[],[[]],[],[[]],[[]]] => 1

{{1},{2,4,8},{3},{5,6},{7}} => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[],[[[]]],[],[[]],[]] => 1

{{1},{2,4,7,8},{3},{5,6}} => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[],[[[[]]]],[],[[]]] => 1

{{1},{2,4,8},{3},{5,7},{6}} => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[],[[[]]],[],[[]],[]] => 1

{{1},{2,4,5,7,8},{3},{6}} => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[],[[[[[]]]]],[],[]] => 1

{{1},{2,4,8},{3},{5,6,7}} => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[],[[[]]],[],[[[]]]] => 1

{{1},{2,4,5,8},{3},{6,7}} => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[],[[[[]]]],[],[[]]] => 1

{{1},{2,4,5,6,8},{3},{7}} => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[],[[[[[]]]]],[],[]] => 1

{{1},{2,4,5,6,7,8},{3}} => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[],[[[[[[]]]]]],[]] => 1

{{1},{2,3,4},{5},{6},{7},{8}} => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[],[]] => 1

{{1},{2,3,4},{5},{6,8},{7}} => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[],[[[]]],[],[[]],[]] => 1

{{1},{2,3,4},{5},{6,7,8}} => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[],[[[]]],[],[[[]]]] => 1

{{1},{2,3,4},{5,6},{7,8}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,3,4},{5,6,7},{8}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,3,4},{5,8},{6,7}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,3,4},{5,6,8},{7}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,5},{3,4},{6,7},{8}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1},{2,5},{3,4},{6,8},{7}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1},{2,5},{3,4},{6,7,8}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1},{2,8},{3,4},{5},{6},{7}} => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[[]],[],[],[]] => 1

{{1},{2,6,7},{3,4},{5},{8}} => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[],[[[]]],[[]],[],[]] => 1

{{1},{2,6,8},{3,4},{5},{7}} => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[],[[[]]],[[]],[],[]] => 1

{{1},{2,7},{3,4},{5,6},{8}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1},{2,8},{3,4},{5,6},{7}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1},{2,7,8},{3,4},{5,6}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,8},{3,4},{5,7},{6}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1},{2,8},{3,4},{5,6,7}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1},{2,5,8},{3,4},{6,7}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,5,6,7,8},{3,4}} => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[],[[[[[]]]]],[[]]] => 1

{{1},{2,3,5},{4},{6},{7},{8}} => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[],[]] => 1

{{1},{2,3,5},{4},{6,7,8}} => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[],[[[]]],[],[[[]]]] => 1

{{1},{2,6},{3,5},{4},{7,8}} => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[[]],[],[[]]] => 1

{{1},{2,7},{3,5},{4},{6},{8}} => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[[]],[],[],[]] => 1

{{1},{2,8},{3,5},{4},{6},{7}} => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[[]],[],[],[]] => 1

{{1},{2,6,7},{3,5},{4},{8}} => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[],[[[]]],[[]],[],[]] => 1

{{1},{2,8},{3,5},{4},{6,7}} => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[[]],[],[[]]] => 1

{{1},{2,6,8},{3,5},{4},{7}} => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[],[[[]]],[[]],[],[]] => 1

{{1},{2,6,7,8},{3,5},{4}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2,3,6},{4},{5},{7},{8}} => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[],[]] => 1

{{1},{2,3,7},{4},{5},{6},{8}} => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[],[]] => 1

{{1},{2,8},{3,7},{4},{5},{6}} => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[[]],[],[],[]] => 1

{{1},{2,3,8},{4},{5},{6},{7}} => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[],[]] => 1

{{1},{2,3,7,8},{4},{5},{6}} => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[],[[[[]]]],[],[],[]] => 1

{{1},{2,3,6,7},{4},{5},{8}} => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[],[[[[]]]],[],[],[]] => 1

{{1},{2,3,6,8},{4},{5},{7}} => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[],[[[[]]]],[],[],[]] => 1

{{1},{2,3,6,7,8},{4},{5}} => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[],[[[[[]]]]],[],[]] => 1

{{1},{2,7},{3,5,6},{4},{8}} => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[],[[]],[[[]]],[],[]] => 1

{{1},{2,8},{3,5,6},{4},{7}} => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[],[[]],[[[]]],[],[]] => 1

{{1},{2,7,8},{3,5,6},{4}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,3,7},{4},{5,6},{8}} => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[],[[[]]],[],[[]],[]] => 1

{{1},{2,8},{3,7},{4},{5,6}} => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[[]],[],[[]]] => 1

{{1},{2,3,5,7},{4},{6},{8}} => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[],[[[[]]]],[],[],[]] => 1

{{1},{2,8},{3,5,7},{4},{6}} => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[],[[]],[[[]]],[],[]] => 1

{{1},{2,3,5,8},{4},{6},{7}} => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[],[[[[]]]],[],[],[]] => 1

{{1},{2,3,5,7,8},{4},{6}} => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[],[[[[[]]]]],[],[]] => 1

{{1},{2,3,5,6,7},{4},{8}} => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[],[[[[[]]]]],[],[]] => 1

{{1},{2,8},{3,5,6,7},{4}} => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 1

{{1},{2,3,8},{4},{5,6,7}} => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[],[[[]]],[],[[[]]]] => 1

{{1},{2,3,5,8},{4},{6,7}} => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[],[[[[]]]],[],[[]]] => 1

{{1},{2,3,5,6,8},{4},{7}} => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[],[[[[[]]]]],[],[]] => 1

{{1},{2,3,5,6,7,8},{4}} => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[],[[[[[[]]]]]],[]] => 1

{{1},{2,8},{3,4,5},{6},{7}} => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[],[[]],[[[]]],[],[]] => 1

{{1},{2,8},{3,4,5},{6,7}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1},{2,6,8},{3,4,5},{7}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,6,7,8},{3,4,5}} => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[],[[[[]]]],[[[]]]] => 1

{{1},{2,3,6},{4,5},{7,8}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,7},{3,6},{4,5},{8}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1},{2,8},{3,6},{4,5},{7}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1},{2,7,8},{3,6},{4,5}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,8},{3,7},{4,5},{6}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1},{2,3,8},{4,5},{6},{7}} => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[],[[[]]],[[]],[],[]] => 1

{{1},{2,3,6,7},{4,5},{8}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2,8},{3,6,7},{4,5}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1},{2,3,8},{4,5},{6,7}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,3,6,8},{4,5},{7}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2,3,4,6},{5},{7,8}} => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[],[[[[]]]],[],[[]]] => 1

{{1},{2,8},{3,4,6},{5},{7}} => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[],[[]],[[[]]],[],[]] => 1

{{1},{2,7,8},{3,4,6},{5}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,8},{3,7},{4,6},{5}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1},{2,3,8},{4,6},{5},{7}} => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[],[[[]]],[[]],[],[]] => 1

{{1},{2,3,7,8},{4,6},{5}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2,8},{3,4,7},{5},{6}} => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[],[[]],[[[]]],[],[]] => 1

{{1},{2,3,4,8},{5},{6},{7}} => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[],[[[[]]]],[],[],[]] => 1

{{1},{2,3,4,7,8},{5},{6}} => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[],[[[[[]]]]],[],[]] => 1

{{1},{2,8},{3,4,6,7},{5}} => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 1

{{1},{2,3,8},{4,6,7},{5}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,3,4,6,8},{5},{7}} => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[],[[[[[]]]]],[],[]] => 1

{{1},{2,3,4,6,7,8},{5}} => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[],[[[[[[]]]]]],[]] => 1

{{1},{2,3,4,5,6},{7},{8}} => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[],[[[[[]]]]],[],[]] => 1

{{1},{2,3,4,5,6},{7,8}} => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[],[[[[[]]]]],[[]]] => 1

{{1},{2,8},{3,4,5,6},{7}} => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 1

{{1},{2,8},{3,7},{4,5,6}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1},{2,3,8},{4,5,6},{7}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,8},{3,4,7},{5,6}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1},{2,3,8},{4,7},{5,6}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,3,4,8},{5,6},{7}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2,3,4,5,7},{6},{8}} => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[],[[[[[]]]]],[],[]] => 1

{{1},{2,8},{3,4,5,7},{6}} => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 1

{{1},{2,3,8},{4,5,7},{6}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,3,4,8},{5,7},{6}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2,3,4,5,8},{6},{7}} => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[],[[[[[]]]]],[],[]] => 1

{{1},{2,3,4,5,7,8},{6}} => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[],[[[[[[]]]]]],[]] => 1

{{1},{2,3,4,5,6,7},{8}} => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[],[[[[[[]]]]]],[]] => 1

{{1},{2,8},{3,4,5,6,7}} => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[],[[]],[[[[[]]]]]] => 1

{{1},{2,3,4,8},{5,6,7}} => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[],[[[[]]]],[[[]]]] => 1

{{1},{2,3,4,5,8},{6,7}} => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[],[[[[[]]]]],[[]]] => 1

{{1},{2,3,4,5,6,8},{7}} => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[],[[[[[[]]]]]],[]] => 1

{{1},{2,3,4,5,6,7,8}} => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[],[[[[[[[]]]]]]]] => 1

{{1,2},{3},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[],[]] => 1

{{1,2},{3},{4},{5},{6},{7,8}} => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[],[],[[]]] => 1

{{1,2},{3},{4},{5},{6,7},{8}} => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[],[[]],[]] => 1

{{1,2},{3},{4},{5},{6,8},{7}} => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[],[[]],[]] => 1

{{1,2},{3},{4},{5},{6,7,8}} => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[]],[],[],[],[[[]]]] => 1

{{1,2},{3},{4},{5,6},{7},{8}} => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[],[[]],[],[]] => 1

{{1,2},{3},{4},{5,8},{6},{7}} => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[],[[]],[],[]] => 1

{{1,2},{3},{4},{5,8},{6,7}} => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[],[[]],[[]]] => 1

{{1,2},{3},{4},{5,6,7,8}} => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[]],[],[],[[[[]]]]] => 1

{{1,2},{3},{4,5},{6},{7},{8}} => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[],[[]],[],[],[]] => 1

{{1,2},{3},{4,5},{6,7,8}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,2},{3},{4,8},{5},{6},{7}} => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[],[[]],[],[],[]] => 1

{{1,2},{3},{4,6,7,8},{5}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1,2},{3},{4,5,6},{7,8}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,2},{3},{4,5,8},{6},{7}} => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[],[[[]]],[],[]] => 1

{{1,2},{3},{4,5,8},{6,7}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,2},{3},{4,5,6,8},{7}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1,2},{3},{4,5,6,7,8}} => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[]],[],[[[[[]]]]]] => 1

{{1,2},{3,4},{5},{6},{7},{8}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,2},{3,4},{5},{6,7,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,2},{3,4},{5,7,8},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,2},{3,4},{5,6,8},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,2},{3,4},{5,6,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1,2},{3,5},{4},{6},{7},{8}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,2},{3,5},{4},{6,7,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,2},{3,6},{4},{5},{7},{8}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,2},{3,8},{4},{5},{6},{7}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,2},{3,6,7,8},{4},{5}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,2},{3,5,6},{4},{7,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,2},{3,7,8},{4},{5,6}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,2},{3,5,7,8},{4},{6}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,2},{3,8},{4},{5,6,7}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,2},{3,5,8},{4},{6,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,2},{3,5,6,8},{4},{7}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,2},{3,5,6,7,8},{4}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1,2},{3,4,5},{6},{7},{8}} => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]] => 1

{{1,2},{3,8},{4,5},{6},{7}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,2},{3,7,8},{4,5},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,2},{3,6,8},{4,5},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,2},{3,6,7,8},{4,5}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,2},{3,4,6},{5},{7,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,2},{3,7,8},{4,6},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,2},{3,4,8},{5},{6},{7}} => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]] => 1

{{1,2},{3,4,7,8},{5},{6}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,2},{3,8},{4,6,7},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,2},{3,4,8},{5},{6,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,2},{3,4,6,8},{5},{7}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,2},{3,4,6,7,8},{5}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1,2},{3,4,5,6},{7,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,2},{3,8},{4,5,6},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,2},{3,4,8},{5,6},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,2},{3,4,5,7},{6},{8}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,2},{3,8},{4,5,7},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,2},{3,4,8},{5,7},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,2},{3,4,5,8},{6},{7}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,2},{3,4,5,7,8},{6}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1,2},{3,4,5,6,7},{8}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1,2},{3,8},{4,5,6,7}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1,2},{3,4,8},{5,6,7}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1,2},{3,4,5,8},{6,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,2},{3,4,5,6,8},{7}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1,2},{3,4,5,6,7,8}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[]],[[[[[[]]]]]]] => 2

{{1,3},{2},{4},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[],[]] => 1

{{1,3},{2},{4},{5},{6},{7,8}} => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[],[],[[]]] => 1

{{1,3},{2},{4},{5},{6,8},{7}} => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[],[[]],[]] => 1

{{1,3},{2},{4},{5},{6,7,8}} => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[]],[],[],[],[[[]]]] => 1

{{1,3},{2},{4},{5,7,8},{6}} => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[],[[[]]],[]] => 1

{{1,3},{2},{4},{5,8},{6,7}} => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[],[[]],[[]]] => 1

{{1,3},{2},{4},{5,6,7,8}} => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[]],[],[],[[[[]]]]] => 1

{{1,3},{2},{4,5},{6,7},{8}} => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[],[[]],[[]],[]] => 1

{{1,3},{2},{4,5},{6,8},{7}} => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[],[[]],[[]],[]] => 1

{{1,3},{2},{4,5},{6,7,8}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,3},{2},{4,6},{5},{7,8}} => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]],[],[[]]] => 1

{{1,3},{2},{4,6,7},{5},{8}} => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[],[[[]]],[],[]] => 1

{{1,3},{2},{4,8},{5},{6,7}} => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]],[],[[]]] => 1

{{1,3},{2},{4,6,8},{5},{7}} => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[],[[[]]],[],[]] => 1

{{1,3},{2},{4,6,7,8},{5}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1,3},{2},{4,5,6},{7,8}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,3},{2},{4,7},{5,6},{8}} => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[],[[]],[[]],[]] => 1

{{1,3},{2},{4,8},{5,6},{7}} => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[],[[]],[[]],[]] => 1

{{1,3},{2},{4,7,8},{5,6}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,3},{2},{4,8},{5,7},{6}} => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[],[[]],[[]],[]] => 1

{{1,3},{2},{4,5,7,8},{6}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1,3},{2},{4,8},{5,6,7}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,3},{2},{4,5,8},{6,7}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,3},{2},{4,5,6,8},{7}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1,3},{2},{4,5,6,7,8}} => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[]],[],[[[[[]]]]]] => 1

{{1,4},{2},{3},{5},{6},{7},{8}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[],[]] => 1

{{1,4},{2},{3},{5},{6,8},{7}} => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[],[[]],[]] => 1

{{1,4},{2},{3},{5},{6,7,8}} => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[]],[],[],[],[[[]]]] => 1

{{1,4},{2},{3},{5,6},{7,8}} => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[],[[]],[[]]] => 1

{{1,4},{2},{3},{5,8},{6},{7}} => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[],[[]],[],[]] => 1

{{1,4},{2},{3},{5,8},{6,7}} => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[],[[]],[[]]] => 1

{{1,4},{2},{3},{5,6,7,8}} => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[]],[],[],[[[[]]]]] => 1

{{1,5},{2},{3},{4},{6},{7},{8}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[],[]] => 1

{{1,5},{2},{3},{4},{6},{7,8}} => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[],[],[[]]] => 1

{{1,5},{2},{3},{4},{6,7,8}} => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[]],[],[],[],[[[]]]] => 1

{{1,6},{2},{3},{4},{5},{7},{8}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[],[]] => 1

{{1,6},{2},{3},{4},{5},{7,8}} => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[],[],[[]]] => 1

{{1,7},{2},{3},{4},{5},{6},{8}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[],[]] => 1

{{1,8},{2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[],[]] => 1

{{1,7,8},{2},{3},{4},{5},{6}} => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => 1

{{1,6,7},{2},{3},{4},{5},{8}} => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => 1

{{1,8},{2},{3},{4},{5},{6,7}} => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[],[],[[]]] => 1

{{1,6,8},{2},{3},{4},{5},{7}} => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => 1

{{1,5,6},{2},{3},{4},{7},{8}} => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => 1

{{1,7},{2},{3},{4},{5,6},{8}} => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[],[[]],[]] => 1

{{1,8},{2},{3},{4},{5,6},{7}} => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[],[[]],[]] => 1

{{1,5,7},{2},{3},{4},{6},{8}} => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => 1

{{1,8},{2},{3},{4},{5,7},{6}} => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[],[[]],[]] => 1

{{1,5,8},{2},{3},{4},{6},{7}} => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => 1

{{1,8},{2},{3},{4},{5,6,7}} => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[]],[],[],[],[[[]]]] => 1

{{1,4,5},{2},{3},{6},{7},{8}} => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => 1

{{1,4,5},{2},{3},{6,8},{7}} => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[],[[]],[]] => 1

{{1,4,5},{2},{3},{6,7,8}} => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[],[[[]]]] => 1

{{1,6},{2},{3},{4,5},{7},{8}} => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[],[[]],[],[]] => 1

{{1,8},{2},{3},{4,5},{6},{7}} => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[],[[]],[],[]] => 1

{{1,6,7},{2},{3},{4,5},{8}} => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[],[[]],[]] => 1

{{1,4,6},{2},{3},{5},{7},{8}} => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => 1

{{1,7},{2},{3},{4,6},{5},{8}} => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[],[[]],[],[]] => 1

{{1,7},{2},{3},{4,5,6},{8}} => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[],[[[]]],[]] => 1

{{1,4,8},{2},{3},{5,6},{7}} => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[],[[]],[]] => 1

{{1,4,8},{2},{3},{5,6,7}} => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[],[[[]]]] => 1

{{1,3,4},{2},{5},{6},{7},{8}} => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => 1

{{1,3,4},{2},{5},{6},{7,8}} => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[]]],[],[],[],[[]]] => 1

{{1,3,4},{2},{5},{6,8},{7}} => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[],[[]],[]] => 1

{{1,3,4},{2},{5},{6,7,8}} => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[],[[[]]]] => 1

{{1,3,4},{2},{5,6},{7,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,3,4},{2},{5,8},{6,7}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,5},{2},{3,4},{6},{7},{8}} => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[],[[]],[],[],[]] => 1

{{1,5},{2},{3,4},{6},{7,8}} => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]],[],[[]]] => 1

{{1,5},{2},{3,4},{6,8},{7}} => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[],[[]],[[]],[]] => 1

{{1,5},{2},{3,4},{6,7,8}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,8},{2},{3,4},{5},{6},{7}} => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[],[[]],[],[],[]] => 1

{{1,5,6},{2},{3,4},{7,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,7,8},{2},{3,4},{5,6}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,5,7},{2},{3,4},{6},{8}} => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[]]],[],[[]],[],[]] => 1

{{1,8},{2},{3,4},{5,6,7}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,5,8},{2},{3,4},{6,7}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,3,5},{2},{4},{6},{7},{8}} => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => 1

{{1,3,5},{2},{4},{6},{7,8}} => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[]]],[],[],[],[[]]] => 1

{{1,3,5},{2},{4},{6,7},{8}} => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[],[[]],[]] => 1

{{1,3,5},{2},{4},{6,8},{7}} => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[],[[]],[]] => 1

{{1,3,5},{2},{4},{6,7,8}} => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[],[[[]]]] => 1

{{1,6},{2},{3,5},{4},{7},{8}} => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[],[[]],[],[],[]] => 1

{{1,6},{2},{3,5},{4},{7,8}} => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]],[],[[]]] => 1

{{1,8},{2},{3,5},{4},{6},{7}} => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[],[[]],[],[],[]] => 1

{{1,6,8},{2},{3,5},{4},{7}} => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[]]],[],[[]],[],[]] => 1

{{1,3,6},{2},{4},{5},{7},{8}} => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => 1

{{1,3,7},{2},{4},{5},{6},{8}} => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => 1

{{1,3,8},{2},{4},{5},{6},{7}} => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => 1

{{1,7},{2},{3,5,6},{4},{8}} => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[],[[[]]],[],[]] => 1

{{1,3,7},{2},{4},{5,6},{8}} => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[],[[]],[]] => 1

{{1,3,8},{2},{4},{5,6,7}} => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[],[[[]]]] => 1

{{1,6},{2},{3,4,5},{7},{8}} => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[],[[[]]],[],[]] => 1

{{1,6},{2},{3,4,5},{7,8}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,8},{2},{3,4,5},{6},{7}} => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[],[[[]]],[],[]] => 1

{{1,8},{2},{3,4,5},{6,7}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,3,6},{2},{4,5},{7,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,7},{2},{3,6},{4,5},{8}} => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[],[[]],[[]],[]] => 1

{{1,7,8},{2},{3,6},{4,5}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,3,7},{2},{4,5},{6},{8}} => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[]]],[],[[]],[],[]] => 1

{{1,8},{2},{3,6,7},{4,5}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,3,8},{2},{4,5},{6,7}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,3,7},{2},{4,6},{5},{8}} => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[]]],[],[[]],[],[]] => 1

{{1,8},{2},{3,4,6,7},{5}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1,8},{2},{3,4,5,6},{7}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1,8},{2},{3,4,7},{5,6}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,3,8},{2},{4,7},{5,6}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,8},{2},{3,4,5,7},{6}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1,8},{2},{3,4,5,6,7}} => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[]],[],[[[[[]]]]]] => 1

{{1,3,4,5,6,7,8},{2}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[[]]]]]]],[]] => 1

{{1,2,3},{4},{5},{6},{7},{8}} => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => 1

{{1,2,3},{4},{5},{6},{7,8}} => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[]]],[],[],[],[[]]] => 1

{{1,2,3},{4},{5},{6,8},{7}} => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[],[[]],[]] => 1

{{1,2,3},{4},{5},{6,7,8}} => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[],[[[]]]] => 1

{{1,2,3},{4},{5,6},{7,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,2,3},{4},{5,8},{6,7}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,4},{2,3},{5},{6},{7},{8}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,4},{2,3},{5},{6},{7,8}} => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[[]],[],[],[[]]] => 1

{{1,4},{2,3},{5},{6,7},{8}} => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[[]],[],[[]],[]] => 1

{{1,4},{2,3},{5},{6,8},{7}} => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[[]],[],[[]],[]] => 1

{{1,4},{2,3},{5},{6,7,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,4},{2,3},{5,6},{7},{8}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,4},{2,3},{5,7},{6},{8}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,4},{2,3},{5,8},{6},{7}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,4},{2,3},{5,7,8},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,4},{2,3},{5,6,7},{8}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,4},{2,3},{5,6,8},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,4},{2,3},{5,6,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1,5},{2,3},{4},{6},{7},{8}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,5},{2,3},{4},{6,7},{8}} => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[[]],[],[[]],[]] => 1

{{1,5},{2,3},{4},{6,8},{7}} => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[[]],[],[[]],[]] => 1

{{1,6},{2,3},{4},{5},{7},{8}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,6},{2,3},{4},{5},{7,8}} => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[[]],[],[],[[]]] => 1

{{1,7},{2,3},{4},{5},{6},{8}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,8},{2,3},{4},{5},{6},{7}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,7},{2,3},{4},{5,6},{8}} => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[[]],[],[[]],[]] => 1

{{1,8},{2,3},{4},{5,6,7}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,7},{2,3},{4,5},{6},{8}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,8},{2,3},{4,5},{6},{7}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,7},{2,3},{4,6},{5},{8}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,8},{2,3},{4,6,7},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,7},{2,3},{4,5,6},{8}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,8},{2,3},{4,5,7},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,2,4},{3},{5},{6},{7},{8}} => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => 1

{{1,2,4},{3},{5,6},{7,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,2,4},{3},{5,8},{6,7}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,5},{2,4},{3},{6},{7},{8}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,5},{2,4},{3},{6},{7,8}} => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[[]],[],[],[[]]] => 1

{{1,5},{2,4},{3},{6,7},{8}} => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[[]],[],[[]],[]] => 1

{{1,5},{2,4},{3},{6,8},{7}} => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[[]],[],[[]],[]] => 1

{{1,5},{2,4},{3},{6,7,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,7},{2,4},{3},{5},{6},{8}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,8},{2,4},{3},{5},{6},{7}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,8},{2,4},{3},{5},{6,7}} => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[[]],[],[],[[]]] => 1

{{1,7},{2,4},{3},{5,6},{8}} => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[[]],[],[[]],[]] => 1

{{1,8},{2,4},{3},{5,7},{6}} => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[[]],[],[[]],[]] => 1

{{1,8},{2,4},{3},{5,6,7}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,2,5},{3},{4},{6},{7},{8}} => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => 1

{{1,2,5},{3},{4},{6},{7,8}} => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[]]],[],[],[],[[]]] => 1

{{1,6},{2,5},{3},{4},{7},{8}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,6},{2,5},{3},{4},{7,8}} => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[[]],[],[],[[]]] => 1

{{1,7},{2,5},{3},{4},{6},{8}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,8},{2,5},{3},{4},{6},{7}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,2,6},{3},{4},{5},{7},{8}} => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => 1

{{1,2,6},{3},{4},{5},{7,8}} => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[]]],[],[],[],[[]]] => 1

{{1,2,7},{3},{4},{5},{6},{8}} => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => 1

{{1,8},{2,7},{3},{4},{5},{6}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,2,8},{3},{4},{5},{6},{7}} => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => 1

{{1,8},{2,5,7},{3},{4},{6}} => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]] => 1

{{1,8},{2,5,6,7},{3},{4}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,6},{2,4,5},{3},{7,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,7},{2,4,5},{3},{6},{8}} => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]] => 1

{{1,8},{2,4,5},{3},{6,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,2,6},{3},{4,5},{7,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,7},{2,6},{3},{4,5},{8}} => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[[]],[],[[]],[]] => 1

{{1,8},{2,6,7},{3},{4,5}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,2,8},{3},{4,5},{6,7}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,7},{2,4,6},{3},{5},{8}} => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]] => 1

{{1,8},{2,4,7},{3},{5},{6}} => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]] => 1

{{1,8},{2,4,6,7},{3},{5}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,7},{2,4,5,6},{3},{8}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,8},{2,4,5,6},{3},{7}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,8},{2,7},{3},{4,5,6}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,8},{2,4,7},{3},{5,6}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,2,8},{3},{4,7},{5,6}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,8},{2,4,5,7},{3},{6}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,8},{2,4,5,6,7},{3}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1,2,4,5,6,7,8},{3}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[[]]]]]]],[]] => 1

{{1,5},{2,3,4},{6},{7},{8}} => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]] => 1

{{1,5},{2,3,4},{6,8},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,5},{2,3,4},{6,7,8}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1,6},{2,3,4},{5},{7},{8}} => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]] => 1

{{1,6},{2,3,4},{5},{7,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,7},{2,3,4},{5},{6},{8}} => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]] => 1

{{1,8},{2,3,4},{5},{6},{7}} => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]] => 1

{{1,8},{2,3,4},{5},{6,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,7},{2,3,4},{5,6},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,8},{2,3,4},{5,6},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,8},{2,3,4},{5,7},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,7},{2,5},{3,4},{6},{8}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,7},{2,6},{3,4},{5},{8}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,8},{2,6},{3,4},{5},{7}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,8},{2,7},{3,4},{5},{6}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,8},{2,6,7},{3,4},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,8},{2,5,6},{3,4},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,8},{2,5,7},{3,4},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,6},{2,3,5},{4},{7,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,8},{2,3,5},{4},{6},{7}} => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]] => 1

{{1,8},{2,3,5},{4},{6,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,7},{2,6},{3,5},{4},{8}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,8},{2,6,7},{3,5},{4}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,8},{2,3,6},{4},{5},{7}} => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]] => 1

{{1,8},{2,3,7},{4},{5},{6}} => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]] => 1

{{1,8},{2,3,6,7},{4},{5}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,7},{2,3,5,6},{4},{8}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,8},{2,3,5,6},{4},{7}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,8},{2,7},{3,5,6},{4}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,8},{2,3,7},{4},{5,6}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,8},{2,3,5,7},{4},{6}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,8},{2,3,5,6,7},{4}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1,2,3,5,6,7,8},{4}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[[]]]]]]],[]] => 1

{{1,6},{2,3,4,5},{7},{8}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,7},{2,3,4,5},{6},{8}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,7},{2,6},{3,4,5},{8}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,8},{2,6},{3,4,5},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,8},{2,7},{3,4,5},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,8},{2,3,6},{4,5},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,8},{2,3,7},{4,5},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,8},{2,3,6,7},{4,5}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,8},{2,3,4,6},{5},{7}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,8},{2,7},{3,4,6},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,8},{2,3,7},{4,6},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,8},{2,3,4,7},{5},{6}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,8},{2,3,4,6,7},{5}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1,2,3,4,6,7,8},{5}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[[]]]]]]],[]] => 1

{{1,7},{2,3,4,5,6},{8}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1,8},{2,3,4,5,6},{7}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1,8},{2,3,7},{4,5,6}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1,8},{2,3,4,7},{5,6}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,8},{2,3,4,5,7},{6}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1,2,3,4,5,7,8},{6}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[[]]]]]]],[]] => 1

{{1,2,3,4,5,6,7},{8}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[[]]]]]]],[]] => 1

{{1,8},{2,3,4,5,6,7}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[]],[[[[[[]]]]]]] => 2

{{1,2,3,4,5,6,8},{7}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[[]]]]]]],[]] => 1

{{1,5},{2,6},{3,7},{4},{8}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,3},{2,6},{4,7},{5},{8}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,3},{2,5},{4,7},{6},{8}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,4},{2,5},{3,6},{7},{8}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,3},{2,5},{4,6},{7},{8}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,7},{2,8},{3},{4},{5},{6}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,6},{2,8},{3},{4},{5},{7}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,4},{2,8},{3},{5},{6},{7}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,3},{2,8},{4},{5},{6},{7}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,5},{2,6},{3},{4},{7},{8}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,4},{2,5},{3},{6},{7},{8}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,3},{2,4},{5},{6},{7},{8}} => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 1

{{1,5},{2,4,8},{3},{6,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1},{2,3,5,8},{4,6},{7}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1,4},{2,5,8},{3},{6,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,4},{2},{3,6,7},{5,8}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,4},{2},{3,6},{5,7,8}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,4},{2},{3,7},{5,6,8}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,4},{2},{3,5,8},{6,7}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,5},{2},{3,4,8},{6,7}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1},{2,3,5,7},{4},{6,8}} => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[],[[[[]]]],[],[[]]] => 1

{{1,5,7},{2},{3,4},{6,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,4,7},{2},{3,5},{6,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,4},{2},{3,8},{5,6,7}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,4,6},{2},{3,8},{5,7}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,4,6},{2},{3,7},{5,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1},{2,6},{3,4,7},{5,8}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1,6},{2,3,7},{4},{5,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,2},{3,6,7},{4,8},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,2},{3,6},{4,7,8},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,6},{2,3},{4},{5,7,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1},{2,6},{3,4},{5,7,8}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1},{2,7},{3,4},{5,6,8}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1,7},{2,3},{4},{5,6,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,2},{3,7},{4,6,8},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,2},{3,5,8},{4,7},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,7},{2,3,8},{4,5},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1},{2,5},{3,4,8},{6,7}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1},{2,4},{3,5,8},{6,7}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1},{2,4},{3,7},{5,6,8}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1},{2,4},{3,6},{5,7,8}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1},{2,4},{3,6,7},{5,8}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1,3},{2,6,7},{4},{5,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,3},{2,6},{4},{5,7,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,3},{2,7},{4},{5,6,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,3},{2,7,8},{4,5},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,3},{2,8},{4},{5,6,7}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1},{2,4,6},{3,7},{5,8}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,4,6},{3,8},{5,7}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,4},{3,8},{5,6,7}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1},{2,4,7},{3,5},{6,8}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,5,7},{3,4},{6,8}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,8},{3,4,6},{5,7}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1,8},{2,3,6},{4},{5,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,7},{2,3,6},{4},{5,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1},{2,7},{3,4,6},{5,8}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1,2},{3,6,8},{4,7},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,2},{3,5,7},{4,8},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,2},{3,7},{4,5,8},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,7},{2,3},{4,5,8},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,7},{2,3,8},{4,6},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,7},{2,3,8},{4},{5,6}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,7},{2,4,6,8},{3},{5}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,7},{2,4,5},{3,8},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,8},{2,5,7},{3,6},{4}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,8},{2,4,6},{3,7},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,5},{2,3,8},{4},{6,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,8},{2,6},{3,4,7},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,6},{2,3,8},{4,7},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,6},{2,3,7,8},{4},{5}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,5},{2,3,7},{4,8},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,5},{2,3,6},{4},{7,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,7},{2,5},{3,4,8},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,7},{2,6,8},{3,4},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,5},{2,4,8},{3,7},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,5},{2,4,7},{3,8},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,5},{2,4,8},{3,6},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,6},{2,4,8},{3,5},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,6},{2,5},{3,4,8},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,6},{2,3,5},{4,8},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,5},{2,3,6},{4,8},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,5},{2,6},{3,4,8},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,5},{2,8},{3,4,7},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,5},{2,3,8},{4,7},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,5},{2,7},{3,4,8},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,7},{2,6},{3,4,8},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,7},{2,3,6},{4,8},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,8},{2,3,6},{4,7},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,8},{2,3,5},{4,7},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,8},{2,5},{3,4,7},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,8},{2,4,7},{3,5},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,8},{2,4,7},{3,6},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,7},{2,4,8},{3,6},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,6},{2,4,8},{3,7},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,6},{2,4,7},{3,8},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,7},{2,4,6},{3,8},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,7},{2,4,8},{3,5},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,7},{2,3,5},{4,8},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,7},{2,8},{3,4,6},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,6},{2,8},{3,4,7},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,6},{2,3,7},{4,8},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,6},{2,7},{3,4,8},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,3},{2,4,6,8},{5},{7}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1},{2,4,6,8},{3},{5,7}} => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[],[[[[]]]],[],[[]]] => 1

{{1,3},{2},{4,6,8},{5,7}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,3,6},{2},{4,8},{5,7}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,3,6},{2},{4,7},{5,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,3,5},{2},{4,7},{6,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,3,7},{2},{4,6},{5,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,3},{2,4,8},{5,7},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1},{2,4,8},{3,5,7},{6}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1,4},{2,8},{3,5,7},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,4},{2,5,7},{3,8},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,3},{2,5,7},{4,8},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,3},{2,7},{4,6,8},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,7},{2,4,6},{3},{5,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1},{2,8},{3,5,7},{4,6}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1,7},{2,4,6},{3,5},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1},{2,5,8},{3,7},{4,6}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,5,8},{3,6},{4,7}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,4,8},{3,6},{5,7}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,4,6,8},{3,5},{7}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1,4},{2,6,8},{3,5},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,4},{2,5},{3,6,8},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,3},{2,5},{4,6,8},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,5},{2,4,6,8},{3},{7}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,5},{2,4},{3,6,8},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1},{2,6,8},{3,5,7},{4}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1,6},{2,8},{3,5,7},{4}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,6},{2,4,8},{3},{5,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,6},{2,4,7},{3},{5,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,5},{2,4,7},{3},{6,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1},{2,6,8},{3,5},{4,7}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,4,6,8},{3,7},{5}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1,6},{2,7},{3,5,8},{4}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,7},{2,6,8},{3,5},{4}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,7},{2,6},{3,5,8},{4}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,2},{3,4,6},{5,8},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,2},{3,6},{4,5,8},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,2},{3,5,6},{4,8},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,6},{2,3},{4,5,8},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,5},{2,8},{3,4,6},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,5},{2,3,8},{4,6},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,6},{2,3,5,8},{4},{7}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,4},{2,3,8},{5},{6,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,4},{2,3,8},{5,7},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,4},{2,3,6},{5},{7,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,4},{2,3,6,8},{5},{7}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,4},{2,3,6},{5,8},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,8},{2,4,5},{3,7},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,6},{2,5,8},{3,4},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,6},{2,4,5},{3,8},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,5},{2,4},{3,7,8},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,4},{2,8},{3,5,6},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,4},{2,7,8},{3,5},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,5},{2,3,7},{4},{6,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,4},{2,7},{3},{5,6,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,4},{2,6,7},{3},{5,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,4},{2,6},{3},{5,7,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,6},{2,5,7,8},{3},{4}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,7},{2,5,6,8},{3},{4}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,7},{2,6,8},{3},{4,5}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,7},{2,3,6,8},{4},{5}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,8},{2,6},{3},{4,5,7}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,8},{2,5,6},{3},{4,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,8},{2,5},{3},{4,6,7}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,8},{2,4},{3,6,7},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,4},{2,3,7},{5,8},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,3},{2,7},{4,5,8},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,3},{2,6,7},{4,8},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,3},{2,6},{4,7,8},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,6},{2,4,7,8},{3},{5}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,7},{2,4,8},{3},{5,6}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,7},{2,4,5,8},{3},{6}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,7},{2,5,8},{3,4},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,7},{2,3,5,8},{4},{6}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,2,7},{3},{4,6},{5,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,7},{2},{3,4,6},{5,8}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,7},{2},{3,6},{4,5,8}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,7},{2},{3,5,6},{4,8}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,6,7},{2},{3,5},{4,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,6},{2},{3,5},{4,7,8}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,5},{2},{3,7,8},{4,6}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,5},{2},{3,8},{4,6,7}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,5,6},{2},{3,8},{4,7}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,6},{2},{3,8},{4,5,7}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,6},{2},{3,4,8},{5,7}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,2,6},{3},{4,8},{5,7}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,6,8},{2},{3,7},{4,5}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,2,3,4,5,6,7,8},{9}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[]]]]]]]],[]] => 1

{{1},{2,3,4,5,6,7,8,9}} => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[],[[[[[[[[]]]]]]]]] => 1

{{1,2,3,4,5,6,7,8,9},{10}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[]]]]]]]]],[]] => 1

{{1},{2,3,4,5,6,7,8,9,10}} => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[],[[[[[[[[[]]]]]]]]]] => 1

{{1,2,3,4,5,6,7,8,9,10},{11}} => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[[]]]]]]]]]],[]] => 1

{{1},{2,3,4,5,6,7,8,9,10,11}} => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[],[[[[[[[[[[]]]]]]]]]]] => 1

{{1,4,8},{2},{3,6},{5,7}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,3,8},{2},{4,6},{5,7}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,4,8},{2},{3,7},{5,6}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,5,8},{2},{3,7},{4,6}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,5,8},{2},{3,6},{4,7}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,3},{2,5,8},{4,7},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,5},{2,4,7,8},{3},{6}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,3},{2,4,6,7},{5},{8}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,3},{2,4,8},{5,6},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,3},{2,5,8},{4,6},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,6},{2,3,4},{5,8},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,6},{2,4},{3,5,8},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,4},{2,6},{3,5,8},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,4},{2,5,6},{3,7},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,4},{2,6,7},{3,8},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,4},{2,3,6},{5,7},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,4},{2,3,7},{5},{6,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,2,7},{3},{4,5},{6,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,2,6},{3},{4},{5,7,8}} => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[],[[[]]]] => 1

{{1,7},{2,3,4},{5},{6,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,7},{2,4},{3,6,8},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,4},{2,7},{3,6,8},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,4},{2,6},{3,5,7},{8}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,6},{2,4},{3,5,7},{8}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,6},{2,3,4},{5,7},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,3},{2,5,7},{4,6},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,3},{2,4,7},{5,6},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,5},{2,7,8},{3},{4,6}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,7},{2,4},{3,5,6},{8}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,6},{2,5},{3,7,8},{4}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,5},{2,6},{3,7,8},{4}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,4},{2,8},{3,6,7},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,4},{2,7},{3,5,6},{8}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,3},{2,4,5,6},{7,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,4},{2,3,5,6},{7,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,4},{2,3,5,7},{6,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,3},{2,4,5,7},{6,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,2},{3,4,5,7},{6,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,3},{2,4,5,6,7,8}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[]],[[[[[[]]]]]]] => 2

{{1,4},{2,3,5,6,7,8}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[]],[[[[[[]]]]]]] => 2

{{1,5},{2,3,4,6,7,8}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[]],[[[[[[]]]]]]] => 2

{{1,2},{3,4,6,7},{5,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,3},{2,4,6,7},{5,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,4},{2,3,6,7},{5,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,5},{2,3,6,7},{4,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,3},{2,4},{5,6,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1,4},{2,5},{3,6,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1,3},{2,5},{4,6,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1,2},{3,5},{4,6,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1,2},{3,6},{4,5,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1,3},{2,6},{4,5,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1,4},{2,6},{3,5,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1,5},{2,6},{3,4,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1,2},{3,5,6,8},{4,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,3},{2,5,6,8},{4,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,4},{2,5,6,8},{3,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,5},{2,4,6,8},{3,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,4},{2},{3,5,6},{7,8}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,4,5},{2},{3,6},{7,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,5},{2},{3,4,6},{7,8}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,6},{2},{3,4,7,8},{5}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1,5},{2},{3,4,7,8},{6}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1,4,5},{2},{3,8},{6,7}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,7},{2},{3,4,8},{5,6}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,3,6},{2},{4},{5,7,8}} => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[],[[[]]]] => 1

{{1,2},{3,6},{4},{5,7,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,4},{2},{3,5,7,8},{6}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1,6},{2,4},{3},{5,7,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,7},{2,4},{3},{5,6,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,2},{3,6,7},{4},{5,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,3,7},{2},{4},{5,6,8}} => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[],[[[]]]] => 1

{{1,2},{3,7},{4},{5,6,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,4,7},{2},{3,8},{5,6}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,7},{2,4,5},{3},{6,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,8},{2,4,5},{3,6},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,8},{2,4},{3,5,6},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,8},{2,5},{3,4,6},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,4},{2},{3,6,8},{5,7}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,4,6},{2},{3},{5,7,8}} => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[],[[[]]]] => 1

{{1},{2,5,6},{3,7},{4,8}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,5,6},{3},{4,7,8}} => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[],[[[]]],[],[[[]]]] => 1

{{1},{2,5},{3,7},{4,6,8}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1},{2},{3,6,7},{4,5,8}} => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[],[],[[[]]],[[[]]]] => 1

{{1},{2,3,6,7},{4},{5,8}} => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[],[[[[]]]],[],[[]]] => 1

{{1},{2,3,6},{4,8},{5,7}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2},{3,4,6,8},{5,7}} => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[],[],[[[[]]]],[[]]] => 1

{{1},{2},{3,6},{4,5,7,8}} => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[],[],[[]],[[[[]]]]] => 1

{{1},{2,5},{3},{4,6,7,8}} => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[],[[]],[],[[[[]]]]] => 1

{{1},{2,5},{3,6},{4,7,8}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1},{2,5},{3,6,7},{4,8}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1},{2},{3,5,6,7},{4,8}} => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[],[],[[[[]]]],[[]]] => 1

{{1},{2},{3,5,6},{4,7,8}} => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[],[],[[[]]],[[[]]]] => 1

{{1},{2},{3,5},{4,6,7,8}} => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[],[],[[]],[[[[]]]]] => 1

{{1},{2,4,8},{3,5},{6,7}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,4},{3,6,8},{5,7}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1},{2,4,7},{3,6},{5,8}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1,3},{2,8},{4,5,7},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,3},{2,4,7,8},{5},{6}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,7},{2,3,4,8},{5},{6}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1},{2,4,7},{3},{5,6,8}} => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[],[[[]]],[],[[[]]]] => 1

{{1,7},{2},{3,4,5},{6,8}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1},{2,3,7},{4,8},{5,6}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2},{3,7},{4,5,6,8}} => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[],[],[[]],[[[[]]]]] => 1

{{1},{2},{3,5,7},{4,6,8}} => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[],[],[[[]]],[[[]]]] => 1

{{1},{2,6},{3,5},{4,7,8}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1},{2,6},{3,5,7},{4,8}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1,5},{2},{3,6,7},{4,8}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,5},{2},{3,6},{4,7,8}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,5},{2},{3},{4,6,7,8}} => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[]],[],[],[[[[]]]]] => 1

{{1},{2,6},{3},{4,5,7,8}} => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[],[[]],[],[[[[]]]]] => 1

{{1,6},{2},{3,4},{5,7,8}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,6},{2},{3,4,7},{5,8}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1},{2,6},{3,7},{4,5,8}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1,5},{2},{3,7},{4,6,8}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,5},{2,6},{3},{4,7,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,5},{2,4,6},{3},{7,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,6},{2,8},{3},{4,5,7}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,6},{2,5,8},{3},{4,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,6},{2,4,5,8},{3},{7}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,5},{2,7},{3},{4,6,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,7},{2,5},{3,6,8},{4}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,8},{2,6},{3,5,7},{4}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,7},{2,3},{4,6,8},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,8},{2,5,6},{3,7},{4}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,5},{2,6,7},{3},{4,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,5},{2},{3,6,8},{4,7}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,5},{2,6,8},{3},{4,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,6},{2,5,7},{3},{4,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,5,7},{2},{3,6},{4,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,5,7},{2},{3,8},{4,6}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,5,6},{2},{3,7},{4,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,7},{2,5,8},{3,6},{4}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,7},{2,5,8},{3},{4,6}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,7},{2,5,6},{3},{4,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,6},{2,5},{3},{4,7,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,6},{2,5,8},{3,7},{4}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,5},{2,8},{3,6,7},{4}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,5},{2,7,8},{3,6},{4}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,8},{2,5},{3,6,7},{4}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,8},{2,5,7},{3},{4,6}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,5},{2,7},{3,6,8},{4}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,7},{2,5},{3},{4,6,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,5},{2,6,8},{3,7},{4}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,6},{2,5,7},{3,8},{4}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,5},{2,8},{3},{4,6,7}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,6},{2,7,8},{3,5},{4}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,7},{2,8},{3,5,6},{4}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,7},{2,5,6},{3,8},{4}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,5},{2,6,7},{3,8},{4}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,8},{2,3,5},{4,6},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,8},{2,4,6},{3,5},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,7},{2,8},{3,4,5},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,3,5},{2},{4,6},{7,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,6},{2},{3,7,8},{4,5}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,6,7},{2},{3,8},{4,5}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,6},{2},{3,5,7,8},{4}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1,4},{2,6,8},{3},{5,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,8},{2,4,6},{3},{5,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,7},{2},{3,6,8},{4,5}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,4},{2},{3,5,7},{6,8}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,2},{3,5,7},{4},{6,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,2},{3,4,7},{5},{6,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,2,5},{3},{4,7},{6,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,2},{3,4,7},{5,8},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,2},{3,5},{4,6,8},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,2,6},{3},{4,7},{5,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,2,5},{3},{4,6},{7,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,3},{2,5,6},{4,8},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,3},{2,8},{4,5,6},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,2,4},{3},{5,7},{6,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,3},{2,4},{5,6,8},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,3},{2,4,7},{5},{6,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,4},{2,5,8},{3,7},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,7},{2,3,4},{5,8},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,3},{2,4,7},{5,8},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,3},{2,4,6},{5},{7,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,6},{2,3,4,8},{5},{7}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,4},{2,5,6},{3,8},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,6},{2,8},{3,4,5},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,4,6},{2},{3,5},{7,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,2},{3,5,8},{4,6},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,3},{2,5,7},{4},{6,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1},{2,3,4,7},{5},{6,8}} => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[],[[[[]]]],[],[[]]] => 1

{{1,4},{2,5,7},{3},{6,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,3},{2,4,6},{5,8},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1},{2,3,4},{5,7},{6,8}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,4,5},{3,7},{6,8}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,3,5},{4,7},{6,8}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,3,5},{4,6},{7,8}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1,4},{2,5,8},{3,6},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1},{2,4,5},{3,6},{7,8}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1,6},{2,4},{3,7,8},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,6},{2,4},{3,7},{5},{8}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,7},{2,8},{3,4},{5},{6}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,5},{2,3},{4,6,7},{8}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,5},{2,3},{4,6,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1,5},{2,3},{4,6,8},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,6},{2,4},{3,8},{5},{7}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,5},{2,3},{4,6},{7},{8}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,5},{2,3},{4,7,8},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,5},{2,3},{4,8},{6},{7}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,5},{2,3},{4,7},{6},{8}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,6},{2,4},{3,5,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1,6},{2,5},{3,4,7,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1,3,7},{2},{4,8},{5,6}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,3,6},{2},{4,7},{5},{8}} => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[]]],[],[[]],[],[]] => 1

{{1,3},{2},{4,7},{5,8},{6}} => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[],[[]],[[]],[]] => 1

{{1},{2,4,7},{3},{5,8},{6}} => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[],[[[]]],[],[[]],[]] => 1

{{1},{2,7},{3,4,5,8},{6}} => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 1

{{1,6},{2,3,4,7},{5},{8}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,7},{2,4},{3,5,8},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1},{2,5,8},{3,7},{4},{6}} => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[],[[[]]],[[]],[],[]] => 1

{{1},{2,7},{3,5,8},{4,6}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1,6},{2,4,7},{3,5},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,7},{2,5},{3,4,6},{8}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1},{2,8},{3,6},{4,5,7}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1,6},{2,3,7},{4,5},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1},{2,7},{3,4,8},{5,6}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1,5},{2,6,8},{3,4},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,4},{2,5,7},{3},{6},{8}} => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]] => 1

{{1,4},{2,5},{3},{6,8},{7}} => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[[]],[],[[]],[]] => 1

{{1,5},{2,3,6,8},{4},{7}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1},{2,5},{3,6,8},{4},{7}} => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[],[[]],[[[]]],[],[]] => 1

{{1},{2,5,6,7},{3,8},{4}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2,8},{3,5},{4,6,7}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1},{2,6,7},{3,4,8},{5}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,6},{3,7},{4,8},{5}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1},{2,6},{3,7},{4},{5},{8}} => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[[]],[],[],[]] => 1

{{1},{2,5,6},{3,4,7},{8}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,4,6},{3,5,7},{8}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,3,5},{4,6,7},{8}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1,6},{2},{3,8},{4},{5},{7}} => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[],[[]],[],[],[]] => 1

{{1},{2},{3,5},{4,6},{7},{8}} => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[[]],[],[]] => 1

{{1,5},{2},{3},{4,8},{6},{7}} => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[],[[]],[],[]] => 1

{{1},{2,5},{3},{4,7},{6},{8}} => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[[]],[],[]] => 1

{{1,7},{2},{3,4},{5,6,8}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,6,8},{2},{3,4},{5,7}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,6,7},{2},{3,4},{5,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,8},{2},{3,4,6},{5,7}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1},{2,4,8},{3,7},{5,6}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1,3},{2,7,8},{4},{5,6}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1},{2,4},{3,7,8},{5,6}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1,3},{2,6,8},{4},{5,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1},{2,6,8},{3,4},{5,7}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,6,7},{3,4},{5,8}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1,3},{2,6,8},{4,7},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,3,4},{2},{5,7},{6,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,3},{2,4},{5,7,8},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,4},{2,5,6},{3},{7,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,5},{2,6,7,8},{3},{4}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,5},{2},{3,6,7,8},{4}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1,5},{2,4,6},{3,8},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,4,5},{2},{3,7},{6,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1},{2,4,7},{3,8},{5,6}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1,6},{2,3,8},{4},{5,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1},{2,6},{3,4,8},{5,7}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1},{2,3},{4,5,7},{6,8}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1},{2,3},{4,6,8},{5,7}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1},{2,3,5,6},{4,7},{8}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2,3,5,7},{4,8},{6}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2,3,7},{4,6},{5,8}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,3,6},{4,7},{5,8}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1,3},{2,5,8},{4,6,7}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1,5},{2},{3,4,6,7},{8}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1,5},{2,6,7},{3,4},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,3},{2,5,7,8},{4,6}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,4},{2},{3,5,6,8},{7}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1,3},{2,5,6,8},{4},{7}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,7},{2},{3,4,6,8},{5}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1},{2,7},{3,4,5},{6,8}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1},{2,6},{3,4,5,8},{7}} => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 1

{{1,6},{2},{3,4,5,7},{8}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1,6},{2,7},{3,4,5},{8}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,7},{2,4},{3,5,6,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1,4},{2,7},{3,5,6,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1,5},{2,7},{3,4,6},{8}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1},{2,4,8},{3,5,6},{7}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1,6},{2,4,5},{3,7},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1},{2,5,7},{3,8},{4},{6}} => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[],[[[]]],[[]],[],[]] => 1

{{1},{2,7},{3,5,6},{4,8}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1},{2,5,8},{3,6,7},{4}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,6,8},{3,4,7},{5}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1,3},{2,6},{4,5,8},{7}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,4},{2,3,8},{5,6},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1},{2,6},{3,8},{4},{5,7}} => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[[]],[],[[]]] => 1

{{1},{2,5,6,7},{3,4,8}} => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[],[[[[]]]],[[[]]]] => 1

{{1,7},{2,8},{3},{4},{5,6}} => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[[]],[],[],[[]]] => 1

{{1},{2,3,5},{4,8},{6,7}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1,3,5},{2},{4,8},{6,7}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,6},{2},{3,8},{4},{5,7}} => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]],[],[[]]] => 1

{{1},{2},{3,5},{4,8},{6,7}} => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[],[],[[]],[[]],[[]]] => 1

{{1,2,5},{3},{4,8},{6,7}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,5},{2},{3},{4,8},{6,7}} => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[],[[]],[[]]] => 1

{{1},{2,5},{3},{4,8},{6,7}} => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[],[[]],[],[[]],[[]]] => 1

{{1,4},{2,7},{3,5,8},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1},{2,7},{3,8},{4,5,6}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1,5},{2,4,6},{3,7},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,6},{2,3,5},{4,7},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1},{2,5},{3,8},{4,6,7}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1},{2,3,7},{4,8},{5},{6}} => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[],[[[]]],[[]],[],[]] => 1

{{1},{2,4},{3,7,8},{5},{6}} => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[],[[]],[[[]]],[],[]] => 1

{{1},{2,5,7},{3,4,8},{6}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,4},{3,5},{6,7},{8}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1},{2,4,8},{3,5},{6},{7}} => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[],[[[]]],[[]],[],[]] => 1

{{1},{2,4,6},{3,5},{7,8}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,5},{3,6},{4},{7,8}} => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[[]],[],[[]]] => 1

{{1},{2,5,7},{3,6,8},{4}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,5,7},{3,8},{4,6}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1,8},{2,4},{3,5,7},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1},{2,5},{3,6},{4,7},{8}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1},{2,5},{3,6,8},{4,7}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1},{2,3,6,7},{4,8},{5}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1,4},{2,6,8},{3,7},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,5},{2,3,7,8},{4},{6}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1},{2,3,6,8},{4},{5,7}} => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[],[[[[]]]],[],[[]]] => 1

{{1,2},{3},{4,6},{5,7,8}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1},{2,5,6,8},{3},{4,7}} => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[],[[[[]]]],[],[[]]] => 1

{{1},{2},{3,5,6,8},{4,7}} => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[],[],[[[[]]]],[[]]] => 1

{{1},{2,4,5,7},{3,8},{6}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2},{3,4,6,7},{5,8}} => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[],[],[[[[]]]],[[]]] => 1

{{1},{2,6},{3,7,8},{4,5}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1},{2,6,7},{3,5},{4,8}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2},{3,6,8},{4,5,7}} => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[],[],[[[]]],[[[]]]] => 1

{{1},{2,3},{4,7},{5,6,8}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1},{2,4,6},{3,7,8},{5}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1,3},{2},{4,6},{5,7,8}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1},{2,4,6,7},{3},{5,8}} => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[],[[[[]]]],[],[[]]] => 1

{{1},{2,5},{3,7,8},{4,6}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1,3},{2,4,5},{6,8},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,3},{2,8},{4,6,7},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,3},{2,4,5},{6,7},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,4},{2,7,8},{3},{5,6}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,4},{2,3,7,8},{5},{6}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,6,8},{2},{3},{4,5,7}} => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[],[[[]]]] => 1

{{1,5},{2,3,7},{4,6},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,4},{2,3,6,7},{5},{8}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,6},{2,4,5,7},{3},{8}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,7},{2,4,5},{3,6},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1},{2,6,7},{3,5,8},{4}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1,3},{2},{4,6,7},{5,8}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,6},{2,5,8},{3,4,7}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1},{2,8},{3,5,6},{4,7}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1},{2,5,6,7},{3},{4,8}} => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[],[[[[]]]],[],[[]]] => 1

{{1,6},{2,7,8},{3,4},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,5},{2,7},{3,4,6,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1,7},{2},{3,8},{4,5,6}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,7},{2,4,5},{3,6,8}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1},{2,6,8},{3,7},{4,5}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,4,5,8},{3,7},{6}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2,4,5},{3,7,8},{6}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,6},{3,8},{4,5,7}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1},{2,4,6,7},{3,8},{5}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1,5},{2,7,8},{3,4},{6}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,3},{2,5},{4,7,8},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,7},{2,6},{3},{4,5,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,3},{2,7,8},{4,6},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,2},{3,5},{4,7,8},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1},{2,3,4,7},{5,8},{6}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2,3,4,6},{5,8},{7}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2,4,5,8},{3,6},{7}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1,6},{2},{3,4,5,8},{7}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1},{2,4},{3,6},{5,8},{7}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1,3},{2},{4,6},{5,8},{7}} => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[],[[]],[[]],[]] => 1

{{1,3},{2,5},{4},{6,8},{7}} => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[[]],[],[[]],[]] => 1

{{1},{2,4,5,6},{3,8},{7}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2,6},{3,5},{4,8},{7}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1,5},{2,4},{3,7},{6},{8}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,5},{2,4,6,7},{3},{8}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1},{2,6},{3,5,7,8},{4}} => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 1

{{1},{2,8},{3,5},{4,7},{6}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1,7},{2,4},{3,6},{5},{8}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1},{2,5,7,8},{3,6},{4}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1,3},{2,5,6,7},{4},{8}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,3},{2,6,7,8},{4},{5}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1},{2,4},{3,6,7,8},{5}} => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 1

{{1},{2,4},{3,8},{5,7},{6}} => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1

{{1,3},{2,7},{4,6},{5},{8}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1},{2,4,7},{3,6,8},{5}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1,5},{2,3,6,7},{4},{8}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,4},{2,3,7},{5,6},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1},{2,5,8},{3,4,6},{7}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,5,7},{3,4,6},{8}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,3,6},{4,5,7},{8}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1,6},{2,3},{4,5,7},{8}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,4},{2,3,5},{6,7},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,6},{2,5,7},{3,4},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,4},{2,3,5},{6,8},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1},{2,3,6},{4,5,8},{7}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,5,8},{3,4,7},{6}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,3,7},{4,6,8},{5}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,3,7},{4,5,8},{6}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1,4,8},{2},{3,5},{6,7}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,6,8},{2},{3,5},{4,7}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,4},{2,3,5,8},{6},{7}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,2},{3,6,8},{4},{5,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,8},{2},{3,6},{4,5,7}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,8},{2},{3,5,6},{4,7}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,3},{2,4,8},{5},{6,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,5},{2,6},{3,4,7},{8}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,5},{2,4},{3,6,7},{8}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,5},{2,3,6},{4,7},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,5},{2,3,4,6},{7},{8}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,4},{2,5,7},{3,6},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,2,7},{3},{4,8},{5,6}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,4},{2,5,7,8},{3},{6}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1},{2,6},{3,4,7,8},{5}} => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 1

{{1,3},{2},{4,7},{5,6,8}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,4},{2},{3,6,7,8},{5}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1},{2,3,7},{4},{5,6,8}} => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[],[[[]]],[],[[[]]]] => 1

{{1},{2,3,6},{4},{5,7,8}} => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[],[[[]]],[],[[[]]]] => 1

{{1},{2,3},{4,6,7},{5,8}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1},{2,3},{4,6},{5,7,8}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1,4},{2,6},{3,7,8},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1},{2,3,5,6},{4,8},{7}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2,3,5},{4,7,8},{6}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,5},{3,4,7,8},{6}} => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 1

{{1,4,7},{2},{3,6},{5,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1},{2,4,8},{3,6,7},{5}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,3,6},{4,7,8},{5}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1,5},{2,3,7},{4,6,8}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1,5},{2,3,6,8},{4,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1},{2,5},{3,4,7},{6,8}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1,5},{2,6,8},{3,4,7}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1,6},{2,5,7},{3,4,8}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1},{2,7},{3,6},{4,5,8}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1,7},{2,4,5,8},{3,6}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,7},{2,5,8},{3,4,6}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1,6},{2,5},{3,4,7},{8}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,6},{2,4,5,8},{3,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1},{2,4,5,7},{3,6},{8}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1,7},{2,5},{3,4,6,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1},{2,6},{3,4,5,7},{8}} => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 1

{{1},{2,7},{3,6,8},{4,5}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1,6},{2,4,5,7},{3,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1},{2,6,8},{3},{4,7},{5}} => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[],[[[]]],[],[[]],[]] => 1

{{1,3},{2},{4,7},{5},{6,8}} => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]],[],[[]]] => 1

{{1,4},{2},{3,5},{6,8},{7}} => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[],[[]],[[]],[]] => 1

{{1,5,7},{2},{3,6},{4},{8}} => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[]]],[],[[]],[],[]] => 1

{{1},{2,7},{3,5},{4},{6,8}} => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[[]],[],[[]]] => 1

{{1,6},{2,4},{3},{5,7},{8}} => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[[]],[],[[]],[]] => 1

{{1},{2,7},{3,5,6,8},{4}} => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 1

{{1},{2,8},{3,6},{4},{5,7}} => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[[]],[],[[]]] => 1

{{1,7},{2,5},{3},{4,6},{8}} => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[[]],[],[[]],[]] => 1

{{1},{2,7},{3,4,6,8},{5}} => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 1

{{1,6},{2,3,5,7},{4},{8}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1},{2,6},{3},{4,8},{5,7}} => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[],[[]],[],[[]],[[]]] => 1

{{1,5},{2},{3,7},{4,6},{8}} => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[],[[]],[[]],[]] => 1

{{1},{2,6},{3,5,8},{4,7}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1,5},{2,4,7},{3,6},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1},{2,5},{3,4,6,8},{7}} => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 1

{{1,4},{2,3,5,7},{6},{8}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1},{2,5,6,8},{3,7},{4}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2,7},{3,5},{4,6,8}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1,5},{2,3,7},{4},{6},{8}} => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]] => 1

{{1,5},{2,3,8},{4},{6},{7}} => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]] => 1

{{1,6},{2,3,8},{4},{5},{7}} => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]] => 1

{{1,6},{2,4,8},{3},{5},{7}} => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]] => 1

{{1,6},{2,3},{4,7},{5},{8}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,6},{2,3},{4,7,8},{5}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,7},{2,3},{4,8},{5},{6}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,7},{2,4},{3,8},{5},{6}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1,5},{2},{3,4,7},{6,8}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1},{2,4},{3,5,7},{6,8}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1,7},{2,5},{3},{4,8},{6}} => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[[]],[],[[]],[]] => 1

{{1},{2,4},{3,5,7},{6},{8}} => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[],[[]],[[[]]],[],[]] => 1

{{1},{2,4},{3,5,8},{6},{7}} => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[],[[]],[[[]]],[],[]] => 1

{{1},{2,4,7},{3,5,6},{8}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1,7},{2,3,5},{4},{6,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1},{2,4,5},{3,8},{6,7}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,3,8},{4,6},{5,7}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,4,5,7},{3},{6,8}} => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[],[[[[]]]],[],[[]]] => 1

{{1,3,7},{2},{4,5},{6,8}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1},{2,4,7},{3,5,8},{6}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2},{3,5,7,8},{4,6}} => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[],[],[[[[]]]],[[]]] => 1

{{1},{2},{3,5,8},{4,6,7}} => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[],[],[[[]]],[[[]]]] => 1

{{1},{2,5,7},{3,6},{4,8}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,5,7,8},{3},{4,6}} => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[],[[[[]]]],[],[[]]] => 1

{{1,3,4,5,6,7,8,9},{2}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[]]]]]]]],[]] => 1

{{1,3,4,5,6,7,8,9,10},{2}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[]]]]]]]]],[]] => 1

{{1,7,8},{2},{3,5},{4,6}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1},{2,3,5},{4,6,7,8}} => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[],[[[]]],[[[[]]]]] => 1

{{1},{2,3,5},{4,6,8},{7}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1,4},{2},{3,5,6,7,8}} => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[]],[],[[[[[]]]]]] => 1

{{1,3},{2,5,6},{4},{7,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,4},{2,5},{3,7,8},{6}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,6},{2},{3,7},{4,5,8}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,7},{2},{3,5},{4,6,8}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,3},{2,5,7,8},{4},{6}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,7},{2},{3,5,6,8},{4}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1,7},{2},{3,5,8},{4,6}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,6},{2},{3,5,7},{4,8}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,8},{2},{3,5,7},{4,6}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,5,8},{2},{3},{4,6,7}} => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[],[[[]]]] => 1

{{1,6},{2,3,5,7,8},{4}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1},{2,4,5,7,8},{3,6}} => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[],[[[[[]]]]],[[]]] => 1

{{1},{2,4,6,8},{3,5,7}} => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[],[[[[]]]],[[[]]]] => 1

{{1,5},{2,4,7},{3,6,8}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1},{2,5,8},{3,4,6,7}} => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[],[[[]]],[[[[]]]]] => 1

{{1,6},{2,4,5,7,8},{3}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1,4},{2,3,5,6,8},{7}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1},{2,3,5,6,8},{4,7}} => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[],[[[[[]]]]],[[]]] => 1

{{1,4},{2,3,5,7,8},{6}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1},{2,3,7},{4,5},{6,8}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1,3},{2},{4,5,7},{6,8}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,2},{3},{4,5,7},{6,8}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1},{2},{3,4,6},{5,7,8}} => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[],[],[[[]]],[[[]]]] => 1

{{1},{2},{3,4,7},{5,6,8}} => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[],[],[[[]]],[[[]]]] => 1

{{1,2},{3},{4,6,8},{5,7}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,2},{3},{4,6,7},{5,8}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1,3},{2,4},{5},{6,7,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,4},{2,5},{3},{6,7,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,3},{2,5},{4},{6,7,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,7},{2,8},{3},{4,5,6}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1,4},{2,8},{3},{5,6,7}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1},{2,6,7},{3},{4,5,8}} => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[],[[[]]],[],[[[]]]] => 1

{{1,3},{2,4,5,8},{6},{7}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,4},{2},{3,5},{6,7,8}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,6},{2,7},{3},{4,5,8}} => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => 1

{{1},{2,3,4,6},{5,7},{8}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2,7,8},{3,5},{4,6}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1,6},{2,7,8},{3},{4,5}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,8},{2},{3,5},{4,6,7}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,6},{2},{3,5,8},{4,7}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1},{2,6,8},{3},{4,5,7}} => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[],[[[]]],[],[[[]]]] => 1

{{1},{2,6,7},{3,8},{4,5}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1},{2,5,6},{3,8},{4,7}} => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => 1

{{1,2,8},{3},{4,6},{5,7}} => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => 1

{{1,7},{2,3,5},{4,6},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,3},{2,5,6},{4,7},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,3},{2,7},{4,5,6},{8}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1},{2,5,8},{3},{4,6,7}} => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[],[[[]]],[],[[[]]]] => 1

{{1,4},{2,6,7},{3,5},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,4},{2,7,8},{3,6},{5}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1},{2,4,5},{3,6,7},{8}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,4,5},{3,6,8},{7}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,5,6},{3,7,8},{4}} => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 1

{{1},{2,4},{3,5,6},{7,8}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1,3},{2,6},{4,5,7},{8}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,4},{2},{3,5,6,7},{8}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1},{2,4,6,7,8},{3,5}} => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[],[[[[[]]]]],[[]]] => 1

{{1},{2,3,5,8},{4,7},{6}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1,2,3,4,5,6,7,9},{8}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[]]]]]]]],[]] => 1

{{1,2,3,4,5,6,7,8,10},{9}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[]]]]]]]]],[]] => 1

{{1,2,3,4,5,6,7,8,9,11},{10}} => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[[]]]]]]]]]],[]] => 1

{{1,6},{2,3,4,5,7,8}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[]],[[[[[[]]]]]]] => 2

{{1,5},{2,3,4,8},{6,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,6},{2,3,5},{4,7,8}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1,5},{2,3,6},{4,7,8}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1,2,3,5,6,7,8,9,10},{4}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[]]]]]]]]],[]] => 1

{{1,2,3,4,6,7,8,9,10},{5}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[]]]]]]]]],[]] => 1

{{1,3,4,5,6,7,8,9,10,11},{2}} => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[[]]]]]]]]]],[]] => 1

{{1},{2},{3},{4},{5,7},{6,8}} => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[],[],[[]],[[]]] => 1

{{1},{2},{3},{4,6},{5,8},{7}} => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[],[[]],[[]],[]] => 1

{{1},{2},{3,5},{4,8},{6},{7}} => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[[]],[],[]] => 1

{{1},{2,4},{3,8},{5},{6},{7}} => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[[]],[],[],[]] => 1

{{1},{2},{3},{4,7},{5,8},{6}} => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[],[[]],[[]],[]] => 1

{{1},{2},{3,6},{4,8},{5},{7}} => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[[]],[],[]] => 1

{{1},{2},{3},{4,6,7},{5,8}} => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[],[],[],[[[]]],[[]]] => 1

{{1},{2,5},{3,8},{4},{6},{7}} => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[[]],[],[],[]] => 1

{{1},{2},{3,5,6},{4,8},{7}} => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[],[[[]]],[[]],[]] => 1

{{1},{2,4,5},{3,8},{6},{7}} => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[],[[[]]],[[]],[],[]] => 1

{{1,7},{2,3,4,5,6,8}} => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[]],[[[[[[]]]]]]] => 2

{{1,6},{2,5,7,8},{3,4}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,6},{2,3,7},{4,5,8}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1,6},{2,3,4,7,8},{5}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1},{2,3,5,7,8},{4,6}} => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[],[[[[[]]]]],[[]]] => 1

{{1},{2,3,5,7},{4,6},{8}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2,3,5,7},{4,6,8}} => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[],[[[[]]]],[[[]]]] => 1

{{1},{2,3,4,5,7},{6,8}} => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[],[[[[[]]]]],[[]]] => 1

{{1},{2,3,5,8},{4,6,7}} => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[],[[[[]]]],[[[]]]] => 1

{{1,3},{2,6,8},{4,5},{7}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1},{2,4,7,8},{3,5},{6}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2,4,7,8},{3,6},{5}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1,4},{2},{3,7,8},{5,6}} => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => 1

{{1},{2,3,4,6,8},{5,7}} => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[],[[[[[]]]]],[[]]] => 1

{{1,3},{2,4,5,6,8},{7}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1,7},{2,3,4},{5,6,8}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1,2},{3,4,6},{5,7,8}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1,5},{2,6,7,8},{3,4}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,7},{2,6,8},{3,4,5}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1},{2,3,6},{4,5,7,8}} => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[],[[[]]],[[[[]]]]] => 1

{{1,2,3,4,5,6,8,9},{7}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[]]]]]]]],[]] => 1

{{1,2,3,4,5,7,8,9},{6}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[]]]]]]]],[]] => 1

{{1,2,3,4,6,7,8,9},{5}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[]]]]]]]],[]] => 1

{{1,2,3,5,6,7,8,9},{4}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[]]]]]]]],[]] => 1

{{1,2,4,5,6,7,8,9},{3}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[]]]]]]]],[]] => 1

{{1,2,3,4,5,6,7,9,10},{8}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[]]]]]]]]],[]] => 1

{{1,2,3,4,5,6,8,9,10},{7}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[]]]]]]]]],[]] => 1

{{1,2,3,4,5,7,8,9,10},{6}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[]]]]]]]]],[]] => 1

{{1,2,4,5,6,7,8,9,10},{3}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[]]]]]]]]],[]] => 1

{{1,3},{2,5,8},{4},{6,7}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1},{2,4},{3,5,6,7,8}} => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[],[[]],[[[[[]]]]]] => 1

{{1,5,6},{2},{3},{4,7,8}} => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[],[[[]]]] => 1

{{1,3,5},{2},{4,6},{7},{8}} => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[]]],[],[[]],[],[]] => 1

{{1,3,7},{2},{4},{5},{6,8}} => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[]]],[],[],[],[[]]] => 1

{{1,3,6},{2},{4},{5,8},{7}} => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[],[[]],[]] => 1

{{1},{2},{3,7},{4,8},{5},{6}} => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[[]],[],[]] => 1

{{1,7},{2},{3},{4},{5},{6,8}} => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[],[],[[]]] => 1

{{1,6},{2},{3},{4},{5,8},{7}} => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[],[[]],[]] => 1

{{1,4},{2,6},{3},{5,8},{7}} => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[[]],[],[[]],[]] => 1

{{1,5},{2,6},{3},{4,8},{7}} => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[[]],[],[[]],[]] => 1

{{1,5,7},{2},{3},{4},{6,8}} => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[]]],[],[],[],[[]]] => 1

{{1,5},{2},{3},{4,6},{7},{8}} => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[],[[]],[],[]] => 1

{{1,4},{2},{3,6},{5},{7},{8}} => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[],[[]],[],[],[]] => 1

{{1},{2,5},{3,6},{4},{7},{8}} => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[[]],[],[],[]] => 1

{{1,6},{2},{3},{4,7},{5},{8}} => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[],[[]],[],[]] => 1

{{1,6},{2},{3},{4,7},{5,8}} => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[],[[]],[[]]] => 1

{{1,5},{2},{3},{4,7},{6,8}} => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[],[[]],[[]]] => 1

{{1,5,7},{2},{3},{4,6},{8}} => [3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[],[[]],[]] => 1

{{1,4,7},{2},{3,6},{5},{8}} => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[]]],[],[[]],[],[]] => 1

{{1,4},{2},{3,7},{5},{6,8}} => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]],[],[[]]] => 1

{{1,5},{2},{3,7},{4,8},{6}} => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[],[[]],[[]],[]] => 1

{{1,5},{2},{3,7},{4},{6},{8}} => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[],[[]],[],[],[]] => 1

{{1,7},{2,5},{3,6},{4},{8}} => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => 1

{{1},{2,6},{3},{4,8},{5},{7}} => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[[]],[],[]] => 1

{{1,5},{2,3,4,8},{6},{7}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,3},{2,5},{4,6,7},{8}} => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 1

{{1,8},{2,3,4,6},{5,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,7},{2,3},{4,5,6,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1,7},{2,3,5,6},{4,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,5},{2},{3,4,6,8},{7}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1,6},{2},{3},{4,5,7,8}} => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[]],[],[],[[[[]]]]] => 1

{{1,4},{2,6,7,8},{3},{5}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1},{2,5},{3,6,7,8},{4}} => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 1

{{1,2},{3,6,8},{4,5,7}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1,7},{2,3,5},{4,6,8}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1,5},{2,4,6,7,8},{3}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1,7},{2,4,5,6,8},{3}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1,3},{2,4,5,6,7},{8}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1},{2,5},{3,4,6,7,8}} => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[],[[]],[[[[[]]]]]] => 1

{{1,4},{2,3,5,6,7},{8}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1},{2,6},{3,4,5,7,8}} => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[],[[]],[[[[[]]]]]] => 1

{{1},{2,3,4,6},{5,7,8}} => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[],[[[[]]]],[[[]]]] => 1

{{1,5},{2,3,4,6,7},{8}} => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 1

{{1},{2,4,6},{3},{5,7,8}} => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[],[[[]]],[],[[[]]]] => 1

{{1},{2,5,7},{3},{4,6,8}} => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[],[[[]]],[],[[[]]]] => 1

{{1,2},{3,5,7},{4,6,8}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1},{2,7},{3,8},{4},{5},{6}} => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[[]],[],[],[]] => 1

{{1,5,6},{2},{3,8},{4},{7}} => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[]]],[],[[]],[],[]] => 1

{{1},{2},{3},{4,6,8},{5,7}} => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[],[],[],[[[]]],[[]]] => 1

{{1},{2},{3,5,8},{4,6},{7}} => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[],[[[]]],[[]],[]] => 1

{{1},{2,4,8},{3,5,6,7}} => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[],[[[]]],[[[[]]]]] => 1

{{1},{2,7},{3,6},{4},{5,8}} => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[[]],[],[[]]] => 1

{{1,5},{2},{3,7},{4},{6,8}} => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]],[],[[]]] => 1

{{1,5},{2,3,4,7},{6,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,3},{2,7},{4,5,6,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1},{2,7},{3},{4,5,6,8}} => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[],[[]],[],[[[[]]]]] => 1

{{1},{2,5},{3},{4,7},{6,8}} => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[],[[]],[],[[]],[[]]] => 1

{{1,2},{3,4,7},{5,6,8}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1,7},{2,3,5,8},{4,6}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,2},{3,5,7,8},{4,6}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1},{2,4},{3,5},{6,7,8}} => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => 1

{{1,4},{2,5,6,8},{3},{7}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,5},{2,3,4,6},{7,8}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,8},{2,3,6},{4,5,7}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1,2},{3,5,6},{4,7,8}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1,7},{2,6},{3,4,5,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1,2},{3,7},{4,5,6,8}} => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => 2

{{1,7},{2,5,6,8},{3,4}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,7},{2},{3,4,5,8},{6}} => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 1

{{1,4},{2,3,5,6},{7},{8}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1,4},{2,5,6,7},{3},{8}} => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 1

{{1},{2},{3,4,5,7},{6,8}} => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[],[],[[[[]]]],[[]]] => 1

{{1,4,7},{2},{3},{5,6,8}} => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[],[[[]]]] => 1

{{1,6},{2,4,7,8},{3,5}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,3},{2,4,5},{6},{7,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1,4},{2,3,5},{6},{7,8}} => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => 1

{{1},{2,5},{3,4,6,7},{8}} => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 1

{{1},{2,4,5,6},{3,7},{8}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2,3,6},{4},{5,8},{7}} => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[],[[[]]],[],[[]],[]] => 1

{{1},{2,3,7},{4},{5,8},{6}} => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[],[[[]]],[],[[]],[]] => 1

{{1},{2,4},{3,7},{5},{6,8}} => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[[]],[],[[]]] => 1

{{1},{2,5},{3},{4,6,8},{7}} => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[],[[]],[],[[[]]],[]] => 1

{{1},{2,5},{3},{4,6,7},{8}} => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[],[[]],[],[[[]]],[]] => 1

{{1,8},{2,5,6},{3,4,7}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1,2},{3,4,6,8},{5,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,2,3,4,5,6,7,8,10,11},{9}} => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[[]]]]]]]]]],[]] => 1

{{1,3},{2,6,7},{4,5},{8}} => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 1

{{1,4},{2,3,6,8},{5,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1,6},{2},{3,4,5,7,8}} => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[]],[],[[[[[]]]]]] => 1

{{1,2},{3,6,7},{4,5,8}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1,4,8},{2},{3,6},{5},{7}} => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[]]],[],[[]],[],[]] => 1

{{1},{2,4},{3,5,6,8},{7}} => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 1

{{1},{2,5},{3,4,6},{7,8}} => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1

{{1,2},{3},{4,7},{5,6,8}} => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => 1

{{1,4},{2,3,6},{5,7,8}} => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => 2

{{1},{2,4,6},{3},{5,7},{8}} => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[],[[[]]],[],[[]],[]] => 1

{{1,6},{2,3,5,8},{4,7}} => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => 2

{{1},{2,3,6,8},{4,7},{5}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

{{1},{2,4,7},{3,5,6,8}} => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[],[[[]]],[[[[]]]]] => 1

{{1},{2,4,5,7},{3,6,8}} => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[],[[[[]]]],[[[]]]] => 1

{{1},{2,3,4,6,7},{5,8}} => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[],[[[[[]]]]],[[]]] => 1

{{1},{2,3,6},{4,7},{5},{8}} => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[],[[[]]],[[]],[],[]] => 1

{{1},{2,4,7},{3,8},{5},{6}} => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[],[[[]]],[[]],[],[]] => 1

{{1},{2,5,7},{3},{4,8},{6}} => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[],[[[]]],[],[[]],[]] => 1

{{1},{2,4,7},{3,5},{6},{8}} => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[],[[[]]],[[]],[],[]] => 1

{{1},{2,5,8},{3,6},{4},{7}} => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[],[[[]]],[[]],[],[]] => 1

{{1},{2,4,6,7},{3,5},{8}} => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 1

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$F_{1} = q$

$F_{2} = q + q^{2}$

$F_{3} = 4\ q + q^{3}$

$F_{4} = 11\ q + 3\ q^{2} + q^{4}$

$F_{5} = 41\ q + 10\ q^{2} + q^{5}$

$F_{6} = 162\ q + 30\ q^{2} + 10\ q^{3} + q^{6}$

$F_{7} = 715\ q + 126\ q^{2} + 35\ q^{3} + q^{7}$

Description

The protection number of an ordered tree.
This is the minimal distance from the root to a leaf.

Map

bounce path

Description

The bounce path determined by an integer composition.

Map

to composition

Description

The integer composition of block sizes of a set partition.
For a set partition of

$\{1,2,\dots,n\}$ , this is the integer composition of

$n$ obtained by sorting the blocks by their minimal element and then taking the block sizes.

Map

to ordered tree

Description

Sends a Dyck path to the ordered tree encoding the heights of the path.
This map is recursively defined as follows: A Dyck path

$D$ of semilength

$n$ may be decomposed, according to its returns (St000011The number of touch points (or returns) of a Dyck path.), into smaller paths

$D_1,\dots,D_k$ of respective semilengths

$n_1,\dots,n_k$ (so one has

$n = n_1 + \dots n_k$ ) each of which has no returns.
Denote by

$\tilde D_i$ the path of semilength

$n_i-1$ obtained from

$D_i$ by removing the initial up- and the final down-step.
This map then sends

$D$ to the tree

$T$ having a root note with ordered children

$T_1,\dots,T_k$ which are again ordered trees computed from

$D_1,\dots,D_k$ respectively.
The unique path of semilength

$1$ is sent to the tree consisting of a single node.