Identifier
-
Mp00071:
Permutations
—descent composition⟶
Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
St000493: Set partitions ⟶ ℤ
Values
[1,2] => [2] => [1,1,0,0] => {{1,2}} => 0
[2,1] => [1,1] => [1,0,1,0] => {{1},{2}} => 1
[1,2,3] => [3] => [1,1,1,0,0,0] => {{1,2,3}} => 0
[1,3,2] => [2,1] => [1,1,0,0,1,0] => {{1,2},{3}} => 1
[2,1,3] => [1,2] => [1,0,1,1,0,0] => {{1},{2,3}} => 2
[2,3,1] => [2,1] => [1,1,0,0,1,0] => {{1,2},{3}} => 1
[3,1,2] => [1,2] => [1,0,1,1,0,0] => {{1},{2,3}} => 2
[3,2,1] => [1,1,1] => [1,0,1,0,1,0] => {{1},{2},{3}} => 3
[1,2,3,4] => [4] => [1,1,1,1,0,0,0,0] => {{1,2,3,4}} => 0
[1,2,4,3] => [3,1] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => 1
[1,3,2,4] => [2,2] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => 2
[1,3,4,2] => [3,1] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => 1
[1,4,2,3] => [2,2] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => 2
[1,4,3,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => 3
[2,1,3,4] => [1,3] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => 3
[2,1,4,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => 4
[2,3,1,4] => [2,2] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => 2
[2,3,4,1] => [3,1] => [1,1,1,0,0,0,1,0] => {{1,2,3},{4}} => 1
[2,4,1,3] => [2,2] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => 2
[2,4,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => 3
[3,1,2,4] => [1,3] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => 3
[3,1,4,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => 4
[3,2,1,4] => [1,1,2] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => 5
[3,2,4,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => 4
[3,4,1,2] => [2,2] => [1,1,0,0,1,1,0,0] => {{1,2},{3,4}} => 2
[3,4,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => {{1,2},{3},{4}} => 3
[4,1,2,3] => [1,3] => [1,0,1,1,1,0,0,0] => {{1},{2,3,4}} => 3
[4,1,3,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => 4
[4,2,1,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => 5
[4,2,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => {{1},{2,3},{4}} => 4
[4,3,1,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => {{1},{2},{3,4}} => 5
[4,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => {{1},{2},{3},{4}} => 6
[1,2,3,4,5] => [5] => [1,1,1,1,1,0,0,0,0,0] => {{1,2,3,4,5}} => 0
[1,2,3,5,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => 1
[1,2,4,3,5] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 2
[1,2,4,5,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => 1
[1,2,5,3,4] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 2
[1,2,5,4,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => 3
[1,3,2,4,5] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => 3
[1,3,2,5,4] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 4
[1,3,4,2,5] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 2
[1,3,4,5,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => 1
[1,3,5,2,4] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 2
[1,3,5,4,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => 3
[1,4,2,3,5] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => 3
[1,4,2,5,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 4
[1,4,3,2,5] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 5
[1,4,3,5,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 4
[1,4,5,2,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 2
[1,4,5,3,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => 3
[1,5,2,3,4] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => 3
[1,5,2,4,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 4
[1,5,3,2,4] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 5
[1,5,3,4,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 4
[1,5,4,2,3] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 5
[1,5,4,3,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 6
[2,1,3,4,5] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => 4
[2,1,3,5,4] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 5
[2,1,4,3,5] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 6
[2,1,4,5,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 5
[2,1,5,3,4] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 6
[2,1,5,4,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 7
[2,3,1,4,5] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => 3
[2,3,1,5,4] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 4
[2,3,4,1,5] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 2
[2,3,4,5,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => {{1,2,3,4},{5}} => 1
[2,3,5,1,4] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 2
[2,3,5,4,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => 3
[2,4,1,3,5] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => 3
[2,4,1,5,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 4
[2,4,3,1,5] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 5
[2,4,3,5,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 4
[2,4,5,1,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 2
[2,4,5,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => 3
[2,5,1,3,4] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => 3
[2,5,1,4,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 4
[2,5,3,1,4] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 5
[2,5,3,4,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 4
[2,5,4,1,3] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 5
[2,5,4,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 6
[3,1,2,4,5] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => 4
[3,1,2,5,4] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 5
[3,1,4,2,5] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 6
[3,1,4,5,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 5
[3,1,5,2,4] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 6
[3,1,5,4,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 7
[3,2,1,4,5] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => 7
[3,2,1,5,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 8
[3,2,4,1,5] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 6
[3,2,4,5,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 5
[3,2,5,1,4] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 6
[3,2,5,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 7
[3,4,1,2,5] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => 3
[3,4,1,5,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 4
[3,4,2,1,5] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 5
[3,4,2,5,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 4
[3,4,5,1,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => {{1,2,3},{4,5}} => 2
[3,4,5,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => {{1,2,3},{4},{5}} => 3
[3,5,1,2,4] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => 3
[3,5,1,4,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 4
[3,5,2,1,4] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 5
>>> Load all 6043 entries. <<<[3,5,2,4,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 4
[3,5,4,1,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 5
[3,5,4,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 6
[4,1,2,3,5] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => 4
[4,1,2,5,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 5
[4,1,3,2,5] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 6
[4,1,3,5,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 5
[4,1,5,2,3] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 6
[4,1,5,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 7
[4,2,1,3,5] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => 7
[4,2,1,5,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 8
[4,2,3,1,5] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 6
[4,2,3,5,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 5
[4,2,5,1,3] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 6
[4,2,5,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 7
[4,3,1,2,5] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => 7
[4,3,1,5,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 8
[4,3,2,1,5] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => 9
[4,3,2,5,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 8
[4,3,5,1,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 6
[4,3,5,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 7
[4,5,1,2,3] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4,5}} => 3
[4,5,1,3,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 4
[4,5,2,1,3] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 5
[4,5,2,3,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5}} => 4
[4,5,3,1,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => {{1,2},{3},{4,5}} => 5
[4,5,3,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5}} => 6
[5,1,2,3,4] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => {{1},{2,3,4,5}} => 4
[5,1,2,4,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 5
[5,1,3,2,4] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 6
[5,1,3,4,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 5
[5,1,4,2,3] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 6
[5,1,4,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 7
[5,2,1,3,4] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => 7
[5,2,1,4,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 8
[5,2,3,1,4] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 6
[5,2,3,4,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => {{1},{2,3,4},{5}} => 5
[5,2,4,1,3] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 6
[5,2,4,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 7
[5,3,1,2,4] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => 7
[5,3,1,4,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 8
[5,3,2,1,4] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => 9
[5,3,2,4,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 8
[5,3,4,1,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5}} => 6
[5,3,4,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4},{5}} => 7
[5,4,1,2,3] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3,4,5}} => 7
[5,4,1,3,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 8
[5,4,2,1,3] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => 9
[5,4,2,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5}} => 8
[5,4,3,1,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4,5}} => 9
[5,4,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5}} => 10
[1,2,3,4,5,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2,3,4,5,6}} => 0
[1,2,3,4,6,5] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => 1
[1,2,3,5,4,6] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 2
[1,2,3,5,6,4] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => 1
[1,2,3,6,4,5] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 2
[1,2,3,6,5,4] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3
[1,2,4,3,5,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[1,2,4,3,6,5] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[1,2,4,5,3,6] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 2
[1,2,4,5,6,3] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => 1
[1,2,4,6,3,5] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 2
[1,2,4,6,5,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3
[1,2,5,3,4,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[1,2,5,3,6,4] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[1,2,5,4,3,6] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[1,2,5,4,6,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[1,2,5,6,3,4] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 2
[1,2,5,6,4,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3
[1,2,6,3,4,5] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[1,2,6,3,5,4] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[1,2,6,4,3,5] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[1,2,6,4,5,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[1,2,6,5,3,4] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[1,2,6,5,4,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => 6
[1,3,2,4,5,6] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 4
[1,3,2,4,6,5] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[1,3,2,5,4,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[1,3,2,5,6,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[1,3,2,6,4,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[1,3,2,6,5,4] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[1,3,4,2,5,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[1,3,4,2,6,5] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[1,3,4,5,2,6] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 2
[1,3,4,5,6,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => 1
[1,3,4,6,2,5] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 2
[1,3,4,6,5,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3
[1,3,5,2,4,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[1,3,5,2,6,4] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[1,3,5,4,2,6] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[1,3,5,4,6,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[1,3,5,6,2,4] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 2
[1,3,5,6,4,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3
[1,3,6,2,4,5] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[1,3,6,2,5,4] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[1,3,6,4,2,5] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[1,3,6,4,5,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[1,3,6,5,2,4] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[1,3,6,5,4,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => 6
[1,4,2,3,5,6] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 4
[1,4,2,3,6,5] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[1,4,2,5,3,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[1,4,2,5,6,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[1,4,2,6,3,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[1,4,2,6,5,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[1,4,3,2,5,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[1,4,3,2,6,5] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[1,4,3,5,2,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[1,4,3,5,6,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[1,4,3,6,2,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[1,4,3,6,5,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[1,4,5,2,3,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[1,4,5,2,6,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[1,4,5,3,2,6] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[1,4,5,3,6,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[1,4,5,6,2,3] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 2
[1,4,5,6,3,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3
[1,4,6,2,3,5] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[1,4,6,2,5,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[1,4,6,3,2,5] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[1,4,6,3,5,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[1,4,6,5,2,3] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[1,4,6,5,3,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => 6
[1,5,2,3,4,6] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 4
[1,5,2,3,6,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[1,5,2,4,3,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[1,5,2,4,6,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[1,5,2,6,3,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[1,5,2,6,4,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[1,5,3,2,4,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[1,5,3,2,6,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[1,5,3,4,2,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[1,5,3,4,6,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[1,5,3,6,2,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[1,5,3,6,4,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[1,5,4,2,3,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[1,5,4,2,6,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[1,5,4,3,2,6] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[1,5,4,3,6,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[1,5,4,6,2,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[1,5,4,6,3,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[1,5,6,2,3,4] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[1,5,6,2,4,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[1,5,6,3,2,4] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[1,5,6,3,4,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[1,5,6,4,2,3] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[1,5,6,4,3,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => 6
[1,6,2,3,4,5] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 4
[1,6,2,3,5,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[1,6,2,4,3,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[1,6,2,4,5,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[1,6,2,5,3,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[1,6,2,5,4,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[1,6,3,2,4,5] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[1,6,3,2,5,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[1,6,3,4,2,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[1,6,3,4,5,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[1,6,3,5,2,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[1,6,3,5,4,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[1,6,4,2,3,5] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[1,6,4,2,5,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[1,6,4,3,2,5] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[1,6,4,3,5,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[1,6,4,5,2,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[1,6,4,5,3,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[1,6,5,2,3,4] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[1,6,5,2,4,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[1,6,5,3,2,4] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[1,6,5,3,4,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[1,6,5,4,2,3] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[1,6,5,4,3,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}} => 10
[2,1,3,4,5,6] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => 5
[2,1,3,4,6,5] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[2,1,3,5,4,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[2,1,3,5,6,4] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[2,1,3,6,4,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[2,1,3,6,5,4] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[2,1,4,3,5,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[2,1,4,3,6,5] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[2,1,4,5,3,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[2,1,4,5,6,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[2,1,4,6,3,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[2,1,4,6,5,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[2,1,5,3,4,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[2,1,5,3,6,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[2,1,5,4,3,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[2,1,5,4,6,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[2,1,5,6,3,4] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[2,1,5,6,4,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[2,1,6,3,4,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[2,1,6,3,5,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[2,1,6,4,3,5] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[2,1,6,4,5,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[2,1,6,5,3,4] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[2,1,6,5,4,3] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => 11
[2,3,1,4,5,6] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 4
[2,3,1,4,6,5] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[2,3,1,5,4,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[2,3,1,5,6,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[2,3,1,6,4,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[2,3,1,6,5,4] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[2,3,4,1,5,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[2,3,4,1,6,5] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[2,3,4,5,1,6] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 2
[2,3,4,5,6,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => {{1,2,3,4,5},{6}} => 1
[2,3,4,6,1,5] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 2
[2,3,4,6,5,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3
[2,3,5,1,4,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[2,3,5,1,6,4] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[2,3,5,4,1,6] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[2,3,5,4,6,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[2,3,5,6,1,4] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 2
[2,3,5,6,4,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3
[2,3,6,1,4,5] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[2,3,6,1,5,4] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[2,3,6,4,1,5] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[2,3,6,4,5,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[2,3,6,5,1,4] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[2,3,6,5,4,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => 6
[2,4,1,3,5,6] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 4
[2,4,1,3,6,5] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[2,4,1,5,3,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[2,4,1,5,6,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[2,4,1,6,3,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[2,4,1,6,5,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[2,4,3,1,5,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[2,4,3,1,6,5] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[2,4,3,5,1,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[2,4,3,5,6,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[2,4,3,6,1,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[2,4,3,6,5,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[2,4,5,1,3,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[2,4,5,1,6,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[2,4,5,3,1,6] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[2,4,5,3,6,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[2,4,5,6,1,3] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 2
[2,4,5,6,3,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3
[2,4,6,1,3,5] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[2,4,6,1,5,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[2,4,6,3,1,5] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[2,4,6,3,5,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[2,4,6,5,1,3] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[2,4,6,5,3,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => 6
[2,5,1,3,4,6] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 4
[2,5,1,3,6,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[2,5,1,4,3,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[2,5,1,4,6,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[2,5,1,6,3,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[2,5,1,6,4,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[2,5,3,1,4,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[2,5,3,1,6,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[2,5,3,4,1,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[2,5,3,4,6,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[2,5,3,6,1,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[2,5,3,6,4,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[2,5,4,1,3,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[2,5,4,1,6,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[2,5,4,3,1,6] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[2,5,4,3,6,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[2,5,4,6,1,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[2,5,4,6,3,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[2,5,6,1,3,4] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[2,5,6,1,4,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[2,5,6,3,1,4] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[2,5,6,3,4,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[2,5,6,4,1,3] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[2,5,6,4,3,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => 6
[2,6,1,3,4,5] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 4
[2,6,1,3,5,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[2,6,1,4,3,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[2,6,1,4,5,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[2,6,1,5,3,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[2,6,1,5,4,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[2,6,3,1,4,5] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[2,6,3,1,5,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[2,6,3,4,1,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[2,6,3,4,5,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[2,6,3,5,1,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[2,6,3,5,4,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[2,6,4,1,3,5] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[2,6,4,1,5,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[2,6,4,3,1,5] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[2,6,4,3,5,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[2,6,4,5,1,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[2,6,4,5,3,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[2,6,5,1,3,4] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[2,6,5,1,4,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[2,6,5,3,1,4] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[2,6,5,3,4,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[2,6,5,4,1,3] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[2,6,5,4,3,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}} => 10
[3,1,2,4,5,6] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => 5
[3,1,2,4,6,5] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[3,1,2,5,4,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[3,1,2,5,6,4] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[3,1,2,6,4,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[3,1,2,6,5,4] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[3,1,4,2,5,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[3,1,4,2,6,5] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[3,1,4,5,2,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[3,1,4,5,6,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[3,1,4,6,2,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[3,1,4,6,5,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[3,1,5,2,4,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[3,1,5,2,6,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[3,1,5,4,2,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[3,1,5,4,6,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[3,1,5,6,2,4] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[3,1,5,6,4,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[3,1,6,2,4,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[3,1,6,2,5,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[3,1,6,4,2,5] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[3,1,6,4,5,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[3,1,6,5,2,4] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[3,1,6,5,4,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => 11
[3,2,1,4,5,6] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => 9
[3,2,1,4,6,5] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[3,2,1,5,4,6] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[3,2,1,5,6,4] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[3,2,1,6,4,5] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[3,2,1,6,5,4] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[3,2,4,1,5,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[3,2,4,1,6,5] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[3,2,4,5,1,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[3,2,4,5,6,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[3,2,4,6,1,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[3,2,4,6,5,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[3,2,5,1,4,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[3,2,5,1,6,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[3,2,5,4,1,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[3,2,5,4,6,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[3,2,5,6,1,4] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[3,2,5,6,4,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[3,2,6,1,4,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[3,2,6,1,5,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[3,2,6,4,1,5] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[3,2,6,4,5,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[3,2,6,5,1,4] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[3,2,6,5,4,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => 11
[3,4,1,2,5,6] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 4
[3,4,1,2,6,5] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[3,4,1,5,2,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[3,4,1,5,6,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[3,4,1,6,2,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[3,4,1,6,5,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[3,4,2,1,5,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[3,4,2,1,6,5] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[3,4,2,5,1,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[3,4,2,5,6,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[3,4,2,6,1,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[3,4,2,6,5,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[3,4,5,1,2,6] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[3,4,5,1,6,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[3,4,5,2,1,6] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[3,4,5,2,6,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[3,4,5,6,1,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => {{1,2,3,4},{5,6}} => 2
[3,4,5,6,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => {{1,2,3,4},{5},{6}} => 3
[3,4,6,1,2,5] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[3,4,6,1,5,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[3,4,6,2,1,5] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[3,4,6,2,5,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[3,4,6,5,1,2] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[3,4,6,5,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => 6
[3,5,1,2,4,6] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 4
[3,5,1,2,6,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[3,5,1,4,2,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[3,5,1,4,6,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[3,5,1,6,2,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[3,5,1,6,4,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[3,5,2,1,4,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[3,5,2,1,6,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[3,5,2,4,1,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[3,5,2,4,6,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[3,5,2,6,1,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[3,5,2,6,4,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[3,5,4,1,2,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[3,5,4,1,6,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[3,5,4,2,1,6] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[3,5,4,2,6,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[3,5,4,6,1,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[3,5,4,6,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[3,5,6,1,2,4] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[3,5,6,1,4,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[3,5,6,2,1,4] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[3,5,6,2,4,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[3,5,6,4,1,2] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[3,5,6,4,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => 6
[3,6,1,2,4,5] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 4
[3,6,1,2,5,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[3,6,1,4,2,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[3,6,1,4,5,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[3,6,1,5,2,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[3,6,1,5,4,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[3,6,2,1,4,5] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[3,6,2,1,5,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[3,6,2,4,1,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[3,6,2,4,5,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[3,6,2,5,1,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[3,6,2,5,4,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[3,6,4,1,2,5] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[3,6,4,1,5,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[3,6,4,2,1,5] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[3,6,4,2,5,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[3,6,4,5,1,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[3,6,4,5,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[3,6,5,1,2,4] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[3,6,5,1,4,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[3,6,5,2,1,4] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[3,6,5,2,4,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[3,6,5,4,1,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[3,6,5,4,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}} => 10
[4,1,2,3,5,6] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => 5
[4,1,2,3,6,5] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[4,1,2,5,3,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[4,1,2,5,6,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[4,1,2,6,3,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[4,1,2,6,5,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[4,1,3,2,5,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[4,1,3,2,6,5] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[4,1,3,5,2,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[4,1,3,5,6,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[4,1,3,6,2,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[4,1,3,6,5,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[4,1,5,2,3,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[4,1,5,2,6,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[4,1,5,3,2,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[4,1,5,3,6,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[4,1,5,6,2,3] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[4,1,5,6,3,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[4,1,6,2,3,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[4,1,6,2,5,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[4,1,6,3,2,5] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[4,1,6,3,5,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[4,1,6,5,2,3] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[4,1,6,5,3,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => 11
[4,2,1,3,5,6] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => 9
[4,2,1,3,6,5] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[4,2,1,5,3,6] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[4,2,1,5,6,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[4,2,1,6,3,5] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[4,2,1,6,5,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[4,2,3,1,5,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[4,2,3,1,6,5] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[4,2,3,5,1,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[4,2,3,5,6,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[4,2,3,6,1,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[4,2,3,6,5,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[4,2,5,1,3,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[4,2,5,1,6,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[4,2,5,3,1,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[4,2,5,3,6,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[4,2,5,6,1,3] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[4,2,5,6,3,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[4,2,6,1,3,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[4,2,6,1,5,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[4,2,6,3,1,5] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[4,2,6,3,5,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[4,2,6,5,1,3] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[4,2,6,5,3,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => 11
[4,3,1,2,5,6] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => 9
[4,3,1,2,6,5] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[4,3,1,5,2,6] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[4,3,1,5,6,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[4,3,1,6,2,5] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[4,3,1,6,5,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[4,3,2,1,5,6] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => 12
[4,3,2,1,6,5] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => 13
[4,3,2,5,1,6] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[4,3,2,5,6,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[4,3,2,6,1,5] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[4,3,2,6,5,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[4,3,5,1,2,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[4,3,5,1,6,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[4,3,5,2,1,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[4,3,5,2,6,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[4,3,5,6,1,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[4,3,5,6,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[4,3,6,1,2,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[4,3,6,1,5,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[4,3,6,2,1,5] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[4,3,6,2,5,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[4,3,6,5,1,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[4,3,6,5,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => 11
[4,5,1,2,3,6] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 4
[4,5,1,2,6,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[4,5,1,3,2,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[4,5,1,3,6,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[4,5,1,6,2,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[4,5,1,6,3,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[4,5,2,1,3,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[4,5,2,1,6,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[4,5,2,3,1,6] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[4,5,2,3,6,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[4,5,2,6,1,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[4,5,2,6,3,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[4,5,3,1,2,6] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[4,5,3,1,6,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[4,5,3,2,1,6] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[4,5,3,2,6,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[4,5,3,6,1,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[4,5,3,6,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[4,5,6,1,2,3] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => {{1,2,3},{4,5,6}} => 3
[4,5,6,1,3,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[4,5,6,2,1,3] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[4,5,6,2,3,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => {{1,2,3},{4,5},{6}} => 4
[4,5,6,3,1,2] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => {{1,2,3},{4},{5,6}} => 5
[4,5,6,3,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6}} => 6
[4,6,1,2,3,5] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 4
[4,6,1,2,5,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[4,6,1,3,2,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[4,6,1,3,5,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[4,6,1,5,2,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[4,6,1,5,3,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[4,6,2,1,3,5] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[4,6,2,1,5,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[4,6,2,3,1,5] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[4,6,2,3,5,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[4,6,2,5,1,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[4,6,2,5,3,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[4,6,3,1,2,5] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[4,6,3,1,5,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[4,6,3,2,1,5] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[4,6,3,2,5,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[4,6,3,5,1,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[4,6,3,5,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[4,6,5,1,2,3] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[4,6,5,1,3,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[4,6,5,2,1,3] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[4,6,5,2,3,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[4,6,5,3,1,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[4,6,5,3,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}} => 10
[5,1,2,3,4,6] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => 5
[5,1,2,3,6,4] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[5,1,2,4,3,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[5,1,2,4,6,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[5,1,2,6,3,4] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[5,1,2,6,4,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[5,1,3,2,4,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[5,1,3,2,6,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[5,1,3,4,2,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[5,1,3,4,6,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[5,1,3,6,2,4] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[5,1,3,6,4,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[5,1,4,2,3,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[5,1,4,2,6,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[5,1,4,3,2,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[5,1,4,3,6,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[5,1,4,6,2,3] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[5,1,4,6,3,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[5,1,6,2,3,4] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[5,1,6,2,4,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[5,1,6,3,2,4] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[5,1,6,3,4,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[5,1,6,4,2,3] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[5,1,6,4,3,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => 11
[5,2,1,3,4,6] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => 9
[5,2,1,3,6,4] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[5,2,1,4,3,6] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[5,2,1,4,6,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[5,2,1,6,3,4] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[5,2,1,6,4,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[5,2,3,1,4,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[5,2,3,1,6,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[5,2,3,4,1,6] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[5,2,3,4,6,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[5,2,3,6,1,4] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[5,2,3,6,4,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[5,2,4,1,3,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[5,2,4,1,6,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[5,2,4,3,1,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[5,2,4,3,6,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[5,2,4,6,1,3] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[5,2,4,6,3,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[5,2,6,1,3,4] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[5,2,6,1,4,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[5,2,6,3,1,4] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[5,2,6,3,4,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[5,2,6,4,1,3] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[5,2,6,4,3,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => 11
[5,3,1,2,4,6] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => 9
[5,3,1,2,6,4] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[5,3,1,4,2,6] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[5,3,1,4,6,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[5,3,1,6,2,4] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[5,3,1,6,4,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[5,3,2,1,4,6] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => 12
[5,3,2,1,6,4] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => 13
[5,3,2,4,1,6] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[5,3,2,4,6,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[5,3,2,6,1,4] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[5,3,2,6,4,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[5,3,4,1,2,6] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[5,3,4,1,6,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[5,3,4,2,1,6] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[5,3,4,2,6,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[5,3,4,6,1,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[5,3,4,6,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[5,3,6,1,2,4] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[5,3,6,1,4,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[5,3,6,2,1,4] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[5,3,6,2,4,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[5,3,6,4,1,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[5,3,6,4,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => 11
[5,4,1,2,3,6] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => 9
[5,4,1,2,6,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[5,4,1,3,2,6] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[5,4,1,3,6,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[5,4,1,6,2,3] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[5,4,1,6,3,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[5,4,2,1,3,6] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => 12
[5,4,2,1,6,3] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => 13
[5,4,2,3,1,6] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[5,4,2,3,6,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[5,4,2,6,1,3] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[5,4,2,6,3,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[5,4,3,1,2,6] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => 12
[5,4,3,1,6,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => 13
[5,4,3,2,1,6] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => 14
[5,4,3,2,6,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => 13
[5,4,3,6,1,2] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[5,4,3,6,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[5,4,6,1,2,3] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[5,4,6,1,3,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[5,4,6,2,1,3] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[5,4,6,2,3,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[5,4,6,3,1,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[5,4,6,3,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => 11
[5,6,1,2,3,4] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => {{1,2},{3,4,5,6}} => 4
[5,6,1,2,4,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[5,6,1,3,2,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[5,6,1,3,4,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[5,6,1,4,2,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[5,6,1,4,3,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[5,6,2,1,3,4] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[5,6,2,1,4,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[5,6,2,3,1,4] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[5,6,2,3,4,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => {{1,2},{3,4,5},{6}} => 5
[5,6,2,4,1,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[5,6,2,4,3,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[5,6,3,1,2,4] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[5,6,3,1,4,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[5,6,3,2,1,4] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[5,6,3,2,4,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[5,6,3,4,1,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => {{1,2},{3,4},{5,6}} => 6
[5,6,3,4,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => {{1,2},{3,4},{5},{6}} => 7
[5,6,4,1,2,3] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4,5,6}} => 7
[5,6,4,1,3,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[5,6,4,2,1,3] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[5,6,4,2,3,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4,5},{6}} => 8
[5,6,4,3,1,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5,6}} => 9
[5,6,4,3,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6}} => 10
[6,1,2,3,4,5] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2,3,4,5,6}} => 5
[6,1,2,3,5,4] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[6,1,2,4,3,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[6,1,2,4,5,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[6,1,2,5,3,4] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[6,1,2,5,4,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[6,1,3,2,4,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[6,1,3,2,5,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[6,1,3,4,2,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[6,1,3,4,5,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[6,1,3,5,2,4] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[6,1,3,5,4,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[6,1,4,2,3,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[6,1,4,2,5,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[6,1,4,3,2,5] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[6,1,4,3,5,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[6,1,4,5,2,3] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[6,1,4,5,3,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[6,1,5,2,3,4] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[6,1,5,2,4,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[6,1,5,3,2,4] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[6,1,5,3,4,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[6,1,5,4,2,3] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[6,1,5,4,3,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => 11
[6,2,1,3,4,5] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => 9
[6,2,1,3,5,4] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[6,2,1,4,3,5] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[6,2,1,4,5,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[6,2,1,5,3,4] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[6,2,1,5,4,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[6,2,3,1,4,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[6,2,3,1,5,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[6,2,3,4,1,5] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[6,2,3,4,5,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2,3,4,5},{6}} => 6
[6,2,3,5,1,4] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[6,2,3,5,4,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[6,2,4,1,3,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[6,2,4,1,5,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[6,2,4,3,1,5] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[6,2,4,3,5,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[6,2,4,5,1,3] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[6,2,4,5,3,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[6,2,5,1,3,4] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[6,2,5,1,4,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[6,2,5,3,1,4] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[6,2,5,3,4,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[6,2,5,4,1,3] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[6,2,5,4,3,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => 11
[6,3,1,2,4,5] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => 9
[6,3,1,2,5,4] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[6,3,1,4,2,5] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[6,3,1,4,5,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[6,3,1,5,2,4] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[6,3,1,5,4,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[6,3,2,1,4,5] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => 12
[6,3,2,1,5,4] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => 13
[6,3,2,4,1,5] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[6,3,2,4,5,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[6,3,2,5,1,4] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[6,3,2,5,4,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[6,3,4,1,2,5] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[6,3,4,1,5,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[6,3,4,2,1,5] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[6,3,4,2,5,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[6,3,4,5,1,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2,3,4},{5,6}} => 7
[6,3,4,5,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2,3,4},{5},{6}} => 8
[6,3,5,1,2,4] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[6,3,5,1,4,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[6,3,5,2,1,4] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[6,3,5,2,4,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[6,3,5,4,1,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[6,3,5,4,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => 11
[6,4,1,2,3,5] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => 9
[6,4,1,2,5,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[6,4,1,3,2,5] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[6,4,1,3,5,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[6,4,1,5,2,3] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[6,4,1,5,3,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[6,4,2,1,3,5] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => 12
[6,4,2,1,5,3] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => 13
[6,4,2,3,1,5] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[6,4,2,3,5,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[6,4,2,5,1,3] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[6,4,2,5,3,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[6,4,3,1,2,5] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => 12
[6,4,3,1,5,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => 13
[6,4,3,2,1,5] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => 14
[6,4,3,2,5,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => 13
[6,4,3,5,1,2] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[6,4,3,5,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[6,4,5,1,2,3] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2,3},{4,5,6}} => 8
[6,4,5,1,3,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[6,4,5,2,1,3] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[6,4,5,2,3,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2,3},{4,5},{6}} => 9
[6,4,5,3,1,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5,6}} => 10
[6,4,5,3,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6}} => 11
[6,5,1,2,3,4] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3,4,5,6}} => 9
[6,5,1,2,4,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[6,5,1,3,2,4] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[6,5,1,3,4,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[6,5,1,4,2,3] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[6,5,1,4,3,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[6,5,2,1,3,4] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => 12
[6,5,2,1,4,3] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => 13
[6,5,2,3,1,4] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[6,5,2,3,4,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3,4,5},{6}} => 10
[6,5,2,4,1,3] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[6,5,2,4,3,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[6,5,3,1,2,4] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => 12
[6,5,3,1,4,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => 13
[6,5,3,2,1,4] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => 14
[6,5,3,2,4,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => 13
[6,5,3,4,1,2] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3,4},{5,6}} => 11
[6,5,3,4,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3,4},{5},{6}} => 12
[6,5,4,1,2,3] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4,5,6}} => 12
[6,5,4,1,3,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => 13
[6,5,4,2,1,3] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => 14
[6,5,4,2,3,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4,5},{6}} => 13
[6,5,4,3,1,2] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5,6}} => 14
[6,5,4,3,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6}} => 15
[1,2,3,4,5,6,7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7}} => 0
[1,2,3,4,5,7,6] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 1
[1,2,3,4,6,5,7] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 2
[1,2,3,4,6,7,5] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 1
[1,2,3,4,7,5,6] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 2
[1,2,3,4,7,6,5] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => 3
[1,2,3,5,4,6,7] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[1,2,3,5,4,7,6] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,2,3,5,6,4,7] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 2
[1,2,3,5,6,7,4] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 1
[1,2,3,5,7,4,6] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 2
[1,2,3,5,7,6,4] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => 3
[1,2,3,6,4,5,7] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[1,2,3,6,4,7,5] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,2,3,6,5,4,7] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,2,3,6,5,7,4] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,2,3,6,7,4,5] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 2
[1,2,3,6,7,5,4] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => 3
[1,2,3,7,4,5,6] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[1,2,3,7,4,6,5] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,2,3,7,5,4,6] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,2,3,7,5,6,4] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,2,3,7,6,4,5] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,2,3,7,6,5,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 6
[1,2,4,3,5,6,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[1,2,4,3,5,7,6] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,2,4,3,6,5,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,2,4,3,6,7,5] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,2,4,3,7,5,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,2,4,3,7,6,5] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,2,4,5,3,6,7] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[1,2,4,5,3,7,6] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,2,4,5,6,3,7] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 2
[1,2,4,5,6,7,3] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 1
[1,2,4,5,7,3,6] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 2
[1,2,4,5,7,6,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => 3
[1,2,4,6,3,5,7] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[1,2,4,6,3,7,5] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,2,4,6,5,3,7] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,2,4,6,5,7,3] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,2,4,6,7,3,5] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 2
[1,2,4,6,7,5,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => 3
[1,2,4,7,3,5,6] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[1,2,4,7,3,6,5] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,2,4,7,5,3,6] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,2,4,7,5,6,3] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,2,4,7,6,3,5] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,2,4,7,6,5,3] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 6
[1,2,5,3,4,6,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[1,2,5,3,4,7,6] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,2,5,3,6,4,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,2,5,3,6,7,4] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,2,5,3,7,4,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,2,5,3,7,6,4] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,2,5,4,3,6,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,2,5,4,3,7,6] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,2,5,4,6,3,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,2,5,4,6,7,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,2,5,4,7,3,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,2,5,4,7,6,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,2,5,6,3,4,7] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[1,2,5,6,3,7,4] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,2,5,6,4,3,7] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,2,5,6,4,7,3] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,2,5,6,7,3,4] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 2
[1,2,5,6,7,4,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => 3
[1,2,5,7,3,4,6] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[1,2,5,7,3,6,4] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,2,5,7,4,3,6] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,2,5,7,4,6,3] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,2,5,7,6,3,4] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,2,5,7,6,4,3] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 6
[1,2,6,3,4,5,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[1,2,6,3,4,7,5] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,2,6,3,5,4,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,2,6,3,5,7,4] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,2,6,3,7,4,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,2,6,3,7,5,4] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,2,6,4,3,5,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,2,6,4,3,7,5] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,2,6,4,5,3,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,2,6,4,5,7,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,2,6,4,7,3,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,2,6,4,7,5,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,2,6,5,3,4,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,2,6,5,3,7,4] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,2,6,5,4,3,7] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[1,2,6,5,4,7,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,2,6,5,7,3,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,2,6,5,7,4,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,2,6,7,3,4,5] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[1,2,6,7,3,5,4] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,2,6,7,4,3,5] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,2,6,7,4,5,3] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,2,6,7,5,3,4] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,2,6,7,5,4,3] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 6
[1,2,7,3,4,5,6] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[1,2,7,3,4,6,5] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,2,7,3,5,4,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,2,7,3,5,6,4] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,2,7,3,6,4,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,2,7,3,6,5,4] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,2,7,4,3,5,6] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,2,7,4,3,6,5] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,2,7,4,5,3,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,2,7,4,5,6,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,2,7,4,6,3,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,2,7,4,6,5,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,2,7,5,3,4,6] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,2,7,5,3,6,4] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,2,7,5,4,3,6] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[1,2,7,5,4,6,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,2,7,5,6,3,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,2,7,5,6,4,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,2,7,6,3,4,5] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,2,7,6,3,5,4] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,2,7,6,4,3,5] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[1,2,7,6,4,5,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,2,7,6,5,3,4] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[1,2,7,6,5,4,3] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 10
[1,3,2,4,5,6,7] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 5
[1,3,2,4,5,7,6] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[1,3,2,4,6,5,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,3,2,4,6,7,5] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[1,3,2,4,7,5,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,3,2,4,7,6,5] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,3,2,5,4,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[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] => {{1,2},{3,4},{5,6},{7}} => 9
[1,3,2,5,6,4,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,3,2,5,6,7,4] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[1,3,2,5,7,4,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,3,2,5,7,6,4] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,3,2,6,4,5,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[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] => {{1,2},{3,4},{5,6},{7}} => 9
[1,3,2,6,5,4,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,3,2,6,5,7,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,3,2,6,7,4,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,3,2,6,7,5,4] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,3,2,7,4,5,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[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] => {{1,2},{3,4},{5,6},{7}} => 9
[1,3,2,7,5,4,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,3,2,7,5,6,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,3,2,7,6,4,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,3,2,7,6,5,4] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[1,3,4,2,5,6,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[1,3,4,2,5,7,6] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,3,4,2,6,5,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,3,4,2,6,7,5] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,3,4,2,7,5,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,3,4,2,7,6,5] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,3,4,5,2,6,7] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[1,3,4,5,2,7,6] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,3,4,5,6,2,7] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 2
[1,3,4,5,6,7,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 1
[1,3,4,5,7,2,6] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 2
[1,3,4,5,7,6,2] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => 3
[1,3,4,6,2,5,7] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[1,3,4,6,2,7,5] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,3,4,6,5,2,7] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,3,4,6,5,7,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,3,4,6,7,2,5] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 2
[1,3,4,6,7,5,2] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => 3
[1,3,4,7,2,5,6] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[1,3,4,7,2,6,5] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,3,4,7,5,2,6] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,3,4,7,5,6,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,3,4,7,6,2,5] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,3,4,7,6,5,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 6
[1,3,5,2,4,6,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[1,3,5,2,4,7,6] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,3,5,2,6,4,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,3,5,2,6,7,4] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,3,5,2,7,4,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,3,5,2,7,6,4] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,3,5,4,2,6,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,3,5,4,2,7,6] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,3,5,4,6,2,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,3,5,4,6,7,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,3,5,4,7,2,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,3,5,4,7,6,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,3,5,6,2,4,7] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[1,3,5,6,2,7,4] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,3,5,6,4,2,7] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,3,5,6,4,7,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,3,5,6,7,2,4] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 2
[1,3,5,6,7,4,2] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => 3
[1,3,5,7,2,4,6] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[1,3,5,7,2,6,4] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,3,5,7,4,2,6] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,3,5,7,4,6,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,3,5,7,6,2,4] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,3,5,7,6,4,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 6
[1,3,6,2,4,5,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[1,3,6,2,4,7,5] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,3,6,2,5,4,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,3,6,2,5,7,4] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,3,6,2,7,4,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,3,6,2,7,5,4] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,3,6,4,2,5,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,3,6,4,2,7,5] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,3,6,4,5,2,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,3,6,4,5,7,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,3,6,4,7,2,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,3,6,4,7,5,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,3,6,5,2,4,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,3,6,5,2,7,4] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,3,6,5,4,2,7] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[1,3,6,5,4,7,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,3,6,5,7,2,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,3,6,5,7,4,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,3,6,7,2,4,5] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[1,3,6,7,2,5,4] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,3,6,7,4,2,5] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,3,6,7,4,5,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,3,6,7,5,2,4] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,3,6,7,5,4,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 6
[1,3,7,2,4,5,6] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[1,3,7,2,4,6,5] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,3,7,2,5,4,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,3,7,2,5,6,4] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,3,7,2,6,4,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,3,7,2,6,5,4] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,3,7,4,2,5,6] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,3,7,4,2,6,5] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,3,7,4,5,2,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,3,7,4,5,6,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,3,7,4,6,2,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,3,7,4,6,5,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,3,7,5,2,4,6] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,3,7,5,2,6,4] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,3,7,5,4,2,6] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[1,3,7,5,4,6,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,3,7,5,6,2,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,3,7,5,6,4,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,3,7,6,2,4,5] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,3,7,6,2,5,4] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,3,7,6,4,2,5] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[1,3,7,6,4,5,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,3,7,6,5,2,4] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[1,3,7,6,5,4,2] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 10
[1,4,2,3,5,6,7] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 5
[1,4,2,3,5,7,6] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[1,4,2,3,6,5,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,4,2,3,6,7,5] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[1,4,2,3,7,5,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,4,2,3,7,6,5] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,4,2,5,3,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[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] => {{1,2},{3,4},{5,6},{7}} => 9
[1,4,2,5,6,3,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,4,2,5,6,7,3] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[1,4,2,5,7,3,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,4,2,5,7,6,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,4,2,6,3,5,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[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] => {{1,2},{3,4},{5,6},{7}} => 9
[1,4,2,6,5,3,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,4,2,6,5,7,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,4,2,6,7,3,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,4,2,6,7,5,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,4,2,7,3,5,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[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] => {{1,2},{3,4},{5,6},{7}} => 9
[1,4,2,7,5,3,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,4,2,7,5,6,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,4,2,7,6,3,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,4,2,7,6,5,3] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[1,4,3,2,5,6,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[1,4,3,2,5,7,6] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,4,3,2,6,5,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,4,3,2,6,7,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,4,3,2,7,5,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,4,3,2,7,6,5] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[1,4,3,5,2,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[1,4,3,5,2,7,6] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,4,3,5,6,2,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,4,3,5,6,7,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[1,4,3,5,7,2,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,4,3,5,7,6,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,4,3,6,2,5,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[1,4,3,6,2,7,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,4,3,6,5,2,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,4,3,6,5,7,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,4,3,6,7,2,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,4,3,6,7,5,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,4,3,7,2,5,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[1,4,3,7,2,6,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,4,3,7,5,2,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,4,3,7,5,6,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,4,3,7,6,2,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,4,3,7,6,5,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[1,4,5,2,3,6,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[1,4,5,2,3,7,6] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,4,5,2,6,3,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,4,5,2,6,7,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,4,5,2,7,3,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,4,5,2,7,6,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,4,5,3,2,6,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,4,5,3,2,7,6] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,4,5,3,6,2,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,4,5,3,6,7,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,4,5,3,7,2,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,4,5,3,7,6,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,4,5,6,2,3,7] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[1,4,5,6,2,7,3] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,4,5,6,3,2,7] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,4,5,6,3,7,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,4,5,6,7,2,3] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 2
[1,4,5,6,7,3,2] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => 3
[1,4,5,7,2,3,6] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[1,4,5,7,2,6,3] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,4,5,7,3,2,6] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,4,5,7,3,6,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,4,5,7,6,2,3] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,4,5,7,6,3,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 6
[1,4,6,2,3,5,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[1,4,6,2,3,7,5] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,4,6,2,5,3,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,4,6,2,5,7,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,4,6,2,7,3,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,4,6,2,7,5,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,4,6,3,2,5,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,4,6,3,2,7,5] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,4,6,3,5,2,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,4,6,3,5,7,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,4,6,3,7,2,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,4,6,3,7,5,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,4,6,5,2,3,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,4,6,5,2,7,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,4,6,5,3,2,7] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[1,4,6,5,3,7,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,4,6,5,7,2,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,4,6,5,7,3,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,4,6,7,2,3,5] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[1,4,6,7,2,5,3] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,4,6,7,3,2,5] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,4,6,7,3,5,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,4,6,7,5,2,3] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,4,6,7,5,3,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 6
[1,4,7,2,3,5,6] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[1,4,7,2,3,6,5] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,4,7,2,5,3,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,4,7,2,5,6,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,4,7,2,6,3,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,4,7,2,6,5,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,4,7,3,2,5,6] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,4,7,3,2,6,5] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,4,7,3,5,2,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,4,7,3,5,6,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,4,7,3,6,2,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,4,7,3,6,5,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,4,7,5,2,3,6] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,4,7,5,2,6,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,4,7,5,3,2,6] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[1,4,7,5,3,6,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,4,7,5,6,2,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,4,7,5,6,3,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,4,7,6,2,3,5] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,4,7,6,2,5,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,4,7,6,3,2,5] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[1,4,7,6,3,5,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,4,7,6,5,2,3] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[1,4,7,6,5,3,2] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 10
[1,5,2,3,4,6,7] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 5
[1,5,2,3,4,7,6] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[1,5,2,3,6,4,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,5,2,3,6,7,4] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[1,5,2,3,7,4,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,5,2,3,7,6,4] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,5,2,4,3,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[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] => {{1,2},{3,4},{5,6},{7}} => 9
[1,5,2,4,6,3,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,5,2,4,6,7,3] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[1,5,2,4,7,3,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,5,2,4,7,6,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,5,2,6,3,4,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[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] => {{1,2},{3,4},{5,6},{7}} => 9
[1,5,2,6,4,3,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,5,2,6,4,7,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,5,2,6,7,3,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,5,2,6,7,4,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,5,2,7,3,4,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[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] => {{1,2},{3,4},{5,6},{7}} => 9
[1,5,2,7,4,3,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,5,2,7,4,6,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,5,2,7,6,3,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,5,2,7,6,4,3] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[1,5,3,2,4,6,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[1,5,3,2,4,7,6] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,5,3,2,6,4,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,5,3,2,6,7,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,5,3,2,7,4,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,5,3,2,7,6,4] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[1,5,3,4,2,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[1,5,3,4,2,7,6] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,5,3,4,6,2,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,5,3,4,6,7,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[1,5,3,4,7,2,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,5,3,4,7,6,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,5,3,6,2,4,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[1,5,3,6,2,7,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,5,3,6,4,2,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,5,3,6,4,7,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,5,3,6,7,2,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,5,3,6,7,4,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,5,3,7,2,4,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[1,5,3,7,2,6,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,5,3,7,4,2,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,5,3,7,4,6,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,5,3,7,6,2,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,5,3,7,6,4,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[1,5,4,2,3,6,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[1,5,4,2,3,7,6] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,5,4,2,6,3,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,5,4,2,6,7,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,5,4,2,7,3,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,5,4,2,7,6,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[1,5,4,3,2,6,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[1,5,4,3,2,7,6] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[1,5,4,3,6,2,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,5,4,3,6,7,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,5,4,3,7,2,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,5,4,3,7,6,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[1,5,4,6,2,3,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[1,5,4,6,2,7,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,5,4,6,3,2,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,5,4,6,3,7,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,5,4,6,7,2,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,5,4,6,7,3,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,5,4,7,2,3,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[1,5,4,7,2,6,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,5,4,7,3,2,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,5,4,7,3,6,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,5,4,7,6,2,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,5,4,7,6,3,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[1,5,6,2,3,4,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[1,5,6,2,3,7,4] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,5,6,2,4,3,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,5,6,2,4,7,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,5,6,2,7,3,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,5,6,2,7,4,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,5,6,3,2,4,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,5,6,3,2,7,4] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,5,6,3,4,2,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,5,6,3,4,7,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,5,6,3,7,2,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,5,6,3,7,4,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,5,6,4,2,3,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,5,6,4,2,7,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,5,6,4,3,2,7] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[1,5,6,4,3,7,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,5,6,4,7,2,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,5,6,4,7,3,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,5,6,7,2,3,4] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[1,5,6,7,2,4,3] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,5,6,7,3,2,4] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,5,6,7,3,4,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[1,5,6,7,4,2,3] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[1,5,6,7,4,3,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 6
[1,5,7,2,3,4,6] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[1,5,7,2,3,6,4] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,5,7,2,4,3,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,5,7,2,4,6,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,5,7,2,6,3,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,5,7,2,6,4,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,5,7,3,2,4,6] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,5,7,3,2,6,4] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,5,7,3,4,2,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,5,7,3,4,6,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,5,7,3,6,2,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,5,7,3,6,4,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,5,7,4,2,3,6] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,5,7,4,2,6,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,5,7,4,3,2,6] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[1,5,7,4,3,6,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,5,7,4,6,2,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,5,7,4,6,3,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,5,7,6,2,3,4] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,5,7,6,2,4,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,5,7,6,3,2,4] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[1,5,7,6,3,4,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,5,7,6,4,2,3] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[1,5,7,6,4,3,2] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 10
[1,6,2,3,4,5,7] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 5
[1,6,2,3,4,7,5] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[1,6,2,3,5,4,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,6,2,3,5,7,4] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[1,6,2,3,7,4,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,6,2,3,7,5,4] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,6,2,4,3,5,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[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] => {{1,2},{3,4},{5,6},{7}} => 9
[1,6,2,4,5,3,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,6,2,4,5,7,3] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[1,6,2,4,7,3,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,6,2,4,7,5,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,6,2,5,3,4,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[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] => {{1,2},{3,4},{5,6},{7}} => 9
[1,6,2,5,4,3,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,6,2,5,4,7,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,6,2,5,7,3,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,6,2,5,7,4,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,6,2,7,3,4,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[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] => {{1,2},{3,4},{5,6},{7}} => 9
[1,6,2,7,4,3,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,6,2,7,4,5,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,6,2,7,5,3,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,6,2,7,5,4,3] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[1,6,3,2,4,5,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[1,6,3,2,4,7,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,6,3,2,5,4,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,6,3,2,5,7,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,6,3,2,7,4,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,6,3,2,7,5,4] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[1,6,3,4,2,5,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[1,6,3,4,2,7,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,6,3,4,5,2,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,6,3,4,5,7,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[1,6,3,4,7,2,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,6,3,4,7,5,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,6,3,5,2,4,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[1,6,3,5,2,7,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,6,3,5,4,2,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,6,3,5,4,7,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,6,3,5,7,2,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,6,3,5,7,4,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,6,3,7,2,4,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[1,6,3,7,2,5,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,6,3,7,4,2,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,6,3,7,4,5,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,6,3,7,5,2,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,6,3,7,5,4,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[1,6,4,2,3,5,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[1,6,4,2,3,7,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,6,4,2,5,3,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,6,4,2,5,7,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,6,4,2,7,3,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,6,4,2,7,5,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[1,6,4,3,2,5,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[1,6,4,3,2,7,5] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[1,6,4,3,5,2,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,6,4,3,5,7,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,6,4,3,7,2,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,6,4,3,7,5,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[1,6,4,5,2,3,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[1,6,4,5,2,7,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,6,4,5,3,2,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,6,4,5,3,7,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,6,4,5,7,2,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,6,4,5,7,3,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,6,4,7,2,3,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[1,6,4,7,2,5,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,6,4,7,3,2,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,6,4,7,3,5,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,6,4,7,5,2,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,6,4,7,5,3,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[1,6,5,2,3,4,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[1,6,5,2,3,7,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,6,5,2,4,3,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,6,5,2,4,7,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,6,5,2,7,3,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,6,5,2,7,4,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[1,6,5,3,2,4,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[1,6,5,3,2,7,4] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[1,6,5,3,4,2,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,6,5,3,4,7,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,6,5,3,7,2,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,6,5,3,7,4,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[1,6,5,4,2,3,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[1,6,5,4,2,7,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[1,6,5,4,3,2,7] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[1,6,5,4,3,7,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[1,6,5,4,7,2,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,6,5,4,7,3,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[1,6,5,7,2,3,4] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[1,6,5,7,2,4,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,6,5,7,3,2,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,6,5,7,3,4,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,6,5,7,4,2,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,6,5,7,4,3,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[1,6,7,2,3,4,5] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[1,6,7,2,3,5,4] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,6,7,2,4,3,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,6,7,2,4,5,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,6,7,2,5,3,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,6,7,2,5,4,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,6,7,3,2,4,5] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,6,7,3,2,5,4] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,6,7,3,4,2,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,6,7,3,4,5,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[1,6,7,3,5,2,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,6,7,3,5,4,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,6,7,4,2,3,5] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,6,7,4,2,5,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,6,7,4,3,2,5] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[1,6,7,4,3,5,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,6,7,4,5,2,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[1,6,7,4,5,3,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[1,6,7,5,2,3,4] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[1,6,7,5,2,4,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,6,7,5,3,2,4] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[1,6,7,5,3,4,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[1,6,7,5,4,2,3] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[1,6,7,5,4,3,2] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 10
[1,7,2,3,4,5,6] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 5
[1,7,2,3,4,6,5] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[1,7,2,3,5,4,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,7,2,3,5,6,4] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[1,7,2,3,6,4,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,7,2,3,6,5,4] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,7,2,4,3,5,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[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] => {{1,2},{3,4},{5,6},{7}} => 9
[1,7,2,4,5,3,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,7,2,4,5,6,3] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[1,7,2,4,6,3,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,7,2,4,6,5,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,7,2,5,3,4,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[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] => {{1,2},{3,4},{5,6},{7}} => 9
[1,7,2,5,4,3,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,7,2,5,4,6,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,7,2,5,6,3,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,7,2,5,6,4,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,7,2,6,3,4,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[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] => {{1,2},{3,4},{5,6},{7}} => 9
[1,7,2,6,4,3,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,7,2,6,4,5,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,7,2,6,5,3,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,7,2,6,5,4,3] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[1,7,3,2,4,5,6] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[1,7,3,2,4,6,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,7,3,2,5,4,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,7,3,2,5,6,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,7,3,2,6,4,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,7,3,2,6,5,4] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[1,7,3,4,2,5,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[1,7,3,4,2,6,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,7,3,4,5,2,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,7,3,4,5,6,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[1,7,3,4,6,2,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,7,3,4,6,5,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,7,3,5,2,4,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[1,7,3,5,2,6,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,7,3,5,4,2,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,7,3,5,4,6,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,7,3,5,6,2,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,7,3,5,6,4,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,7,3,6,2,4,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[1,7,3,6,2,5,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,7,3,6,4,2,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,7,3,6,4,5,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,7,3,6,5,2,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,7,3,6,5,4,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[1,7,4,2,3,5,6] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[1,7,4,2,3,6,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,7,4,2,5,3,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,7,4,2,5,6,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,7,4,2,6,3,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,7,4,2,6,5,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[1,7,4,3,2,5,6] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[1,7,4,3,2,6,5] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[1,7,4,3,5,2,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,7,4,3,5,6,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,7,4,3,6,2,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,7,4,3,6,5,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[1,7,4,5,2,3,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[1,7,4,5,2,6,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,7,4,5,3,2,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,7,4,5,3,6,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,7,4,5,6,2,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[1,7,4,5,6,3,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[1,7,4,6,2,3,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[1,7,4,6,2,5,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,7,4,6,3,2,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,7,4,6,3,5,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,7,4,6,5,2,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,7,4,6,5,3,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[1,7,5,2,3,4,6] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[1,7,5,2,3,6,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,7,5,2,4,3,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,7,5,2,4,6,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,7,5,2,6,3,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,7,5,2,6,4,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[1,7,5,3,2,4,6] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[1,7,5,3,2,6,4] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[1,7,5,3,4,2,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,7,5,3,4,6,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,7,5,3,6,2,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,7,5,3,6,4,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[1,7,5,4,2,3,6] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[1,7,5,4,2,6,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[1,7,5,4,3,2,6] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[1,7,5,4,3,6,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[1,7,5,4,6,2,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,7,5,4,6,3,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[1,7,5,6,2,3,4] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[1,7,5,6,2,4,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,7,5,6,3,2,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,7,5,6,3,4,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[1,7,5,6,4,2,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[1,7,5,6,4,3,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[1,7,6,2,3,4,5] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[1,7,6,2,3,5,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,7,6,2,4,3,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,7,6,2,4,5,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,7,6,2,5,3,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,7,6,2,5,4,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[1,7,6,3,2,4,5] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[1,7,6,3,2,5,4] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[1,7,6,3,4,2,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,7,6,3,4,5,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[1,7,6,3,5,2,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,7,6,3,5,4,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[1,7,6,4,2,3,5] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[1,7,6,4,2,5,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[1,7,6,4,3,2,5] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[1,7,6,4,3,5,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[1,7,6,4,5,2,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[1,7,6,4,5,3,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[1,7,6,5,2,3,4] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[1,7,6,5,2,4,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[1,7,6,5,3,2,4] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[1,7,6,5,3,4,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[1,7,6,5,4,2,3] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[1,7,6,5,4,3,2] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}} => 15
[2,1,3,4,5,6,7] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => 6
[2,1,3,4,5,7,6] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[2,1,3,4,6,5,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[2,1,3,4,6,7,5] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[2,1,3,4,7,5,6] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[2,1,3,4,7,6,5] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[2,1,3,5,4,6,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[2,1,3,5,4,7,6] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[2,1,3,5,6,4,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[2,1,3,5,6,7,4] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[2,1,3,5,7,4,6] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[2,1,3,5,7,6,4] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[2,1,3,6,4,5,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[2,1,3,6,4,7,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[2,1,3,6,5,4,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[2,1,3,6,5,7,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[2,1,3,6,7,4,5] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[2,1,3,6,7,5,4] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[2,1,3,7,4,5,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[2,1,3,7,4,6,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[2,1,3,7,5,4,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[2,1,3,7,5,6,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[2,1,3,7,6,4,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[2,1,3,7,6,5,4] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[2,1,4,3,5,6,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[2,1,4,3,5,7,6] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[2,1,4,3,6,5,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[2,1,4,3,6,7,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[2,1,4,3,7,5,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[2,1,4,3,7,6,5] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[2,1,4,5,3,6,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[2,1,4,5,3,7,6] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[2,1,4,5,6,3,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[2,1,4,5,6,7,3] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[2,1,4,5,7,3,6] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[2,1,4,5,7,6,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[2,1,4,6,3,5,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[2,1,4,6,3,7,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[2,1,4,6,5,3,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[2,1,4,6,5,7,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[2,1,4,6,7,3,5] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[2,1,4,6,7,5,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[2,1,4,7,3,5,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[2,1,4,7,3,6,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[2,1,4,7,5,3,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[2,1,4,7,5,6,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[2,1,4,7,6,3,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[2,1,4,7,6,5,3] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[2,1,5,3,4,6,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[2,1,5,3,4,7,6] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[2,1,5,3,6,4,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[2,1,5,3,6,7,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[2,1,5,3,7,4,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[2,1,5,3,7,6,4] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[2,1,5,4,3,6,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[2,1,5,4,3,7,6] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[2,1,5,4,6,3,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[2,1,5,4,6,7,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[2,1,5,4,7,3,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[2,1,5,4,7,6,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[2,1,5,6,3,4,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[2,1,5,6,3,7,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[2,1,5,6,4,3,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[2,1,5,6,4,7,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[2,1,5,6,7,3,4] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[2,1,5,6,7,4,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[2,1,5,7,3,4,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[2,1,5,7,3,6,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[2,1,5,7,4,3,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[2,1,5,7,4,6,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[2,1,5,7,6,3,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[2,1,5,7,6,4,3] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[2,1,6,3,4,5,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[2,1,6,3,4,7,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[2,1,6,3,5,4,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[2,1,6,3,5,7,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[2,1,6,3,7,4,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[2,1,6,3,7,5,4] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[2,1,6,4,3,5,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[2,1,6,4,3,7,5] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[2,1,6,4,5,3,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[2,1,6,4,5,7,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[2,1,6,4,7,3,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[2,1,6,4,7,5,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[2,1,6,5,3,4,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[2,1,6,5,3,7,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[2,1,6,5,4,3,7] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[2,1,6,5,4,7,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[2,1,6,5,7,3,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[2,1,6,5,7,4,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[2,1,6,7,3,4,5] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[2,1,6,7,3,5,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[2,1,6,7,4,3,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[2,1,6,7,4,5,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[2,1,6,7,5,3,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[2,1,6,7,5,4,3] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[2,1,7,3,4,5,6] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[2,1,7,3,4,6,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[2,1,7,3,5,4,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[2,1,7,3,5,6,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[2,1,7,3,6,4,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[2,1,7,3,6,5,4] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[2,1,7,4,3,5,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[2,1,7,4,3,6,5] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[2,1,7,4,5,3,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[2,1,7,4,5,6,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[2,1,7,4,6,3,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[2,1,7,4,6,5,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[2,1,7,5,3,4,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[2,1,7,5,3,6,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[2,1,7,5,4,3,6] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[2,1,7,5,4,6,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[2,1,7,5,6,3,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[2,1,7,5,6,4,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[2,1,7,6,3,4,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[2,1,7,6,3,5,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[2,1,7,6,4,3,5] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[2,1,7,6,4,5,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[2,1,7,6,5,3,4] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[2,1,7,6,5,4,3] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 16
[2,3,1,4,5,6,7] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 5
[2,3,1,4,5,7,6] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[2,3,1,4,6,5,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,3,1,4,6,7,5] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[2,3,1,4,7,5,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,3,1,4,7,6,5] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,3,1,5,4,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,3,1,5,4,7,6] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,3,1,5,6,4,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,3,1,5,6,7,4] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[2,3,1,5,7,4,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,3,1,5,7,6,4] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,3,1,6,4,5,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,3,1,6,4,7,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,3,1,6,5,4,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,3,1,6,5,7,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,3,1,6,7,4,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,3,1,6,7,5,4] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,3,1,7,4,5,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,3,1,7,4,6,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,3,1,7,5,4,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,3,1,7,5,6,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,3,1,7,6,4,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,3,1,7,6,5,4] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[2,3,4,1,5,6,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[2,3,4,1,5,7,6] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,3,4,1,6,5,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,3,4,1,6,7,5] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,3,4,1,7,5,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,3,4,1,7,6,5] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,3,4,5,1,6,7] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[2,3,4,5,1,7,6] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[2,3,4,5,6,1,7] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 2
[2,3,4,5,6,7,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6},{7}} => 1
[2,3,4,5,7,1,6] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 2
[2,3,4,5,7,6,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => 3
[2,3,4,6,1,5,7] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[2,3,4,6,1,7,5] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[2,3,4,6,5,1,7] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[2,3,4,6,5,7,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[2,3,4,6,7,1,5] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 2
[2,3,4,6,7,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => 3
[2,3,4,7,1,5,6] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[2,3,4,7,1,6,5] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[2,3,4,7,5,1,6] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[2,3,4,7,5,6,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[2,3,4,7,6,1,5] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[2,3,4,7,6,5,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 6
[2,3,5,1,4,6,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[2,3,5,1,4,7,6] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,3,5,1,6,4,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,3,5,1,6,7,4] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,3,5,1,7,4,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,3,5,1,7,6,4] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,3,5,4,1,6,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[2,3,5,4,1,7,6] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,3,5,4,6,1,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,3,5,4,6,7,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,3,5,4,7,1,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,3,5,4,7,6,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,3,5,6,1,4,7] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[2,3,5,6,1,7,4] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[2,3,5,6,4,1,7] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[2,3,5,6,4,7,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[2,3,5,6,7,1,4] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 2
[2,3,5,6,7,4,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => 3
[2,3,5,7,1,4,6] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[2,3,5,7,1,6,4] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[2,3,5,7,4,1,6] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[2,3,5,7,4,6,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[2,3,5,7,6,1,4] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[2,3,5,7,6,4,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 6
[2,3,6,1,4,5,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[2,3,6,1,4,7,5] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,3,6,1,5,4,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,3,6,1,5,7,4] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,3,6,1,7,4,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,3,6,1,7,5,4] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,3,6,4,1,5,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[2,3,6,4,1,7,5] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,3,6,4,5,1,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,3,6,4,5,7,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,3,6,4,7,1,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,3,6,4,7,5,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,3,6,5,1,4,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[2,3,6,5,1,7,4] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,3,6,5,4,1,7] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[2,3,6,5,4,7,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,3,6,5,7,1,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,3,6,5,7,4,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,3,6,7,1,4,5] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[2,3,6,7,1,5,4] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[2,3,6,7,4,1,5] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[2,3,6,7,4,5,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[2,3,6,7,5,1,4] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[2,3,6,7,5,4,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 6
[2,3,7,1,4,5,6] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[2,3,7,1,4,6,5] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,3,7,1,5,4,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,3,7,1,5,6,4] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,3,7,1,6,4,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,3,7,1,6,5,4] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,3,7,4,1,5,6] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[2,3,7,4,1,6,5] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,3,7,4,5,1,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,3,7,4,5,6,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,3,7,4,6,1,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,3,7,4,6,5,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,3,7,5,1,4,6] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[2,3,7,5,1,6,4] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,3,7,5,4,1,6] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[2,3,7,5,4,6,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,3,7,5,6,1,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,3,7,5,6,4,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,3,7,6,1,4,5] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[2,3,7,6,1,5,4] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,3,7,6,4,1,5] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[2,3,7,6,4,5,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,3,7,6,5,1,4] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[2,3,7,6,5,4,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 10
[2,4,1,3,5,6,7] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 5
[2,4,1,3,5,7,6] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[2,4,1,3,6,5,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,4,1,3,6,7,5] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[2,4,1,3,7,5,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,4,1,3,7,6,5] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,4,1,5,3,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,4,1,5,3,7,6] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,4,1,5,6,3,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,4,1,5,6,7,3] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[2,4,1,5,7,3,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,4,1,5,7,6,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,4,1,6,3,5,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,4,1,6,3,7,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,4,1,6,5,3,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,4,1,6,5,7,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,4,1,6,7,3,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,4,1,6,7,5,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,4,1,7,3,5,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,4,1,7,3,6,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,4,1,7,5,3,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,4,1,7,5,6,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,4,1,7,6,3,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,4,1,7,6,5,3] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[2,4,3,1,5,6,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[2,4,3,1,5,7,6] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,4,3,1,6,5,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,4,3,1,6,7,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,4,3,1,7,5,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,4,3,1,7,6,5] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[2,4,3,5,1,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,4,3,5,1,7,6] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,4,3,5,6,1,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,4,3,5,6,7,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[2,4,3,5,7,1,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,4,3,5,7,6,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,4,3,6,1,5,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,4,3,6,1,7,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,4,3,6,5,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,4,3,6,5,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,4,3,6,7,1,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,4,3,6,7,5,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,4,3,7,1,5,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,4,3,7,1,6,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,4,3,7,5,1,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,4,3,7,5,6,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,4,3,7,6,1,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,4,3,7,6,5,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[2,4,5,1,3,6,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[2,4,5,1,3,7,6] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,4,5,1,6,3,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,4,5,1,6,7,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,4,5,1,7,3,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,4,5,1,7,6,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,4,5,3,1,6,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[2,4,5,3,1,7,6] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,4,5,3,6,1,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,4,5,3,6,7,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,4,5,3,7,1,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,4,5,3,7,6,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,4,5,6,1,3,7] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[2,4,5,6,1,7,3] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[2,4,5,6,3,1,7] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[2,4,5,6,3,7,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[2,4,5,6,7,1,3] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 2
[2,4,5,6,7,3,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => 3
[2,4,5,7,1,3,6] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[2,4,5,7,1,6,3] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[2,4,5,7,3,1,6] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[2,4,5,7,3,6,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[2,4,5,7,6,1,3] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[2,4,5,7,6,3,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 6
[2,4,6,1,3,5,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[2,4,6,1,3,7,5] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,4,6,1,5,3,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,4,6,1,5,7,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,4,6,1,7,3,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,4,6,1,7,5,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,4,6,3,1,5,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[2,4,6,3,1,7,5] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,4,6,3,5,1,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,4,6,3,5,7,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,4,6,3,7,1,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,4,6,3,7,5,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,4,6,5,1,3,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[2,4,6,5,1,7,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,4,6,5,3,1,7] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[2,4,6,5,3,7,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,4,6,5,7,1,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,4,6,5,7,3,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,4,6,7,1,3,5] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[2,4,6,7,1,5,3] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[2,4,6,7,3,1,5] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[2,4,6,7,3,5,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[2,4,6,7,5,1,3] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[2,4,6,7,5,3,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 6
[2,4,7,1,3,5,6] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[2,4,7,1,3,6,5] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,4,7,1,5,3,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,4,7,1,5,6,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,4,7,1,6,3,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,4,7,1,6,5,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,4,7,3,1,5,6] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[2,4,7,3,1,6,5] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,4,7,3,5,1,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,4,7,3,5,6,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,4,7,3,6,1,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,4,7,3,6,5,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,4,7,5,1,3,6] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[2,4,7,5,1,6,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,4,7,5,3,1,6] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[2,4,7,5,3,6,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,4,7,5,6,1,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,4,7,5,6,3,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,4,7,6,1,3,5] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[2,4,7,6,1,5,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,4,7,6,3,1,5] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[2,4,7,6,3,5,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,4,7,6,5,1,3] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[2,4,7,6,5,3,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 10
[2,5,1,3,4,6,7] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 5
[2,5,1,3,4,7,6] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[2,5,1,3,6,4,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,5,1,3,6,7,4] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[2,5,1,3,7,4,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,5,1,3,7,6,4] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,5,1,4,3,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,5,1,4,3,7,6] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,5,1,4,6,3,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,5,1,4,6,7,3] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[2,5,1,4,7,3,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,5,1,4,7,6,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,5,1,6,3,4,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,5,1,6,3,7,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,5,1,6,4,3,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,5,1,6,4,7,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,5,1,6,7,3,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,5,1,6,7,4,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,5,1,7,3,4,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,5,1,7,3,6,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,5,1,7,4,3,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,5,1,7,4,6,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,5,1,7,6,3,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,5,1,7,6,4,3] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[2,5,3,1,4,6,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[2,5,3,1,4,7,6] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,5,3,1,6,4,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,5,3,1,6,7,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,5,3,1,7,4,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,5,3,1,7,6,4] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[2,5,3,4,1,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,5,3,4,1,7,6] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,5,3,4,6,1,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,5,3,4,6,7,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[2,5,3,4,7,1,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,5,3,4,7,6,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,5,3,6,1,4,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,5,3,6,1,7,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,5,3,6,4,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,5,3,6,4,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,5,3,6,7,1,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,5,3,6,7,4,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,5,3,7,1,4,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,5,3,7,1,6,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,5,3,7,4,1,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,5,3,7,4,6,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,5,3,7,6,1,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,5,3,7,6,4,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[2,5,4,1,3,6,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[2,5,4,1,3,7,6] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,5,4,1,6,3,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,5,4,1,6,7,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,5,4,1,7,3,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,5,4,1,7,6,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[2,5,4,3,1,6,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[2,5,4,3,1,7,6] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[2,5,4,3,6,1,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,5,4,3,6,7,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,5,4,3,7,1,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,5,4,3,7,6,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[2,5,4,6,1,3,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,5,4,6,1,7,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,5,4,6,3,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,5,4,6,3,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,5,4,6,7,1,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,5,4,6,7,3,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,5,4,7,1,3,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,5,4,7,1,6,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,5,4,7,3,1,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,5,4,7,3,6,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,5,4,7,6,1,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,5,4,7,6,3,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[2,5,6,1,3,4,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[2,5,6,1,3,7,4] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,5,6,1,4,3,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,5,6,1,4,7,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,5,6,1,7,3,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,5,6,1,7,4,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,5,6,3,1,4,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[2,5,6,3,1,7,4] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,5,6,3,4,1,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,5,6,3,4,7,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,5,6,3,7,1,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,5,6,3,7,4,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,5,6,4,1,3,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[2,5,6,4,1,7,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,5,6,4,3,1,7] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[2,5,6,4,3,7,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,5,6,4,7,1,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,5,6,4,7,3,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,5,6,7,1,3,4] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[2,5,6,7,1,4,3] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[2,5,6,7,3,1,4] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[2,5,6,7,3,4,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[2,5,6,7,4,1,3] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[2,5,6,7,4,3,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 6
[2,5,7,1,3,4,6] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[2,5,7,1,3,6,4] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,5,7,1,4,3,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,5,7,1,4,6,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,5,7,1,6,3,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,5,7,1,6,4,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,5,7,3,1,4,6] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[2,5,7,3,1,6,4] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,5,7,3,4,1,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,5,7,3,4,6,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,5,7,3,6,1,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,5,7,3,6,4,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,5,7,4,1,3,6] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[2,5,7,4,1,6,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,5,7,4,3,1,6] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[2,5,7,4,3,6,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,5,7,4,6,1,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,5,7,4,6,3,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,5,7,6,1,3,4] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[2,5,7,6,1,4,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,5,7,6,3,1,4] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[2,5,7,6,3,4,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,5,7,6,4,1,3] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[2,5,7,6,4,3,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 10
[2,6,1,3,4,5,7] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 5
[2,6,1,3,4,7,5] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[2,6,1,3,5,4,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,6,1,3,5,7,4] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[2,6,1,3,7,4,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,6,1,3,7,5,4] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,6,1,4,3,5,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,6,1,4,3,7,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,6,1,4,5,3,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,6,1,4,5,7,3] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[2,6,1,4,7,3,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,6,1,4,7,5,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,6,1,5,3,4,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,6,1,5,3,7,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,6,1,5,4,3,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,6,1,5,4,7,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,6,1,5,7,3,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,6,1,5,7,4,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,6,1,7,3,4,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,6,1,7,3,5,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,6,1,7,4,3,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,6,1,7,4,5,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,6,1,7,5,3,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,6,1,7,5,4,3] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[2,6,3,1,4,5,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[2,6,3,1,4,7,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,6,3,1,5,4,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,6,3,1,5,7,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,6,3,1,7,4,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,6,3,1,7,5,4] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[2,6,3,4,1,5,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,6,3,4,1,7,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,6,3,4,5,1,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,6,3,4,5,7,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[2,6,3,4,7,1,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,6,3,4,7,5,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,6,3,5,1,4,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,6,3,5,1,7,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,6,3,5,4,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,6,3,5,4,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,6,3,5,7,1,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,6,3,5,7,4,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,6,3,7,1,4,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,6,3,7,1,5,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,6,3,7,4,1,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,6,3,7,4,5,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,6,3,7,5,1,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,6,3,7,5,4,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[2,6,4,1,3,5,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[2,6,4,1,3,7,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,6,4,1,5,3,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,6,4,1,5,7,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,6,4,1,7,3,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,6,4,1,7,5,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[2,6,4,3,1,5,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[2,6,4,3,1,7,5] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[2,6,4,3,5,1,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,6,4,3,5,7,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,6,4,3,7,1,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,6,4,3,7,5,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[2,6,4,5,1,3,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,6,4,5,1,7,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,6,4,5,3,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,6,4,5,3,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,6,4,5,7,1,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,6,4,5,7,3,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,6,4,7,1,3,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,6,4,7,1,5,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,6,4,7,3,1,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,6,4,7,3,5,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,6,4,7,5,1,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,6,4,7,5,3,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[2,6,5,1,3,4,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[2,6,5,1,3,7,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,6,5,1,4,3,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,6,5,1,4,7,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,6,5,1,7,3,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,6,5,1,7,4,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[2,6,5,3,1,4,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[2,6,5,3,1,7,4] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[2,6,5,3,4,1,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,6,5,3,4,7,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,6,5,3,7,1,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,6,5,3,7,4,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[2,6,5,4,1,3,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[2,6,5,4,1,7,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[2,6,5,4,3,1,7] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[2,6,5,4,3,7,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[2,6,5,4,7,1,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,6,5,4,7,3,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[2,6,5,7,1,3,4] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,6,5,7,1,4,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,6,5,7,3,1,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,6,5,7,3,4,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,6,5,7,4,1,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,6,5,7,4,3,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[2,6,7,1,3,4,5] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[2,6,7,1,3,5,4] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,6,7,1,4,3,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,6,7,1,4,5,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,6,7,1,5,3,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,6,7,1,5,4,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,6,7,3,1,4,5] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[2,6,7,3,1,5,4] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,6,7,3,4,1,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,6,7,3,4,5,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[2,6,7,3,5,1,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,6,7,3,5,4,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,6,7,4,1,3,5] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[2,6,7,4,1,5,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,6,7,4,3,1,5] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[2,6,7,4,3,5,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,6,7,4,5,1,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[2,6,7,4,5,3,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[2,6,7,5,1,3,4] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[2,6,7,5,1,4,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,6,7,5,3,1,4] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[2,6,7,5,3,4,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[2,6,7,5,4,1,3] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[2,6,7,5,4,3,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 10
[2,7,1,3,4,5,6] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 5
[2,7,1,3,4,6,5] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[2,7,1,3,5,4,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,7,1,3,5,6,4] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[2,7,1,3,6,4,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,7,1,3,6,5,4] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,7,1,4,3,5,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,7,1,4,3,6,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,7,1,4,5,3,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,7,1,4,5,6,3] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[2,7,1,4,6,3,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,7,1,4,6,5,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,7,1,5,3,4,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,7,1,5,3,6,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,7,1,5,4,3,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,7,1,5,4,6,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,7,1,5,6,3,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,7,1,5,6,4,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,7,1,6,3,4,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,7,1,6,3,5,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,7,1,6,4,3,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,7,1,6,4,5,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,7,1,6,5,3,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,7,1,6,5,4,3] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[2,7,3,1,4,5,6] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[2,7,3,1,4,6,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,7,3,1,5,4,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,7,3,1,5,6,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,7,3,1,6,4,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,7,3,1,6,5,4] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[2,7,3,4,1,5,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,7,3,4,1,6,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,7,3,4,5,1,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,7,3,4,5,6,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[2,7,3,4,6,1,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,7,3,4,6,5,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,7,3,5,1,4,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,7,3,5,1,6,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,7,3,5,4,1,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,7,3,5,4,6,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,7,3,5,6,1,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,7,3,5,6,4,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,7,3,6,1,4,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,7,3,6,1,5,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,7,3,6,4,1,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,7,3,6,4,5,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,7,3,6,5,1,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,7,3,6,5,4,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[2,7,4,1,3,5,6] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[2,7,4,1,3,6,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,7,4,1,5,3,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,7,4,1,5,6,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,7,4,1,6,3,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,7,4,1,6,5,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[2,7,4,3,1,5,6] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[2,7,4,3,1,6,5] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[2,7,4,3,5,1,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,7,4,3,5,6,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,7,4,3,6,1,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,7,4,3,6,5,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[2,7,4,5,1,3,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,7,4,5,1,6,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,7,4,5,3,1,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,7,4,5,3,6,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,7,4,5,6,1,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[2,7,4,5,6,3,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[2,7,4,6,1,3,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,7,4,6,1,5,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,7,4,6,3,1,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,7,4,6,3,5,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,7,4,6,5,1,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,7,4,6,5,3,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[2,7,5,1,3,4,6] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[2,7,5,1,3,6,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,7,5,1,4,3,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,7,5,1,4,6,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,7,5,1,6,3,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,7,5,1,6,4,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[2,7,5,3,1,4,6] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[2,7,5,3,1,6,4] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[2,7,5,3,4,1,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,7,5,3,4,6,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,7,5,3,6,1,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,7,5,3,6,4,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[2,7,5,4,1,3,6] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[2,7,5,4,1,6,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[2,7,5,4,3,1,6] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[2,7,5,4,3,6,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[2,7,5,4,6,1,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,7,5,4,6,3,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[2,7,5,6,1,3,4] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[2,7,5,6,1,4,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,7,5,6,3,1,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,7,5,6,3,4,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[2,7,5,6,4,1,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[2,7,5,6,4,3,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[2,7,6,1,3,4,5] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[2,7,6,1,3,5,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,7,6,1,4,3,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,7,6,1,4,5,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,7,6,1,5,3,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,7,6,1,5,4,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[2,7,6,3,1,4,5] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[2,7,6,3,1,5,4] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[2,7,6,3,4,1,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,7,6,3,4,5,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[2,7,6,3,5,1,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,7,6,3,5,4,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[2,7,6,4,1,3,5] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[2,7,6,4,1,5,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[2,7,6,4,3,1,5] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[2,7,6,4,3,5,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[2,7,6,4,5,1,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[2,7,6,4,5,3,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[2,7,6,5,1,3,4] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[2,7,6,5,1,4,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[2,7,6,5,3,1,4] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[2,7,6,5,3,4,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[2,7,6,5,4,1,3] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[2,7,6,5,4,3,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}} => 15
[3,1,2,4,5,6,7] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => 6
[3,1,2,4,5,7,6] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[3,1,2,4,6,5,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[3,1,2,4,6,7,5] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[3,1,2,4,7,5,6] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[3,1,2,4,7,6,5] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[3,1,2,5,4,6,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[3,1,2,5,4,7,6] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,1,2,5,6,4,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[3,1,2,5,6,7,4] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[3,1,2,5,7,4,6] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[3,1,2,5,7,6,4] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[3,1,2,6,4,5,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[3,1,2,6,4,7,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,1,2,6,5,4,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[3,1,2,6,5,7,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,1,2,6,7,4,5] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[3,1,2,6,7,5,4] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[3,1,2,7,4,5,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[3,1,2,7,4,6,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,1,2,7,5,4,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[3,1,2,7,5,6,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,1,2,7,6,4,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[3,1,2,7,6,5,4] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[3,1,4,2,5,6,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[3,1,4,2,5,7,6] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,1,4,2,6,5,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,1,4,2,6,7,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,1,4,2,7,5,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,1,4,2,7,6,5] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[3,1,4,5,2,6,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[3,1,4,5,2,7,6] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,1,4,5,6,2,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[3,1,4,5,6,7,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[3,1,4,5,7,2,6] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[3,1,4,5,7,6,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[3,1,4,6,2,5,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[3,1,4,6,2,7,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,1,4,6,5,2,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[3,1,4,6,5,7,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,1,4,6,7,2,5] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[3,1,4,6,7,5,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[3,1,4,7,2,5,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[3,1,4,7,2,6,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,1,4,7,5,2,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[3,1,4,7,5,6,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,1,4,7,6,2,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[3,1,4,7,6,5,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[3,1,5,2,4,6,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[3,1,5,2,4,7,6] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,1,5,2,6,4,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,1,5,2,6,7,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,1,5,2,7,4,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,1,5,2,7,6,4] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[3,1,5,4,2,6,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[3,1,5,4,2,7,6] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[3,1,5,4,6,2,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,1,5,4,6,7,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,1,5,4,7,2,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,1,5,4,7,6,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[3,1,5,6,2,4,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[3,1,5,6,2,7,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,1,5,6,4,2,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[3,1,5,6,4,7,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,1,5,6,7,2,4] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[3,1,5,6,7,4,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[3,1,5,7,2,4,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[3,1,5,7,2,6,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,1,5,7,4,2,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[3,1,5,7,4,6,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,1,5,7,6,2,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[3,1,5,7,6,4,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[3,1,6,2,4,5,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[3,1,6,2,4,7,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,1,6,2,5,4,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,1,6,2,5,7,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,1,6,2,7,4,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,1,6,2,7,5,4] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[3,1,6,4,2,5,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[3,1,6,4,2,7,5] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[3,1,6,4,5,2,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,1,6,4,5,7,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,1,6,4,7,2,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,1,6,4,7,5,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[3,1,6,5,2,4,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[3,1,6,5,2,7,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[3,1,6,5,4,2,7] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[3,1,6,5,4,7,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[3,1,6,5,7,2,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,1,6,5,7,4,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[3,1,6,7,2,4,5] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[3,1,6,7,2,5,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,1,6,7,4,2,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[3,1,6,7,4,5,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,1,6,7,5,2,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[3,1,6,7,5,4,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[3,1,7,2,4,5,6] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[3,1,7,2,4,6,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,1,7,2,5,4,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,1,7,2,5,6,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,1,7,2,6,4,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,1,7,2,6,5,4] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[3,1,7,4,2,5,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[3,1,7,4,2,6,5] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[3,1,7,4,5,2,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,1,7,4,5,6,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,1,7,4,6,2,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,1,7,4,6,5,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[3,1,7,5,2,4,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[3,1,7,5,2,6,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[3,1,7,5,4,2,6] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[3,1,7,5,4,6,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[3,1,7,5,6,2,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,1,7,5,6,4,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[3,1,7,6,2,4,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[3,1,7,6,2,5,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[3,1,7,6,4,2,5] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[3,1,7,6,4,5,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[3,1,7,6,5,2,4] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[3,1,7,6,5,4,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 16
[3,2,1,4,5,6,7] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 11
[3,2,1,4,5,7,6] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[3,2,1,4,6,5,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[3,2,1,4,6,7,5] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[3,2,1,4,7,5,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[3,2,1,4,7,6,5] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[3,2,1,5,4,6,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[3,2,1,5,4,7,6] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[3,2,1,5,6,4,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[3,2,1,5,6,7,4] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[3,2,1,5,7,4,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[3,2,1,5,7,6,4] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[3,2,1,6,4,5,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[3,2,1,6,4,7,5] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[3,2,1,6,5,4,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[3,2,1,6,5,7,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[3,2,1,6,7,4,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[3,2,1,6,7,5,4] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[3,2,1,7,4,5,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[3,2,1,7,4,6,5] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[3,2,1,7,5,4,6] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[3,2,1,7,5,6,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[3,2,1,7,6,4,5] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[3,2,1,7,6,5,4] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[3,2,4,1,5,6,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[3,2,4,1,5,7,6] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,2,4,1,6,5,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,2,4,1,6,7,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,2,4,1,7,5,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,2,4,1,7,6,5] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[3,2,4,5,1,6,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[3,2,4,5,1,7,6] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,2,4,5,6,1,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[3,2,4,5,6,7,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[3,2,4,5,7,1,6] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[3,2,4,5,7,6,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[3,2,4,6,1,5,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[3,2,4,6,1,7,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,2,4,6,5,1,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[3,2,4,6,5,7,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,2,4,6,7,1,5] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[3,2,4,6,7,5,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[3,2,4,7,1,5,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[3,2,4,7,1,6,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,2,4,7,5,1,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[3,2,4,7,5,6,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,2,4,7,6,1,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[3,2,4,7,6,5,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[3,2,5,1,4,6,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[3,2,5,1,4,7,6] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,2,5,1,6,4,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,2,5,1,6,7,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,2,5,1,7,4,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,2,5,1,7,6,4] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[3,2,5,4,1,6,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[3,2,5,4,1,7,6] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[3,2,5,4,6,1,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,2,5,4,6,7,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,2,5,4,7,1,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,2,5,4,7,6,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[3,2,5,6,1,4,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[3,2,5,6,1,7,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,2,5,6,4,1,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[3,2,5,6,4,7,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,2,5,6,7,1,4] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[3,2,5,6,7,4,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[3,2,5,7,1,4,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[3,2,5,7,1,6,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,2,5,7,4,1,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[3,2,5,7,4,6,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,2,5,7,6,1,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[3,2,5,7,6,4,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[3,2,6,1,4,5,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[3,2,6,1,4,7,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,2,6,1,5,4,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,2,6,1,5,7,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,2,6,1,7,4,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,2,6,1,7,5,4] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[3,2,6,4,1,5,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[3,2,6,4,1,7,5] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[3,2,6,4,5,1,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,2,6,4,5,7,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,2,6,4,7,1,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,2,6,4,7,5,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[3,2,6,5,1,4,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[3,2,6,5,1,7,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[3,2,6,5,4,1,7] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[3,2,6,5,4,7,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[3,2,6,5,7,1,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,2,6,5,7,4,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[3,2,6,7,1,4,5] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[3,2,6,7,1,5,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,2,6,7,4,1,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[3,2,6,7,4,5,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[3,2,6,7,5,1,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[3,2,6,7,5,4,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[3,2,7,1,4,5,6] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[3,2,7,1,4,6,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,2,7,1,5,4,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,2,7,1,5,6,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,2,7,1,6,4,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,2,7,1,6,5,4] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[3,2,7,4,1,5,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[3,2,7,4,1,6,5] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[3,2,7,4,5,1,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,2,7,4,5,6,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[3,2,7,4,6,1,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,2,7,4,6,5,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[3,2,7,5,1,4,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[3,2,7,5,1,6,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[3,2,7,5,4,1,6] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[3,2,7,5,4,6,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[3,2,7,5,6,1,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[3,2,7,5,6,4,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[3,2,7,6,1,4,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[3,2,7,6,1,5,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[3,2,7,6,4,1,5] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[3,2,7,6,4,5,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[3,2,7,6,5,1,4] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[3,2,7,6,5,4,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 16
[3,4,1,2,5,6,7] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 5
[3,4,1,2,5,7,6] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[3,4,1,2,6,5,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,4,1,2,6,7,5] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[3,4,1,2,7,5,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,4,1,2,7,6,5] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,4,1,5,2,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,4,1,5,2,7,6] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,4,1,5,6,2,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,4,1,5,6,7,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[3,4,1,5,7,2,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,4,1,5,7,6,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,4,1,6,2,5,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,4,1,6,2,7,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,4,1,6,5,2,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,4,1,6,5,7,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,4,1,6,7,2,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,4,1,6,7,5,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,4,1,7,2,5,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,4,1,7,2,6,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,4,1,7,5,2,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,4,1,7,5,6,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,4,1,7,6,2,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,4,1,7,6,5,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[3,4,2,1,5,6,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[3,4,2,1,5,7,6] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,4,2,1,6,5,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,4,2,1,6,7,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,4,2,1,7,5,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,4,2,1,7,6,5] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[3,4,2,5,1,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,4,2,5,1,7,6] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,4,2,5,6,1,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,4,2,5,6,7,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[3,4,2,5,7,1,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,4,2,5,7,6,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,4,2,6,1,5,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,4,2,6,1,7,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,4,2,6,5,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,4,2,6,5,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,4,2,6,7,1,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,4,2,6,7,5,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,4,2,7,1,5,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,4,2,7,1,6,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,4,2,7,5,1,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,4,2,7,5,6,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,4,2,7,6,1,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,4,2,7,6,5,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[3,4,5,1,2,6,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[3,4,5,1,2,7,6] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[3,4,5,1,6,2,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,4,5,1,6,7,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[3,4,5,1,7,2,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,4,5,1,7,6,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[3,4,5,2,1,6,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[3,4,5,2,1,7,6] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,4,5,2,6,1,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,4,5,2,6,7,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[3,4,5,2,7,1,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,4,5,2,7,6,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[3,4,5,6,1,2,7] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[3,4,5,6,1,7,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[3,4,5,6,2,1,7] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[3,4,5,6,2,7,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[3,4,5,6,7,1,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5},{6,7}} => 2
[3,4,5,6,7,2,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => {{1,2,3,4,5},{6},{7}} => 3
[3,4,5,7,1,2,6] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[3,4,5,7,1,6,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[3,4,5,7,2,1,6] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[3,4,5,7,2,6,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[3,4,5,7,6,1,2] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[3,4,5,7,6,2,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 6
[3,4,6,1,2,5,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[3,4,6,1,2,7,5] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[3,4,6,1,5,2,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,4,6,1,5,7,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[3,4,6,1,7,2,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,4,6,1,7,5,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[3,4,6,2,1,5,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[3,4,6,2,1,7,5] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,4,6,2,5,1,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,4,6,2,5,7,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[3,4,6,2,7,1,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,4,6,2,7,5,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[3,4,6,5,1,2,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[3,4,6,5,1,7,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,4,6,5,2,1,7] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[3,4,6,5,2,7,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,4,6,5,7,1,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,4,6,5,7,2,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[3,4,6,7,1,2,5] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[3,4,6,7,1,5,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[3,4,6,7,2,1,5] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[3,4,6,7,2,5,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[3,4,6,7,5,1,2] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[3,4,6,7,5,2,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 6
[3,4,7,1,2,5,6] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[3,4,7,1,2,6,5] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[3,4,7,1,5,2,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,4,7,1,5,6,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[3,4,7,1,6,2,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,4,7,1,6,5,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[3,4,7,2,1,5,6] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[3,4,7,2,1,6,5] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,4,7,2,5,1,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,4,7,2,5,6,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[3,4,7,2,6,1,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,4,7,2,6,5,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[3,4,7,5,1,2,6] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[3,4,7,5,1,6,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,4,7,5,2,1,6] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[3,4,7,5,2,6,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,4,7,5,6,1,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,4,7,5,6,2,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[3,4,7,6,1,2,5] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[3,4,7,6,1,5,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,4,7,6,2,1,5] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[3,4,7,6,2,5,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,4,7,6,5,1,2] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[3,4,7,6,5,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 10
[3,5,1,2,4,6,7] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 5
[3,5,1,2,4,7,6] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[3,5,1,2,6,4,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,5,1,2,6,7,4] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[3,5,1,2,7,4,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,5,1,2,7,6,4] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,5,1,4,2,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,5,1,4,2,7,6] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,5,1,4,6,2,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,5,1,4,6,7,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[3,5,1,4,7,2,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,5,1,4,7,6,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,5,1,6,2,4,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,5,1,6,2,7,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,5,1,6,4,2,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,5,1,6,4,7,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,5,1,6,7,2,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,5,1,6,7,4,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,5,1,7,2,4,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,5,1,7,2,6,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,5,1,7,4,2,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,5,1,7,4,6,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,5,1,7,6,2,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,5,1,7,6,4,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[3,5,2,1,4,6,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[3,5,2,1,4,7,6] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,5,2,1,6,4,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,5,2,1,6,7,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,5,2,1,7,4,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,5,2,1,7,6,4] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[3,5,2,4,1,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,5,2,4,1,7,6] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,5,2,4,6,1,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,5,2,4,6,7,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[3,5,2,4,7,1,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,5,2,4,7,6,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,5,2,6,1,4,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,5,2,6,1,7,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,5,2,6,4,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,5,2,6,4,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,5,2,6,7,1,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,5,2,6,7,4,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,5,2,7,1,4,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,5,2,7,1,6,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,5,2,7,4,1,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,5,2,7,4,6,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,5,2,7,6,1,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,5,2,7,6,4,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[3,5,4,1,2,6,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[3,5,4,1,2,7,6] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,5,4,1,6,2,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,5,4,1,6,7,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,5,4,1,7,2,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,5,4,1,7,6,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[3,5,4,2,1,6,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[3,5,4,2,1,7,6] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[3,5,4,2,6,1,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,5,4,2,6,7,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,5,4,2,7,1,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,5,4,2,7,6,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[3,5,4,6,1,2,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,5,4,6,1,7,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,5,4,6,2,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,5,4,6,2,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,5,4,6,7,1,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,5,4,6,7,2,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,5,4,7,1,2,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,5,4,7,1,6,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,5,4,7,2,1,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,5,4,7,2,6,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,5,4,7,6,1,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,5,4,7,6,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[3,5,6,1,2,4,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[3,5,6,1,2,7,4] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[3,5,6,1,4,2,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,5,6,1,4,7,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[3,5,6,1,7,2,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,5,6,1,7,4,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[3,5,6,2,1,4,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[3,5,6,2,1,7,4] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,5,6,2,4,1,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,5,6,2,4,7,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[3,5,6,2,7,1,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,5,6,2,7,4,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[3,5,6,4,1,2,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[3,5,6,4,1,7,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,5,6,4,2,1,7] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[3,5,6,4,2,7,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,5,6,4,7,1,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,5,6,4,7,2,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[3,5,6,7,1,2,4] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[3,5,6,7,1,4,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[3,5,6,7,2,1,4] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[3,5,6,7,2,4,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[3,5,6,7,4,1,2] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[3,5,6,7,4,2,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 6
[3,5,7,1,2,4,6] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[3,5,7,1,2,6,4] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[3,5,7,1,4,2,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,5,7,1,4,6,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[3,5,7,1,6,2,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,5,7,1,6,4,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[3,5,7,2,1,4,6] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[3,5,7,2,1,6,4] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,5,7,2,4,1,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,5,7,2,4,6,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[3,5,7,2,6,1,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,5,7,2,6,4,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[3,5,7,4,1,2,6] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[3,5,7,4,1,6,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,5,7,4,2,1,6] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[3,5,7,4,2,6,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,5,7,4,6,1,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,5,7,4,6,2,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[3,5,7,6,1,2,4] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[3,5,7,6,1,4,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,5,7,6,2,1,4] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[3,5,7,6,2,4,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,5,7,6,4,1,2] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[3,5,7,6,4,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 10
[3,6,1,2,4,5,7] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 5
[3,6,1,2,4,7,5] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[3,6,1,2,5,4,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,6,1,2,5,7,4] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[3,6,1,2,7,4,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,6,1,2,7,5,4] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,6,1,4,2,5,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,6,1,4,2,7,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,6,1,4,5,2,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,6,1,4,5,7,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[3,6,1,4,7,2,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,6,1,4,7,5,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,6,1,5,2,4,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,6,1,5,2,7,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,6,1,5,4,2,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,6,1,5,4,7,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,6,1,5,7,2,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,6,1,5,7,4,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,6,1,7,2,4,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,6,1,7,2,5,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,6,1,7,4,2,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,6,1,7,4,5,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,6,1,7,5,2,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,6,1,7,5,4,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[3,6,2,1,4,5,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[3,6,2,1,4,7,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,6,2,1,5,4,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,6,2,1,5,7,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,6,2,1,7,4,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,6,2,1,7,5,4] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[3,6,2,4,1,5,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,6,2,4,1,7,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,6,2,4,5,1,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,6,2,4,5,7,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[3,6,2,4,7,1,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,6,2,4,7,5,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,6,2,5,1,4,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,6,2,5,1,7,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,6,2,5,4,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,6,2,5,4,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,6,2,5,7,1,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,6,2,5,7,4,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,6,2,7,1,4,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,6,2,7,1,5,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,6,2,7,4,1,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,6,2,7,4,5,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,6,2,7,5,1,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,6,2,7,5,4,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[3,6,4,1,2,5,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[3,6,4,1,2,7,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,6,4,1,5,2,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,6,4,1,5,7,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,6,4,1,7,2,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,6,4,1,7,5,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[3,6,4,2,1,5,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[3,6,4,2,1,7,5] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[3,6,4,2,5,1,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,6,4,2,5,7,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,6,4,2,7,1,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,6,4,2,7,5,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[3,6,4,5,1,2,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,6,4,5,1,7,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,6,4,5,2,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,6,4,5,2,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,6,4,5,7,1,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,6,4,5,7,2,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,6,4,7,1,2,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,6,4,7,1,5,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,6,4,7,2,1,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,6,4,7,2,5,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,6,4,7,5,1,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,6,4,7,5,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[3,6,5,1,2,4,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[3,6,5,1,2,7,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,6,5,1,4,2,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,6,5,1,4,7,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,6,5,1,7,2,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,6,5,1,7,4,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[3,6,5,2,1,4,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[3,6,5,2,1,7,4] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[3,6,5,2,4,1,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,6,5,2,4,7,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,6,5,2,7,1,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,6,5,2,7,4,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[3,6,5,4,1,2,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[3,6,5,4,1,7,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[3,6,5,4,2,1,7] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[3,6,5,4,2,7,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[3,6,5,4,7,1,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,6,5,4,7,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[3,6,5,7,1,2,4] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,6,5,7,1,4,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,6,5,7,2,1,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,6,5,7,2,4,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,6,5,7,4,1,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,6,5,7,4,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[3,6,7,1,2,4,5] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[3,6,7,1,2,5,4] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[3,6,7,1,4,2,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,6,7,1,4,5,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[3,6,7,1,5,2,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,6,7,1,5,4,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[3,6,7,2,1,4,5] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[3,6,7,2,1,5,4] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,6,7,2,4,1,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,6,7,2,4,5,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[3,6,7,2,5,1,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,6,7,2,5,4,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[3,6,7,4,1,2,5] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[3,6,7,4,1,5,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,6,7,4,2,1,5] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[3,6,7,4,2,5,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,6,7,4,5,1,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[3,6,7,4,5,2,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[3,6,7,5,1,2,4] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[3,6,7,5,1,4,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,6,7,5,2,1,4] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[3,6,7,5,2,4,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[3,6,7,5,4,1,2] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[3,6,7,5,4,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 10
[3,7,1,2,4,5,6] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 5
[3,7,1,2,4,6,5] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[3,7,1,2,5,4,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,7,1,2,5,6,4] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[3,7,1,2,6,4,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,7,1,2,6,5,4] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,7,1,4,2,5,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,7,1,4,2,6,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,7,1,4,5,2,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,7,1,4,5,6,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[3,7,1,4,6,2,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,7,1,4,6,5,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,7,1,5,2,4,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,7,1,5,2,6,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,7,1,5,4,2,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,7,1,5,4,6,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,7,1,5,6,2,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,7,1,5,6,4,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,7,1,6,2,4,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,7,1,6,2,5,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,7,1,6,4,2,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,7,1,6,4,5,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,7,1,6,5,2,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,7,1,6,5,4,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[3,7,2,1,4,5,6] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[3,7,2,1,4,6,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,7,2,1,5,4,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,7,2,1,5,6,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,7,2,1,6,4,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,7,2,1,6,5,4] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[3,7,2,4,1,5,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,7,2,4,1,6,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,7,2,4,5,1,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,7,2,4,5,6,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[3,7,2,4,6,1,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,7,2,4,6,5,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,7,2,5,1,4,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,7,2,5,1,6,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,7,2,5,4,1,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,7,2,5,4,6,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,7,2,5,6,1,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,7,2,5,6,4,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,7,2,6,1,4,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,7,2,6,1,5,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,7,2,6,4,1,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,7,2,6,4,5,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,7,2,6,5,1,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,7,2,6,5,4,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[3,7,4,1,2,5,6] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[3,7,4,1,2,6,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,7,4,1,5,2,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,7,4,1,5,6,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,7,4,1,6,2,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,7,4,1,6,5,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[3,7,4,2,1,5,6] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[3,7,4,2,1,6,5] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[3,7,4,2,5,1,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,7,4,2,5,6,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,7,4,2,6,1,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,7,4,2,6,5,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[3,7,4,5,1,2,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,7,4,5,1,6,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,7,4,5,2,1,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,7,4,5,2,6,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,7,4,5,6,1,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[3,7,4,5,6,2,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[3,7,4,6,1,2,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,7,4,6,1,5,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,7,4,6,2,1,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,7,4,6,2,5,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,7,4,6,5,1,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,7,4,6,5,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[3,7,5,1,2,4,6] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[3,7,5,1,2,6,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,7,5,1,4,2,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,7,5,1,4,6,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,7,5,1,6,2,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,7,5,1,6,4,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[3,7,5,2,1,4,6] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[3,7,5,2,1,6,4] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[3,7,5,2,4,1,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,7,5,2,4,6,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,7,5,2,6,1,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,7,5,2,6,4,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[3,7,5,4,1,2,6] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[3,7,5,4,1,6,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[3,7,5,4,2,1,6] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[3,7,5,4,2,6,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[3,7,5,4,6,1,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,7,5,4,6,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[3,7,5,6,1,2,4] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[3,7,5,6,1,4,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,7,5,6,2,1,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,7,5,6,2,4,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[3,7,5,6,4,1,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[3,7,5,6,4,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[3,7,6,1,2,4,5] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[3,7,6,1,2,5,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,7,6,1,4,2,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,7,6,1,4,5,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,7,6,1,5,2,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,7,6,1,5,4,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[3,7,6,2,1,4,5] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[3,7,6,2,1,5,4] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[3,7,6,2,4,1,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,7,6,2,4,5,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[3,7,6,2,5,1,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,7,6,2,5,4,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[3,7,6,4,1,2,5] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[3,7,6,4,1,5,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[3,7,6,4,2,1,5] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[3,7,6,4,2,5,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[3,7,6,4,5,1,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[3,7,6,4,5,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[3,7,6,5,1,2,4] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[3,7,6,5,1,4,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[3,7,6,5,2,1,4] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[3,7,6,5,2,4,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[3,7,6,5,4,1,2] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[3,7,6,5,4,2,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}} => 15
[4,1,2,3,5,6,7] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => 6
[4,1,2,3,5,7,6] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[4,1,2,3,6,5,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[4,1,2,3,6,7,5] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[4,1,2,3,7,5,6] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[4,1,2,3,7,6,5] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[4,1,2,5,3,6,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[4,1,2,5,3,7,6] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,1,2,5,6,3,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[4,1,2,5,6,7,3] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[4,1,2,5,7,3,6] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[4,1,2,5,7,6,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[4,1,2,6,3,5,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[4,1,2,6,3,7,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,1,2,6,5,3,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,1,2,6,5,7,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,1,2,6,7,3,5] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[4,1,2,6,7,5,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[4,1,2,7,3,5,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[4,1,2,7,3,6,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,1,2,7,5,3,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,1,2,7,5,6,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,1,2,7,6,3,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,1,2,7,6,5,3] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[4,1,3,2,5,6,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[4,1,3,2,5,7,6] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,1,3,2,6,5,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,1,3,2,6,7,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,1,3,2,7,5,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,1,3,2,7,6,5] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,1,3,5,2,6,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[4,1,3,5,2,7,6] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,1,3,5,6,2,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[4,1,3,5,6,7,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[4,1,3,5,7,2,6] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[4,1,3,5,7,6,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[4,1,3,6,2,5,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[4,1,3,6,2,7,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,1,3,6,5,2,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,1,3,6,5,7,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,1,3,6,7,2,5] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[4,1,3,6,7,5,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[4,1,3,7,2,5,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[4,1,3,7,2,6,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,1,3,7,5,2,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,1,3,7,5,6,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,1,3,7,6,2,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,1,3,7,6,5,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[4,1,5,2,3,6,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[4,1,5,2,3,7,6] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,1,5,2,6,3,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,1,5,2,6,7,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,1,5,2,7,3,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,1,5,2,7,6,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,1,5,3,2,6,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[4,1,5,3,2,7,6] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,1,5,3,6,2,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,1,5,3,6,7,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,1,5,3,7,2,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,1,5,3,7,6,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,1,5,6,2,3,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[4,1,5,6,2,7,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,1,5,6,3,2,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,1,5,6,3,7,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,1,5,6,7,2,3] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[4,1,5,6,7,3,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[4,1,5,7,2,3,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[4,1,5,7,2,6,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,1,5,7,3,2,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,1,5,7,3,6,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,1,5,7,6,2,3] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,1,5,7,6,3,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[4,1,6,2,3,5,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[4,1,6,2,3,7,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,1,6,2,5,3,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,1,6,2,5,7,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,1,6,2,7,3,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,1,6,2,7,5,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,1,6,3,2,5,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[4,1,6,3,2,7,5] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,1,6,3,5,2,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,1,6,3,5,7,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,1,6,3,7,2,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,1,6,3,7,5,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,1,6,5,2,3,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[4,1,6,5,2,7,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,1,6,5,3,2,7] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[4,1,6,5,3,7,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,1,6,5,7,2,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,1,6,5,7,3,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,1,6,7,2,3,5] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[4,1,6,7,2,5,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,1,6,7,3,2,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,1,6,7,3,5,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,1,6,7,5,2,3] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,1,6,7,5,3,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[4,1,7,2,3,5,6] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[4,1,7,2,3,6,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,1,7,2,5,3,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,1,7,2,5,6,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,1,7,2,6,3,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,1,7,2,6,5,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,1,7,3,2,5,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[4,1,7,3,2,6,5] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,1,7,3,5,2,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,1,7,3,5,6,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,1,7,3,6,2,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,1,7,3,6,5,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,1,7,5,2,3,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[4,1,7,5,2,6,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,1,7,5,3,2,6] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[4,1,7,5,3,6,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,1,7,5,6,2,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,1,7,5,6,3,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,1,7,6,2,3,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[4,1,7,6,2,5,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,1,7,6,3,2,5] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[4,1,7,6,3,5,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,1,7,6,5,2,3] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[4,1,7,6,5,3,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 16
[4,2,1,3,5,6,7] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 11
[4,2,1,3,5,7,6] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[4,2,1,3,6,5,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[4,2,1,3,6,7,5] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[4,2,1,3,7,5,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[4,2,1,3,7,6,5] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[4,2,1,5,3,6,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[4,2,1,5,3,7,6] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[4,2,1,5,6,3,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[4,2,1,5,6,7,3] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[4,2,1,5,7,3,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[4,2,1,5,7,6,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[4,2,1,6,3,5,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[4,2,1,6,3,7,5] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[4,2,1,6,5,3,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[4,2,1,6,5,7,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[4,2,1,6,7,3,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[4,2,1,6,7,5,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[4,2,1,7,3,5,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[4,2,1,7,3,6,5] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[4,2,1,7,5,3,6] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[4,2,1,7,5,6,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[4,2,1,7,6,3,5] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[4,2,1,7,6,5,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[4,2,3,1,5,6,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[4,2,3,1,5,7,6] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,2,3,1,6,5,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,2,3,1,6,7,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,2,3,1,7,5,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,2,3,1,7,6,5] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,2,3,5,1,6,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[4,2,3,5,1,7,6] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,2,3,5,6,1,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[4,2,3,5,6,7,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[4,2,3,5,7,1,6] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[4,2,3,5,7,6,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[4,2,3,6,1,5,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[4,2,3,6,1,7,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,2,3,6,5,1,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,2,3,6,5,7,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,2,3,6,7,1,5] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[4,2,3,6,7,5,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[4,2,3,7,1,5,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[4,2,3,7,1,6,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,2,3,7,5,1,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,2,3,7,5,6,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,2,3,7,6,1,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,2,3,7,6,5,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[4,2,5,1,3,6,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[4,2,5,1,3,7,6] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,2,5,1,6,3,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,2,5,1,6,7,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,2,5,1,7,3,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,2,5,1,7,6,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,2,5,3,1,6,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[4,2,5,3,1,7,6] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,2,5,3,6,1,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,2,5,3,6,7,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,2,5,3,7,1,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,2,5,3,7,6,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,2,5,6,1,3,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[4,2,5,6,1,7,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,2,5,6,3,1,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,2,5,6,3,7,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,2,5,6,7,1,3] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[4,2,5,6,7,3,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[4,2,5,7,1,3,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[4,2,5,7,1,6,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,2,5,7,3,1,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,2,5,7,3,6,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,2,5,7,6,1,3] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,2,5,7,6,3,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[4,2,6,1,3,5,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[4,2,6,1,3,7,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,2,6,1,5,3,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,2,6,1,5,7,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,2,6,1,7,3,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,2,6,1,7,5,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,2,6,3,1,5,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[4,2,6,3,1,7,5] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,2,6,3,5,1,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,2,6,3,5,7,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,2,6,3,7,1,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,2,6,3,7,5,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,2,6,5,1,3,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[4,2,6,5,1,7,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,2,6,5,3,1,7] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[4,2,6,5,3,7,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,2,6,5,7,1,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,2,6,5,7,3,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,2,6,7,1,3,5] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[4,2,6,7,1,5,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,2,6,7,3,1,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,2,6,7,3,5,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,2,6,7,5,1,3] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,2,6,7,5,3,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[4,2,7,1,3,5,6] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[4,2,7,1,3,6,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,2,7,1,5,3,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,2,7,1,5,6,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,2,7,1,6,3,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,2,7,1,6,5,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,2,7,3,1,5,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[4,2,7,3,1,6,5] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,2,7,3,5,1,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,2,7,3,5,6,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,2,7,3,6,1,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,2,7,3,6,5,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,2,7,5,1,3,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[4,2,7,5,1,6,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,2,7,5,3,1,6] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[4,2,7,5,3,6,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,2,7,5,6,1,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,2,7,5,6,3,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,2,7,6,1,3,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[4,2,7,6,1,5,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,2,7,6,3,1,5] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[4,2,7,6,3,5,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,2,7,6,5,1,3] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[4,2,7,6,5,3,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 16
[4,3,1,2,5,6,7] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 11
[4,3,1,2,5,7,6] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[4,3,1,2,6,5,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[4,3,1,2,6,7,5] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[4,3,1,2,7,5,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[4,3,1,2,7,6,5] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[4,3,1,5,2,6,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[4,3,1,5,2,7,6] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[4,3,1,5,6,2,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[4,3,1,5,6,7,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[4,3,1,5,7,2,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[4,3,1,5,7,6,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[4,3,1,6,2,5,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[4,3,1,6,2,7,5] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[4,3,1,6,5,2,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[4,3,1,6,5,7,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[4,3,1,6,7,2,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[4,3,1,6,7,5,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[4,3,1,7,2,5,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[4,3,1,7,2,6,5] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[4,3,1,7,5,2,6] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[4,3,1,7,5,6,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[4,3,1,7,6,2,5] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[4,3,1,7,6,5,2] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[4,3,2,1,5,6,7] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 15
[4,3,2,1,5,7,6] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[4,3,2,1,6,5,7] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[4,3,2,1,6,7,5] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[4,3,2,1,7,5,6] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[4,3,2,1,7,6,5] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[4,3,2,5,1,6,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[4,3,2,5,1,7,6] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[4,3,2,5,6,1,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[4,3,2,5,6,7,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[4,3,2,5,7,1,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[4,3,2,5,7,6,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[4,3,2,6,1,5,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[4,3,2,6,1,7,5] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[4,3,2,6,5,1,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[4,3,2,6,5,7,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[4,3,2,6,7,1,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[4,3,2,6,7,5,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[4,3,2,7,1,5,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[4,3,2,7,1,6,5] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[4,3,2,7,5,1,6] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[4,3,2,7,5,6,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[4,3,2,7,6,1,5] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[4,3,2,7,6,5,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[4,3,5,1,2,6,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[4,3,5,1,2,7,6] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,3,5,1,6,2,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,3,5,1,6,7,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,3,5,1,7,2,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,3,5,1,7,6,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,3,5,2,1,6,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[4,3,5,2,1,7,6] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,3,5,2,6,1,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,3,5,2,6,7,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,3,5,2,7,1,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,3,5,2,7,6,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,3,5,6,1,2,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[4,3,5,6,1,7,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,3,5,6,2,1,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,3,5,6,2,7,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,3,5,6,7,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[4,3,5,6,7,2,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[4,3,5,7,1,2,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[4,3,5,7,1,6,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,3,5,7,2,1,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,3,5,7,2,6,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,3,5,7,6,1,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,3,5,7,6,2,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[4,3,6,1,2,5,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[4,3,6,1,2,7,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,3,6,1,5,2,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,3,6,1,5,7,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,3,6,1,7,2,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,3,6,1,7,5,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,3,6,2,1,5,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[4,3,6,2,1,7,5] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,3,6,2,5,1,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,3,6,2,5,7,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,3,6,2,7,1,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,3,6,2,7,5,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,3,6,5,1,2,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[4,3,6,5,1,7,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,3,6,5,2,1,7] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[4,3,6,5,2,7,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,3,6,5,7,1,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,3,6,5,7,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,3,6,7,1,2,5] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[4,3,6,7,1,5,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,3,6,7,2,1,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,3,6,7,2,5,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[4,3,6,7,5,1,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[4,3,6,7,5,2,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[4,3,7,1,2,5,6] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[4,3,7,1,2,6,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,3,7,1,5,2,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,3,7,1,5,6,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,3,7,1,6,2,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,3,7,1,6,5,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,3,7,2,1,5,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[4,3,7,2,1,6,5] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,3,7,2,5,1,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,3,7,2,5,6,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[4,3,7,2,6,1,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,3,7,2,6,5,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,3,7,5,1,2,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[4,3,7,5,1,6,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,3,7,5,2,1,6] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[4,3,7,5,2,6,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,3,7,5,6,1,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[4,3,7,5,6,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[4,3,7,6,1,2,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[4,3,7,6,1,5,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,3,7,6,2,1,5] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[4,3,7,6,2,5,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[4,3,7,6,5,1,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[4,3,7,6,5,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 16
[4,5,1,2,3,6,7] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 5
[4,5,1,2,3,7,6] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[4,5,1,2,6,3,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,5,1,2,6,7,3] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[4,5,1,2,7,3,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,5,1,2,7,6,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[4,5,1,3,2,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,5,1,3,2,7,6] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,5,1,3,6,2,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,5,1,3,6,7,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[4,5,1,3,7,2,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,5,1,3,7,6,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[4,5,1,6,2,3,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,5,1,6,2,7,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,5,1,6,3,2,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,5,1,6,3,7,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,5,1,6,7,2,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,5,1,6,7,3,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[4,5,1,7,2,3,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,5,1,7,2,6,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,5,1,7,3,2,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,5,1,7,3,6,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,5,1,7,6,2,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,5,1,7,6,3,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[4,5,2,1,3,6,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[4,5,2,1,3,7,6] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,5,2,1,6,3,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,5,2,1,6,7,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,5,2,1,7,3,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,5,2,1,7,6,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[4,5,2,3,1,6,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,5,2,3,1,7,6] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,5,2,3,6,1,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,5,2,3,6,7,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[4,5,2,3,7,1,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,5,2,3,7,6,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[4,5,2,6,1,3,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,5,2,6,1,7,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,5,2,6,3,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,5,2,6,3,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,5,2,6,7,1,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,5,2,6,7,3,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[4,5,2,7,1,3,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,5,2,7,1,6,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,5,2,7,3,1,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,5,2,7,3,6,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,5,2,7,6,1,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,5,2,7,6,3,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[4,5,3,1,2,6,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[4,5,3,1,2,7,6] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,5,3,1,6,2,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,5,3,1,6,7,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,5,3,1,7,2,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,5,3,1,7,6,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[4,5,3,2,1,6,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[4,5,3,2,1,7,6] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[4,5,3,2,6,1,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,5,3,2,6,7,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,5,3,2,7,1,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,5,3,2,7,6,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[4,5,3,6,1,2,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,5,3,6,1,7,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,5,3,6,2,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,5,3,6,2,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,5,3,6,7,1,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,5,3,6,7,2,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[4,5,3,7,1,2,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,5,3,7,1,6,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,5,3,7,2,1,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,5,3,7,2,6,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,5,3,7,6,1,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,5,3,7,6,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[4,5,6,1,2,3,7] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[4,5,6,1,2,7,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[4,5,6,1,3,2,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[4,5,6,1,3,7,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[4,5,6,1,7,2,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[4,5,6,1,7,3,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[4,5,6,2,1,3,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[4,5,6,2,1,7,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[4,5,6,2,3,1,7] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[4,5,6,2,3,7,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[4,5,6,2,7,1,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[4,5,6,2,7,3,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[4,5,6,3,1,2,7] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[4,5,6,3,1,7,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[4,5,6,3,2,1,7] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[4,5,6,3,2,7,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[4,5,6,3,7,1,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[4,5,6,3,7,2,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[4,5,6,7,1,2,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => {{1,2,3,4},{5,6,7}} => 3
[4,5,6,7,1,3,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[4,5,6,7,2,1,3] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[4,5,6,7,2,3,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => {{1,2,3,4},{5,6},{7}} => 4
[4,5,6,7,3,1,2] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => {{1,2,3,4},{5},{6,7}} => 5
[4,5,6,7,3,2,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => {{1,2,3,4},{5},{6},{7}} => 6
[4,5,7,1,2,3,6] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[4,5,7,1,2,6,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[4,5,7,1,3,2,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[4,5,7,1,3,6,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[4,5,7,1,6,2,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[4,5,7,1,6,3,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[4,5,7,2,1,3,6] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[4,5,7,2,1,6,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[4,5,7,2,3,1,6] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[4,5,7,2,3,6,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[4,5,7,2,6,1,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[4,5,7,2,6,3,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[4,5,7,3,1,2,6] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[4,5,7,3,1,6,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[4,5,7,3,2,1,6] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[4,5,7,3,2,6,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[4,5,7,3,6,1,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[4,5,7,3,6,2,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[4,5,7,6,1,2,3] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[4,5,7,6,1,3,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[4,5,7,6,2,1,3] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[4,5,7,6,2,3,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[4,5,7,6,3,1,2] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[4,5,7,6,3,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 10
[4,6,1,2,3,5,7] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 5
[4,6,1,2,3,7,5] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[4,6,1,2,5,3,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,6,1,2,5,7,3] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[4,6,1,2,7,3,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,6,1,2,7,5,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[4,6,1,3,2,5,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,6,1,3,2,7,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,6,1,3,5,2,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,6,1,3,5,7,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[4,6,1,3,7,2,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,6,1,3,7,5,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[4,6,1,5,2,3,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,6,1,5,2,7,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,6,1,5,3,2,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,6,1,5,3,7,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,6,1,5,7,2,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,6,1,5,7,3,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[4,6,1,7,2,3,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,6,1,7,2,5,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,6,1,7,3,2,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,6,1,7,3,5,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,6,1,7,5,2,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,6,1,7,5,3,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[4,6,2,1,3,5,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[4,6,2,1,3,7,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,6,2,1,5,3,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,6,2,1,5,7,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,6,2,1,7,3,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,6,2,1,7,5,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[4,6,2,3,1,5,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,6,2,3,1,7,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,6,2,3,5,1,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,6,2,3,5,7,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[4,6,2,3,7,1,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,6,2,3,7,5,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[4,6,2,5,1,3,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,6,2,5,1,7,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,6,2,5,3,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,6,2,5,3,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,6,2,5,7,1,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,6,2,5,7,3,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[4,6,2,7,1,3,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,6,2,7,1,5,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,6,2,7,3,1,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,6,2,7,3,5,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,6,2,7,5,1,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,6,2,7,5,3,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[4,6,3,1,2,5,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[4,6,3,1,2,7,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,6,3,1,5,2,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,6,3,1,5,7,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,6,3,1,7,2,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,6,3,1,7,5,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[4,6,3,2,1,5,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[4,6,3,2,1,7,5] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[4,6,3,2,5,1,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,6,3,2,5,7,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,6,3,2,7,1,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,6,3,2,7,5,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[4,6,3,5,1,2,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,6,3,5,1,7,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,6,3,5,2,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,6,3,5,2,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,6,3,5,7,1,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,6,3,5,7,2,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[4,6,3,7,1,2,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,6,3,7,1,5,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,6,3,7,2,1,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,6,3,7,2,5,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,6,3,7,5,1,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,6,3,7,5,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[4,6,5,1,2,3,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[4,6,5,1,2,7,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,6,5,1,3,2,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,6,5,1,3,7,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,6,5,1,7,2,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,6,5,1,7,3,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[4,6,5,2,1,3,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[4,6,5,2,1,7,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[4,6,5,2,3,1,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,6,5,2,3,7,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,6,5,2,7,1,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,6,5,2,7,3,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[4,6,5,3,1,2,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[4,6,5,3,1,7,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[4,6,5,3,2,1,7] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[4,6,5,3,2,7,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[4,6,5,3,7,1,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,6,5,3,7,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[4,6,5,7,1,2,3] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,6,5,7,1,3,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,6,5,7,2,1,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,6,5,7,2,3,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,6,5,7,3,1,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,6,5,7,3,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[4,6,7,1,2,3,5] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[4,6,7,1,2,5,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[4,6,7,1,3,2,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[4,6,7,1,3,5,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[4,6,7,1,5,2,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[4,6,7,1,5,3,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[4,6,7,2,1,3,5] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[4,6,7,2,1,5,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[4,6,7,2,3,1,5] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[4,6,7,2,3,5,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[4,6,7,2,5,1,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[4,6,7,2,5,3,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[4,6,7,3,1,2,5] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[4,6,7,3,1,5,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[4,6,7,3,2,1,5] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[4,6,7,3,2,5,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[4,6,7,3,5,1,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[4,6,7,3,5,2,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[4,6,7,5,1,2,3] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[4,6,7,5,1,3,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[4,6,7,5,2,1,3] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[4,6,7,5,2,3,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[4,6,7,5,3,1,2] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[4,6,7,5,3,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 10
[4,7,1,2,3,5,6] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 5
[4,7,1,2,3,6,5] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[4,7,1,2,5,3,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,7,1,2,5,6,3] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[4,7,1,2,6,3,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,7,1,2,6,5,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[4,7,1,3,2,5,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,7,1,3,2,6,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,7,1,3,5,2,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,7,1,3,5,6,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[4,7,1,3,6,2,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,7,1,3,6,5,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[4,7,1,5,2,3,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,7,1,5,2,6,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,7,1,5,3,2,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,7,1,5,3,6,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,7,1,5,6,2,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,7,1,5,6,3,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[4,7,1,6,2,3,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,7,1,6,2,5,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,7,1,6,3,2,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,7,1,6,3,5,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,7,1,6,5,2,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,7,1,6,5,3,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[4,7,2,1,3,5,6] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[4,7,2,1,3,6,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,7,2,1,5,3,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,7,2,1,5,6,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,7,2,1,6,3,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,7,2,1,6,5,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[4,7,2,3,1,5,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,7,2,3,1,6,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,7,2,3,5,1,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,7,2,3,5,6,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[4,7,2,3,6,1,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,7,2,3,6,5,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[4,7,2,5,1,3,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,7,2,5,1,6,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,7,2,5,3,1,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,7,2,5,3,6,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,7,2,5,6,1,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,7,2,5,6,3,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[4,7,2,6,1,3,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,7,2,6,1,5,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,7,2,6,3,1,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,7,2,6,3,5,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,7,2,6,5,1,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,7,2,6,5,3,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[4,7,3,1,2,5,6] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[4,7,3,1,2,6,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,7,3,1,5,2,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,7,3,1,5,6,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,7,3,1,6,2,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,7,3,1,6,5,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[4,7,3,2,1,5,6] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[4,7,3,2,1,6,5] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[4,7,3,2,5,1,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,7,3,2,5,6,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,7,3,2,6,1,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,7,3,2,6,5,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[4,7,3,5,1,2,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,7,3,5,1,6,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,7,3,5,2,1,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,7,3,5,2,6,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,7,3,5,6,1,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[4,7,3,5,6,2,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[4,7,3,6,1,2,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,7,3,6,1,5,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,7,3,6,2,1,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,7,3,6,2,5,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,7,3,6,5,1,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,7,3,6,5,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[4,7,5,1,2,3,6] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[4,7,5,1,2,6,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,7,5,1,3,2,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,7,5,1,3,6,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,7,5,1,6,2,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,7,5,1,6,3,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[4,7,5,2,1,3,6] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[4,7,5,2,1,6,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[4,7,5,2,3,1,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,7,5,2,3,6,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,7,5,2,6,1,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,7,5,2,6,3,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[4,7,5,3,1,2,6] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[4,7,5,3,1,6,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[4,7,5,3,2,1,6] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[4,7,5,3,2,6,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[4,7,5,3,6,1,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,7,5,3,6,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[4,7,5,6,1,2,3] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[4,7,5,6,1,3,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,7,5,6,2,1,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,7,5,6,2,3,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[4,7,5,6,3,1,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[4,7,5,6,3,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[4,7,6,1,2,3,5] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[4,7,6,1,2,5,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,7,6,1,3,2,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,7,6,1,3,5,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,7,6,1,5,2,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,7,6,1,5,3,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[4,7,6,2,1,3,5] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[4,7,6,2,1,5,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[4,7,6,2,3,1,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,7,6,2,3,5,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[4,7,6,2,5,1,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,7,6,2,5,3,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[4,7,6,3,1,2,5] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[4,7,6,3,1,5,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[4,7,6,3,2,1,5] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[4,7,6,3,2,5,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[4,7,6,3,5,1,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[4,7,6,3,5,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[4,7,6,5,1,2,3] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[4,7,6,5,1,3,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[4,7,6,5,2,1,3] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[4,7,6,5,2,3,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[4,7,6,5,3,1,2] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[4,7,6,5,3,2,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}} => 15
[5,1,2,3,4,6,7] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => 6
[5,1,2,3,4,7,6] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[5,1,2,3,6,4,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[5,1,2,3,6,7,4] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[5,1,2,3,7,4,6] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[5,1,2,3,7,6,4] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[5,1,2,4,3,6,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[5,1,2,4,3,7,6] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,1,2,4,6,3,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[5,1,2,4,6,7,3] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[5,1,2,4,7,3,6] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[5,1,2,4,7,6,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[5,1,2,6,3,4,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[5,1,2,6,3,7,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,1,2,6,4,3,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,1,2,6,4,7,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,1,2,6,7,3,4] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[5,1,2,6,7,4,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[5,1,2,7,3,4,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[5,1,2,7,3,6,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,1,2,7,4,3,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,1,2,7,4,6,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,1,2,7,6,3,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,1,2,7,6,4,3] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[5,1,3,2,4,6,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[5,1,3,2,4,7,6] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,1,3,2,6,4,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,1,3,2,6,7,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,1,3,2,7,4,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,1,3,2,7,6,4] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,1,3,4,2,6,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[5,1,3,4,2,7,6] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,1,3,4,6,2,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[5,1,3,4,6,7,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[5,1,3,4,7,2,6] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[5,1,3,4,7,6,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[5,1,3,6,2,4,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[5,1,3,6,2,7,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,1,3,6,4,2,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,1,3,6,4,7,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,1,3,6,7,2,4] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[5,1,3,6,7,4,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[5,1,3,7,2,4,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[5,1,3,7,2,6,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,1,3,7,4,2,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,1,3,7,4,6,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,1,3,7,6,2,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,1,3,7,6,4,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[5,1,4,2,3,6,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[5,1,4,2,3,7,6] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,1,4,2,6,3,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,1,4,2,6,7,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,1,4,2,7,3,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,1,4,2,7,6,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,1,4,3,2,6,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,1,4,3,2,7,6] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,1,4,3,6,2,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,1,4,3,6,7,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,1,4,3,7,2,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,1,4,3,7,6,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,1,4,6,2,3,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[5,1,4,6,2,7,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,1,4,6,3,2,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,1,4,6,3,7,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,1,4,6,7,2,3] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[5,1,4,6,7,3,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[5,1,4,7,2,3,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[5,1,4,7,2,6,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,1,4,7,3,2,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,1,4,7,3,6,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,1,4,7,6,2,3] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,1,4,7,6,3,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[5,1,6,2,3,4,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[5,1,6,2,3,7,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,1,6,2,4,3,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,1,6,2,4,7,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,1,6,2,7,3,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,1,6,2,7,4,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,1,6,3,2,4,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,1,6,3,2,7,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,1,6,3,4,2,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,1,6,3,4,7,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,1,6,3,7,2,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,1,6,3,7,4,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,1,6,4,2,3,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,1,6,4,2,7,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,1,6,4,3,2,7] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[5,1,6,4,3,7,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,1,6,4,7,2,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,1,6,4,7,3,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,1,6,7,2,3,4] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[5,1,6,7,2,4,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,1,6,7,3,2,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,1,6,7,3,4,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,1,6,7,4,2,3] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,1,6,7,4,3,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[5,1,7,2,3,4,6] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[5,1,7,2,3,6,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,1,7,2,4,3,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,1,7,2,4,6,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,1,7,2,6,3,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,1,7,2,6,4,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,1,7,3,2,4,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,1,7,3,2,6,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,1,7,3,4,2,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,1,7,3,4,6,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,1,7,3,6,2,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,1,7,3,6,4,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,1,7,4,2,3,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,1,7,4,2,6,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,1,7,4,3,2,6] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[5,1,7,4,3,6,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,1,7,4,6,2,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,1,7,4,6,3,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,1,7,6,2,3,4] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,1,7,6,2,4,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,1,7,6,3,2,4] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[5,1,7,6,3,4,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,1,7,6,4,2,3] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[5,1,7,6,4,3,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 16
[5,2,1,3,4,6,7] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 11
[5,2,1,3,4,7,6] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[5,2,1,3,6,4,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,2,1,3,6,7,4] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[5,2,1,3,7,4,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,2,1,3,7,6,4] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[5,2,1,4,3,6,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[5,2,1,4,3,7,6] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,2,1,4,6,3,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,2,1,4,6,7,3] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[5,2,1,4,7,3,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,2,1,4,7,6,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[5,2,1,6,3,4,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[5,2,1,6,3,7,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,2,1,6,4,3,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[5,2,1,6,4,7,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,2,1,6,7,3,4] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,2,1,6,7,4,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[5,2,1,7,3,4,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[5,2,1,7,3,6,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,2,1,7,4,3,6] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[5,2,1,7,4,6,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,2,1,7,6,3,4] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[5,2,1,7,6,4,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[5,2,3,1,4,6,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[5,2,3,1,4,7,6] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,2,3,1,6,4,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,2,3,1,6,7,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,2,3,1,7,4,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,2,3,1,7,6,4] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,2,3,4,1,6,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[5,2,3,4,1,7,6] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,2,3,4,6,1,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[5,2,3,4,6,7,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[5,2,3,4,7,1,6] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[5,2,3,4,7,6,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[5,2,3,6,1,4,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[5,2,3,6,1,7,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,2,3,6,4,1,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,2,3,6,4,7,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,2,3,6,7,1,4] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[5,2,3,6,7,4,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[5,2,3,7,1,4,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[5,2,3,7,1,6,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,2,3,7,4,1,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,2,3,7,4,6,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,2,3,7,6,1,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,2,3,7,6,4,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[5,2,4,1,3,6,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[5,2,4,1,3,7,6] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,2,4,1,6,3,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,2,4,1,6,7,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,2,4,1,7,3,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,2,4,1,7,6,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,2,4,3,1,6,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,2,4,3,1,7,6] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,2,4,3,6,1,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,2,4,3,6,7,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,2,4,3,7,1,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,2,4,3,7,6,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,2,4,6,1,3,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[5,2,4,6,1,7,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,2,4,6,3,1,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,2,4,6,3,7,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,2,4,6,7,1,3] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[5,2,4,6,7,3,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[5,2,4,7,1,3,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[5,2,4,7,1,6,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,2,4,7,3,1,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,2,4,7,3,6,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,2,4,7,6,1,3] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,2,4,7,6,3,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[5,2,6,1,3,4,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[5,2,6,1,3,7,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,2,6,1,4,3,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,2,6,1,4,7,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,2,6,1,7,3,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,2,6,1,7,4,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,2,6,3,1,4,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,2,6,3,1,7,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,2,6,3,4,1,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,2,6,3,4,7,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,2,6,3,7,1,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,2,6,3,7,4,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,2,6,4,1,3,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,2,6,4,1,7,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,2,6,4,3,1,7] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[5,2,6,4,3,7,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,2,6,4,7,1,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,2,6,4,7,3,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,2,6,7,1,3,4] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[5,2,6,7,1,4,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,2,6,7,3,1,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,2,6,7,3,4,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,2,6,7,4,1,3] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,2,6,7,4,3,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[5,2,7,1,3,4,6] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[5,2,7,1,3,6,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,2,7,1,4,3,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,2,7,1,4,6,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,2,7,1,6,3,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,2,7,1,6,4,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,2,7,3,1,4,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,2,7,3,1,6,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,2,7,3,4,1,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,2,7,3,4,6,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,2,7,3,6,1,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,2,7,3,6,4,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,2,7,4,1,3,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,2,7,4,1,6,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,2,7,4,3,1,6] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[5,2,7,4,3,6,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,2,7,4,6,1,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,2,7,4,6,3,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,2,7,6,1,3,4] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,2,7,6,1,4,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,2,7,6,3,1,4] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[5,2,7,6,3,4,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,2,7,6,4,1,3] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[5,2,7,6,4,3,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 16
[5,3,1,2,4,6,7] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 11
[5,3,1,2,4,7,6] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[5,3,1,2,6,4,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,3,1,2,6,7,4] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[5,3,1,2,7,4,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,3,1,2,7,6,4] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[5,3,1,4,2,6,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[5,3,1,4,2,7,6] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,3,1,4,6,2,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,3,1,4,6,7,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[5,3,1,4,7,2,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,3,1,4,7,6,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[5,3,1,6,2,4,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[5,3,1,6,2,7,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,3,1,6,4,2,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[5,3,1,6,4,7,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,3,1,6,7,2,4] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,3,1,6,7,4,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[5,3,1,7,2,4,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[5,3,1,7,2,6,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,3,1,7,4,2,6] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[5,3,1,7,4,6,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,3,1,7,6,2,4] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[5,3,1,7,6,4,2] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[5,3,2,1,4,6,7] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 15
[5,3,2,1,4,7,6] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[5,3,2,1,6,4,7] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[5,3,2,1,6,7,4] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[5,3,2,1,7,4,6] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[5,3,2,1,7,6,4] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[5,3,2,4,1,6,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[5,3,2,4,1,7,6] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,3,2,4,6,1,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,3,2,4,6,7,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[5,3,2,4,7,1,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,3,2,4,7,6,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[5,3,2,6,1,4,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[5,3,2,6,1,7,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,3,2,6,4,1,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[5,3,2,6,4,7,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,3,2,6,7,1,4] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,3,2,6,7,4,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[5,3,2,7,1,4,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[5,3,2,7,1,6,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,3,2,7,4,1,6] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[5,3,2,7,4,6,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,3,2,7,6,1,4] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[5,3,2,7,6,4,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[5,3,4,1,2,6,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[5,3,4,1,2,7,6] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,3,4,1,6,2,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,3,4,1,6,7,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,3,4,1,7,2,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,3,4,1,7,6,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,3,4,2,1,6,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,3,4,2,1,7,6] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,3,4,2,6,1,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,3,4,2,6,7,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,3,4,2,7,1,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,3,4,2,7,6,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,3,4,6,1,2,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[5,3,4,6,1,7,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,3,4,6,2,1,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,3,4,6,2,7,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,3,4,6,7,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[5,3,4,6,7,2,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[5,3,4,7,1,2,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[5,3,4,7,1,6,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,3,4,7,2,1,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,3,4,7,2,6,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,3,4,7,6,1,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,3,4,7,6,2,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[5,3,6,1,2,4,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[5,3,6,1,2,7,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,3,6,1,4,2,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,3,6,1,4,7,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,3,6,1,7,2,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,3,6,1,7,4,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,3,6,2,1,4,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,3,6,2,1,7,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,3,6,2,4,1,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,3,6,2,4,7,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,3,6,2,7,1,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,3,6,2,7,4,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,3,6,4,1,2,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,3,6,4,1,7,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,3,6,4,2,1,7] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[5,3,6,4,2,7,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,3,6,4,7,1,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,3,6,4,7,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,3,6,7,1,2,4] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[5,3,6,7,1,4,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,3,6,7,2,1,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,3,6,7,2,4,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,3,6,7,4,1,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,3,6,7,4,2,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[5,3,7,1,2,4,6] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[5,3,7,1,2,6,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,3,7,1,4,2,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,3,7,1,4,6,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,3,7,1,6,2,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,3,7,1,6,4,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,3,7,2,1,4,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,3,7,2,1,6,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,3,7,2,4,1,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,3,7,2,4,6,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,3,7,2,6,1,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,3,7,2,6,4,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,3,7,4,1,2,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,3,7,4,1,6,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,3,7,4,2,1,6] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[5,3,7,4,2,6,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,3,7,4,6,1,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,3,7,4,6,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,3,7,6,1,2,4] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,3,7,6,1,4,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,3,7,6,2,1,4] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[5,3,7,6,2,4,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,3,7,6,4,1,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[5,3,7,6,4,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 16
[5,4,1,2,3,6,7] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 11
[5,4,1,2,3,7,6] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[5,4,1,2,6,3,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,4,1,2,6,7,3] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[5,4,1,2,7,3,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,4,1,2,7,6,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[5,4,1,3,2,6,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[5,4,1,3,2,7,6] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,4,1,3,6,2,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,4,1,3,6,7,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[5,4,1,3,7,2,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,4,1,3,7,6,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[5,4,1,6,2,3,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[5,4,1,6,2,7,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,4,1,6,3,2,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[5,4,1,6,3,7,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,4,1,6,7,2,3] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,4,1,6,7,3,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[5,4,1,7,2,3,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[5,4,1,7,2,6,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,4,1,7,3,2,6] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[5,4,1,7,3,6,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,4,1,7,6,2,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[5,4,1,7,6,3,2] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[5,4,2,1,3,6,7] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 15
[5,4,2,1,3,7,6] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[5,4,2,1,6,3,7] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[5,4,2,1,6,7,3] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[5,4,2,1,7,3,6] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[5,4,2,1,7,6,3] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[5,4,2,3,1,6,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[5,4,2,3,1,7,6] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,4,2,3,6,1,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,4,2,3,6,7,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[5,4,2,3,7,1,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,4,2,3,7,6,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[5,4,2,6,1,3,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[5,4,2,6,1,7,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,4,2,6,3,1,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[5,4,2,6,3,7,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,4,2,6,7,1,3] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,4,2,6,7,3,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[5,4,2,7,1,3,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[5,4,2,7,1,6,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,4,2,7,3,1,6] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[5,4,2,7,3,6,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,4,2,7,6,1,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[5,4,2,7,6,3,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[5,4,3,1,2,6,7] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 15
[5,4,3,1,2,7,6] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[5,4,3,1,6,2,7] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[5,4,3,1,6,7,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[5,4,3,1,7,2,6] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[5,4,3,1,7,6,2] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[5,4,3,2,1,6,7] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 18
[5,4,3,2,1,7,6] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 19
[5,4,3,2,6,1,7] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[5,4,3,2,6,7,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[5,4,3,2,7,1,6] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[5,4,3,2,7,6,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[5,4,3,6,1,2,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[5,4,3,6,1,7,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,4,3,6,2,1,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[5,4,3,6,2,7,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,4,3,6,7,1,2] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[5,4,3,6,7,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[5,4,3,7,1,2,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[5,4,3,7,1,6,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,4,3,7,2,1,6] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[5,4,3,7,2,6,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[5,4,3,7,6,1,2] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[5,4,3,7,6,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[5,4,6,1,2,3,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[5,4,6,1,2,7,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,4,6,1,3,2,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,4,6,1,3,7,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,4,6,1,7,2,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,4,6,1,7,3,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,4,6,2,1,3,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,4,6,2,1,7,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,4,6,2,3,1,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,4,6,2,3,7,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,4,6,2,7,1,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,4,6,2,7,3,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,4,6,3,1,2,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,4,6,3,1,7,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,4,6,3,2,1,7] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[5,4,6,3,2,7,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,4,6,3,7,1,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,4,6,3,7,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,4,6,7,1,2,3] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[5,4,6,7,1,3,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,4,6,7,2,1,3] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,4,6,7,2,3,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[5,4,6,7,3,1,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[5,4,6,7,3,2,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[5,4,7,1,2,3,6] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[5,4,7,1,2,6,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,4,7,1,3,2,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,4,7,1,3,6,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,4,7,1,6,2,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,4,7,1,6,3,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,4,7,2,1,3,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,4,7,2,1,6,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,4,7,2,3,1,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,4,7,2,3,6,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[5,4,7,2,6,1,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,4,7,2,6,3,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,4,7,3,1,2,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,4,7,3,1,6,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,4,7,3,2,1,6] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[5,4,7,3,2,6,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,4,7,3,6,1,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[5,4,7,3,6,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[5,4,7,6,1,2,3] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[5,4,7,6,1,3,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,4,7,6,2,1,3] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[5,4,7,6,2,3,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[5,4,7,6,3,1,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[5,4,7,6,3,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 16
[5,6,1,2,3,4,7] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 5
[5,6,1,2,3,7,4] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[5,6,1,2,4,3,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[5,6,1,2,4,7,3] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[5,6,1,2,7,3,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[5,6,1,2,7,4,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[5,6,1,3,2,4,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[5,6,1,3,2,7,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,6,1,3,4,2,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[5,6,1,3,4,7,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[5,6,1,3,7,2,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[5,6,1,3,7,4,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[5,6,1,4,2,3,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[5,6,1,4,2,7,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,6,1,4,3,2,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,6,1,4,3,7,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,6,1,4,7,2,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[5,6,1,4,7,3,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[5,6,1,7,2,3,4] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[5,6,1,7,2,4,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,6,1,7,3,2,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,6,1,7,3,4,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,6,1,7,4,2,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,6,1,7,4,3,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[5,6,2,1,3,4,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[5,6,2,1,3,7,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[5,6,2,1,4,3,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,6,2,1,4,7,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[5,6,2,1,7,3,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,6,2,1,7,4,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[5,6,2,3,1,4,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[5,6,2,3,1,7,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,6,2,3,4,1,7] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[5,6,2,3,4,7,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[5,6,2,3,7,1,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[5,6,2,3,7,4,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[5,6,2,4,1,3,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[5,6,2,4,1,7,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,6,2,4,3,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,6,2,4,3,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,6,2,4,7,1,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[5,6,2,4,7,3,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[5,6,2,7,1,3,4] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[5,6,2,7,1,4,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,6,2,7,3,1,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,6,2,7,3,4,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,6,2,7,4,1,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,6,2,7,4,3,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[5,6,3,1,2,4,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[5,6,3,1,2,7,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[5,6,3,1,4,2,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,6,3,1,4,7,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[5,6,3,1,7,2,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,6,3,1,7,4,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[5,6,3,2,1,4,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[5,6,3,2,1,7,4] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[5,6,3,2,4,1,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,6,3,2,4,7,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[5,6,3,2,7,1,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,6,3,2,7,4,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[5,6,3,4,1,2,7] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[5,6,3,4,1,7,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,6,3,4,2,1,7] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,6,3,4,2,7,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,6,3,4,7,1,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[5,6,3,4,7,2,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[5,6,3,7,1,2,4] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[5,6,3,7,1,4,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,6,3,7,2,1,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,6,3,7,2,4,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,6,3,7,4,1,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,6,3,7,4,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[5,6,4,1,2,3,7] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[5,6,4,1,2,7,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[5,6,4,1,3,2,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,6,4,1,3,7,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[5,6,4,1,7,2,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,6,4,1,7,3,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[5,6,4,2,1,3,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[5,6,4,2,1,7,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[5,6,4,2,3,1,7] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,6,4,2,3,7,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[5,6,4,2,7,1,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,6,4,2,7,3,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[5,6,4,3,1,2,7] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[5,6,4,3,1,7,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[5,6,4,3,2,1,7] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[5,6,4,3,2,7,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[5,6,4,3,7,1,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,6,4,3,7,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[5,6,4,7,1,2,3] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[5,6,4,7,1,3,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,6,4,7,2,1,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,6,4,7,2,3,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,6,4,7,3,1,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,6,4,7,3,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[5,6,7,1,2,3,4] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => {{1,2,3},{4,5,6,7}} => 4
[5,6,7,1,2,4,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[5,6,7,1,3,2,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[5,6,7,1,3,4,2] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[5,6,7,1,4,2,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[5,6,7,1,4,3,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[5,6,7,2,1,3,4] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[5,6,7,2,1,4,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[5,6,7,2,3,1,4] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[5,6,7,2,3,4,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => {{1,2,3},{4,5,6},{7}} => 5
[5,6,7,2,4,1,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[5,6,7,2,4,3,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[5,6,7,3,1,2,4] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[5,6,7,3,1,4,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[5,6,7,3,2,1,4] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[5,6,7,3,2,4,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[5,6,7,3,4,1,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => {{1,2,3},{4,5},{6,7}} => 6
[5,6,7,3,4,2,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => {{1,2,3},{4,5},{6},{7}} => 7
[5,6,7,4,1,2,3] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => {{1,2,3},{4},{5,6,7}} => 7
[5,6,7,4,1,3,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[5,6,7,4,2,1,3] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[5,6,7,4,2,3,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => {{1,2,3},{4},{5,6},{7}} => 8
[5,6,7,4,3,1,2] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => {{1,2,3},{4},{5},{6,7}} => 9
[5,6,7,4,3,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => {{1,2,3},{4},{5},{6},{7}} => 10
[5,7,1,2,3,4,6] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 5
[5,7,1,2,3,6,4] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[5,7,1,2,4,3,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[5,7,1,2,4,6,3] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[5,7,1,2,6,3,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[5,7,1,2,6,4,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[5,7,1,3,2,4,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[5,7,1,3,2,6,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,7,1,3,4,2,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[5,7,1,3,4,6,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[5,7,1,3,6,2,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[5,7,1,3,6,4,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[5,7,1,4,2,3,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[5,7,1,4,2,6,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,7,1,4,3,2,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,7,1,4,3,6,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,7,1,4,6,2,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[5,7,1,4,6,3,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[5,7,1,6,2,3,4] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[5,7,1,6,2,4,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,7,1,6,3,2,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,7,1,6,3,4,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,7,1,6,4,2,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,7,1,6,4,3,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[5,7,2,1,3,4,6] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[5,7,2,1,3,6,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[5,7,2,1,4,3,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,7,2,1,4,6,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[5,7,2,1,6,3,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,7,2,1,6,4,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[5,7,2,3,1,4,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[5,7,2,3,1,6,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,7,2,3,4,1,6] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[5,7,2,3,4,6,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[5,7,2,3,6,1,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[5,7,2,3,6,4,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[5,7,2,4,1,3,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[5,7,2,4,1,6,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,7,2,4,3,1,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,7,2,4,3,6,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,7,2,4,6,1,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[5,7,2,4,6,3,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[5,7,2,6,1,3,4] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[5,7,2,6,1,4,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,7,2,6,3,1,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,7,2,6,3,4,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,7,2,6,4,1,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,7,2,6,4,3,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[5,7,3,1,2,4,6] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[5,7,3,1,2,6,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[5,7,3,1,4,2,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,7,3,1,4,6,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[5,7,3,1,6,2,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,7,3,1,6,4,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[5,7,3,2,1,4,6] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[5,7,3,2,1,6,4] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[5,7,3,2,4,1,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,7,3,2,4,6,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[5,7,3,2,6,1,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,7,3,2,6,4,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[5,7,3,4,1,2,6] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[5,7,3,4,1,6,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,7,3,4,2,1,6] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,7,3,4,2,6,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,7,3,4,6,1,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[5,7,3,4,6,2,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[5,7,3,6,1,2,4] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[5,7,3,6,1,4,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,7,3,6,2,1,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,7,3,6,2,4,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,7,3,6,4,1,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,7,3,6,4,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[5,7,4,1,2,3,6] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[5,7,4,1,2,6,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[5,7,4,1,3,2,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,7,4,1,3,6,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[5,7,4,1,6,2,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,7,4,1,6,3,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[5,7,4,2,1,3,6] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[5,7,4,2,1,6,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[5,7,4,2,3,1,6] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,7,4,2,3,6,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[5,7,4,2,6,1,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,7,4,2,6,3,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[5,7,4,3,1,2,6] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[5,7,4,3,1,6,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[5,7,4,3,2,1,6] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[5,7,4,3,2,6,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[5,7,4,3,6,1,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,7,4,3,6,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[5,7,4,6,1,2,3] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[5,7,4,6,1,3,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,7,4,6,2,1,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,7,4,6,2,3,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[5,7,4,6,3,1,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[5,7,4,6,3,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[5,7,6,1,2,3,4] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[5,7,6,1,2,4,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[5,7,6,1,3,2,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,7,6,1,3,4,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[5,7,6,1,4,2,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,7,6,1,4,3,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[5,7,6,2,1,3,4] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[5,7,6,2,1,4,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[5,7,6,2,3,1,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,7,6,2,3,4,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[5,7,6,2,4,1,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,7,6,2,4,3,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[5,7,6,3,1,2,4] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[5,7,6,3,1,4,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[5,7,6,3,2,1,4] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[5,7,6,3,2,4,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[5,7,6,3,4,1,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[5,7,6,3,4,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[5,7,6,4,1,2,3] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[5,7,6,4,1,3,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[5,7,6,4,2,1,3] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[5,7,6,4,2,3,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[5,7,6,4,3,1,2] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[5,7,6,4,3,2,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}} => 15
[6,1,2,3,4,5,7] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => 6
[6,1,2,3,4,7,5] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[6,1,2,3,5,4,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[6,1,2,3,5,7,4] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[6,1,2,3,7,4,5] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[6,1,2,3,7,5,4] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[6,1,2,4,3,5,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[6,1,2,4,3,7,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,1,2,4,5,3,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[6,1,2,4,5,7,3] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[6,1,2,4,7,3,5] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[6,1,2,4,7,5,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[6,1,2,5,3,4,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[6,1,2,5,3,7,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,1,2,5,4,3,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,1,2,5,4,7,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,1,2,5,7,3,4] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[6,1,2,5,7,4,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[6,1,2,7,3,4,5] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[6,1,2,7,3,5,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,1,2,7,4,3,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,1,2,7,4,5,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,1,2,7,5,3,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,1,2,7,5,4,3] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[6,1,3,2,4,5,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[6,1,3,2,4,7,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,1,3,2,5,4,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,1,3,2,5,7,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,1,3,2,7,4,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,1,3,2,7,5,4] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,1,3,4,2,5,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[6,1,3,4,2,7,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,1,3,4,5,2,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[6,1,3,4,5,7,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[6,1,3,4,7,2,5] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[6,1,3,4,7,5,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[6,1,3,5,2,4,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[6,1,3,5,2,7,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,1,3,5,4,2,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,1,3,5,4,7,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,1,3,5,7,2,4] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[6,1,3,5,7,4,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[6,1,3,7,2,4,5] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[6,1,3,7,2,5,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,1,3,7,4,2,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,1,3,7,4,5,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,1,3,7,5,2,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,1,3,7,5,4,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[6,1,4,2,3,5,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[6,1,4,2,3,7,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,1,4,2,5,3,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,1,4,2,5,7,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,1,4,2,7,3,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,1,4,2,7,5,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,1,4,3,2,5,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,1,4,3,2,7,5] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,1,4,3,5,2,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,1,4,3,5,7,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,1,4,3,7,2,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,1,4,3,7,5,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,1,4,5,2,3,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[6,1,4,5,2,7,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,1,4,5,3,2,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,1,4,5,3,7,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,1,4,5,7,2,3] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[6,1,4,5,7,3,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[6,1,4,7,2,3,5] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[6,1,4,7,2,5,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,1,4,7,3,2,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,1,4,7,3,5,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,1,4,7,5,2,3] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,1,4,7,5,3,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[6,1,5,2,3,4,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[6,1,5,2,3,7,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,1,5,2,4,3,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,1,5,2,4,7,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,1,5,2,7,3,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,1,5,2,7,4,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,1,5,3,2,4,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,1,5,3,2,7,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,1,5,3,4,2,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,1,5,3,4,7,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,1,5,3,7,2,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,1,5,3,7,4,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,1,5,4,2,3,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,1,5,4,2,7,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,1,5,4,3,2,7] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[6,1,5,4,3,7,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,1,5,4,7,2,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,1,5,4,7,3,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,1,5,7,2,3,4] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[6,1,5,7,2,4,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,1,5,7,3,2,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,1,5,7,3,4,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,1,5,7,4,2,3] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,1,5,7,4,3,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[6,1,7,2,3,4,5] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[6,1,7,2,3,5,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,1,7,2,4,3,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,1,7,2,4,5,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,1,7,2,5,3,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,1,7,2,5,4,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,1,7,3,2,4,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,1,7,3,2,5,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,1,7,3,4,2,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,1,7,3,4,5,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,1,7,3,5,2,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,1,7,3,5,4,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,1,7,4,2,3,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,1,7,4,2,5,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,1,7,4,3,2,5] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[6,1,7,4,3,5,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,1,7,4,5,2,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,1,7,4,5,3,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,1,7,5,2,3,4] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,1,7,5,2,4,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,1,7,5,3,2,4] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[6,1,7,5,3,4,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,1,7,5,4,2,3] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[6,1,7,5,4,3,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 16
[6,2,1,3,4,5,7] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 11
[6,2,1,3,4,7,5] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[6,2,1,3,5,4,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,2,1,3,5,7,4] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[6,2,1,3,7,4,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,2,1,3,7,5,4] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[6,2,1,4,3,5,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,2,1,4,3,7,5] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,2,1,4,5,3,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,2,1,4,5,7,3] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[6,2,1,4,7,3,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,2,1,4,7,5,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[6,2,1,5,3,4,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,2,1,5,3,7,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,2,1,5,4,3,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,2,1,5,4,7,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,2,1,5,7,3,4] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,2,1,5,7,4,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[6,2,1,7,3,4,5] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,2,1,7,3,5,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,2,1,7,4,3,5] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,2,1,7,4,5,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,2,1,7,5,3,4] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,2,1,7,5,4,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[6,2,3,1,4,5,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[6,2,3,1,4,7,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,2,3,1,5,4,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,2,3,1,5,7,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,2,3,1,7,4,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,2,3,1,7,5,4] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,2,3,4,1,5,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[6,2,3,4,1,7,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,2,3,4,5,1,7] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[6,2,3,4,5,7,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[6,2,3,4,7,1,5] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[6,2,3,4,7,5,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[6,2,3,5,1,4,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[6,2,3,5,1,7,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,2,3,5,4,1,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,2,3,5,4,7,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,2,3,5,7,1,4] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[6,2,3,5,7,4,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[6,2,3,7,1,4,5] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[6,2,3,7,1,5,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,2,3,7,4,1,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,2,3,7,4,5,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,2,3,7,5,1,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,2,3,7,5,4,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[6,2,4,1,3,5,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[6,2,4,1,3,7,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,2,4,1,5,3,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,2,4,1,5,7,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,2,4,1,7,3,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,2,4,1,7,5,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,2,4,3,1,5,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,2,4,3,1,7,5] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,2,4,3,5,1,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,2,4,3,5,7,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,2,4,3,7,1,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,2,4,3,7,5,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,2,4,5,1,3,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[6,2,4,5,1,7,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,2,4,5,3,1,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,2,4,5,3,7,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,2,4,5,7,1,3] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[6,2,4,5,7,3,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[6,2,4,7,1,3,5] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[6,2,4,7,1,5,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,2,4,7,3,1,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,2,4,7,3,5,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,2,4,7,5,1,3] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,2,4,7,5,3,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[6,2,5,1,3,4,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[6,2,5,1,3,7,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,2,5,1,4,3,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,2,5,1,4,7,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,2,5,1,7,3,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,2,5,1,7,4,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,2,5,3,1,4,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,2,5,3,1,7,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,2,5,3,4,1,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,2,5,3,4,7,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,2,5,3,7,1,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,2,5,3,7,4,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,2,5,4,1,3,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,2,5,4,1,7,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,2,5,4,3,1,7] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[6,2,5,4,3,7,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,2,5,4,7,1,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,2,5,4,7,3,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,2,5,7,1,3,4] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[6,2,5,7,1,4,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,2,5,7,3,1,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,2,5,7,3,4,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,2,5,7,4,1,3] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,2,5,7,4,3,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[6,2,7,1,3,4,5] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[6,2,7,1,3,5,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,2,7,1,4,3,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,2,7,1,4,5,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,2,7,1,5,3,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,2,7,1,5,4,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,2,7,3,1,4,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,2,7,3,1,5,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,2,7,3,4,1,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,2,7,3,4,5,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,2,7,3,5,1,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,2,7,3,5,4,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,2,7,4,1,3,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,2,7,4,1,5,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,2,7,4,3,1,5] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[6,2,7,4,3,5,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,2,7,4,5,1,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,2,7,4,5,3,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,2,7,5,1,3,4] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,2,7,5,1,4,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,2,7,5,3,1,4] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[6,2,7,5,3,4,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,2,7,5,4,1,3] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[6,2,7,5,4,3,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 16
[6,3,1,2,4,5,7] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 11
[6,3,1,2,4,7,5] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[6,3,1,2,5,4,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,3,1,2,5,7,4] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[6,3,1,2,7,4,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,3,1,2,7,5,4] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[6,3,1,4,2,5,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,3,1,4,2,7,5] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,3,1,4,5,2,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,3,1,4,5,7,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[6,3,1,4,7,2,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,3,1,4,7,5,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[6,3,1,5,2,4,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,3,1,5,2,7,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,3,1,5,4,2,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,3,1,5,4,7,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,3,1,5,7,2,4] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,3,1,5,7,4,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[6,3,1,7,2,4,5] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,3,1,7,2,5,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,3,1,7,4,2,5] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,3,1,7,4,5,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,3,1,7,5,2,4] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,3,1,7,5,4,2] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[6,3,2,1,4,5,7] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 15
[6,3,2,1,4,7,5] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[6,3,2,1,5,4,7] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[6,3,2,1,5,7,4] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[6,3,2,1,7,4,5] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[6,3,2,1,7,5,4] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[6,3,2,4,1,5,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,3,2,4,1,7,5] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,3,2,4,5,1,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,3,2,4,5,7,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[6,3,2,4,7,1,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,3,2,4,7,5,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[6,3,2,5,1,4,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,3,2,5,1,7,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,3,2,5,4,1,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,3,2,5,4,7,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,3,2,5,7,1,4] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,3,2,5,7,4,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[6,3,2,7,1,4,5] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,3,2,7,1,5,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,3,2,7,4,1,5] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,3,2,7,4,5,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,3,2,7,5,1,4] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,3,2,7,5,4,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[6,3,4,1,2,5,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[6,3,4,1,2,7,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,3,4,1,5,2,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,3,4,1,5,7,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,3,4,1,7,2,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,3,4,1,7,5,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,3,4,2,1,5,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,3,4,2,1,7,5] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,3,4,2,5,1,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,3,4,2,5,7,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,3,4,2,7,1,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,3,4,2,7,5,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,3,4,5,1,2,7] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[6,3,4,5,1,7,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,3,4,5,2,1,7] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,3,4,5,2,7,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,3,4,5,7,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[6,3,4,5,7,2,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[6,3,4,7,1,2,5] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[6,3,4,7,1,5,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,3,4,7,2,1,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,3,4,7,2,5,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,3,4,7,5,1,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,3,4,7,5,2,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[6,3,5,1,2,4,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[6,3,5,1,2,7,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,3,5,1,4,2,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,3,5,1,4,7,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,3,5,1,7,2,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,3,5,1,7,4,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,3,5,2,1,4,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,3,5,2,1,7,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,3,5,2,4,1,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,3,5,2,4,7,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,3,5,2,7,1,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,3,5,2,7,4,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,3,5,4,1,2,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,3,5,4,1,7,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,3,5,4,2,1,7] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[6,3,5,4,2,7,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,3,5,4,7,1,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,3,5,4,7,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,3,5,7,1,2,4] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[6,3,5,7,1,4,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,3,5,7,2,1,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,3,5,7,2,4,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,3,5,7,4,1,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,3,5,7,4,2,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[6,3,7,1,2,4,5] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[6,3,7,1,2,5,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,3,7,1,4,2,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,3,7,1,4,5,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,3,7,1,5,2,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,3,7,1,5,4,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,3,7,2,1,4,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,3,7,2,1,5,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,3,7,2,4,1,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,3,7,2,4,5,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,3,7,2,5,1,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,3,7,2,5,4,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,3,7,4,1,2,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,3,7,4,1,5,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,3,7,4,2,1,5] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[6,3,7,4,2,5,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,3,7,4,5,1,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,3,7,4,5,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,3,7,5,1,2,4] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,3,7,5,1,4,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,3,7,5,2,1,4] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[6,3,7,5,2,4,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,3,7,5,4,1,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[6,3,7,5,4,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 16
[6,4,1,2,3,5,7] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 11
[6,4,1,2,3,7,5] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[6,4,1,2,5,3,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,4,1,2,5,7,3] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[6,4,1,2,7,3,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,4,1,2,7,5,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[6,4,1,3,2,5,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,4,1,3,2,7,5] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,4,1,3,5,2,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,4,1,3,5,7,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[6,4,1,3,7,2,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,4,1,3,7,5,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[6,4,1,5,2,3,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,4,1,5,2,7,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,4,1,5,3,2,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,4,1,5,3,7,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,4,1,5,7,2,3] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,4,1,5,7,3,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[6,4,1,7,2,3,5] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,4,1,7,2,5,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,4,1,7,3,2,5] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,4,1,7,3,5,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,4,1,7,5,2,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,4,1,7,5,3,2] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[6,4,2,1,3,5,7] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 15
[6,4,2,1,3,7,5] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[6,4,2,1,5,3,7] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[6,4,2,1,5,7,3] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[6,4,2,1,7,3,5] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[6,4,2,1,7,5,3] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[6,4,2,3,1,5,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,4,2,3,1,7,5] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,4,2,3,5,1,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,4,2,3,5,7,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[6,4,2,3,7,1,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,4,2,3,7,5,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[6,4,2,5,1,3,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,4,2,5,1,7,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,4,2,5,3,1,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,4,2,5,3,7,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,4,2,5,7,1,3] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,4,2,5,7,3,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[6,4,2,7,1,3,5] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,4,2,7,1,5,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,4,2,7,3,1,5] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,4,2,7,3,5,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,4,2,7,5,1,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,4,2,7,5,3,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[6,4,3,1,2,5,7] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 15
[6,4,3,1,2,7,5] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[6,4,3,1,5,2,7] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[6,4,3,1,5,7,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[6,4,3,1,7,2,5] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[6,4,3,1,7,5,2] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[6,4,3,2,1,5,7] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 18
[6,4,3,2,1,7,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 19
[6,4,3,2,5,1,7] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[6,4,3,2,5,7,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[6,4,3,2,7,1,5] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[6,4,3,2,7,5,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[6,4,3,5,1,2,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,4,3,5,1,7,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,4,3,5,2,1,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,4,3,5,2,7,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,4,3,5,7,1,2] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,4,3,5,7,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[6,4,3,7,1,2,5] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,4,3,7,1,5,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,4,3,7,2,1,5] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,4,3,7,2,5,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,4,3,7,5,1,2] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,4,3,7,5,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[6,4,5,1,2,3,7] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[6,4,5,1,2,7,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,4,5,1,3,2,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,4,5,1,3,7,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,4,5,1,7,2,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,4,5,1,7,3,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,4,5,2,1,3,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,4,5,2,1,7,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,4,5,2,3,1,7] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,4,5,2,3,7,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,4,5,2,7,1,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,4,5,2,7,3,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,4,5,3,1,2,7] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,4,5,3,1,7,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,4,5,3,2,1,7] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[6,4,5,3,2,7,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,4,5,3,7,1,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,4,5,3,7,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,4,5,7,1,2,3] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[6,4,5,7,1,3,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,4,5,7,2,1,3] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,4,5,7,2,3,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[6,4,5,7,3,1,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[6,4,5,7,3,2,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[6,4,7,1,2,3,5] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[6,4,7,1,2,5,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,4,7,1,3,2,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,4,7,1,3,5,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,4,7,1,5,2,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,4,7,1,5,3,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,4,7,2,1,3,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,4,7,2,1,5,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,4,7,2,3,1,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,4,7,2,3,5,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,4,7,2,5,1,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,4,7,2,5,3,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,4,7,3,1,2,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,4,7,3,1,5,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,4,7,3,2,1,5] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[6,4,7,3,2,5,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,4,7,3,5,1,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,4,7,3,5,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,4,7,5,1,2,3] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,4,7,5,1,3,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,4,7,5,2,1,3] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[6,4,7,5,2,3,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,4,7,5,3,1,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[6,4,7,5,3,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 16
[6,5,1,2,3,4,7] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 11
[6,5,1,2,3,7,4] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[6,5,1,2,4,3,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,5,1,2,4,7,3] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[6,5,1,2,7,3,4] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,5,1,2,7,4,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[6,5,1,3,2,4,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,5,1,3,2,7,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,5,1,3,4,2,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,5,1,3,4,7,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[6,5,1,3,7,2,4] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,5,1,3,7,4,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[6,5,1,4,2,3,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,5,1,4,2,7,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,5,1,4,3,2,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,5,1,4,3,7,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,5,1,4,7,2,3] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,5,1,4,7,3,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[6,5,1,7,2,3,4] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,5,1,7,2,4,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,5,1,7,3,2,4] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,5,1,7,3,4,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,5,1,7,4,2,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,5,1,7,4,3,2] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[6,5,2,1,3,4,7] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 15
[6,5,2,1,3,7,4] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[6,5,2,1,4,3,7] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[6,5,2,1,4,7,3] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[6,5,2,1,7,3,4] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[6,5,2,1,7,4,3] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[6,5,2,3,1,4,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,5,2,3,1,7,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,5,2,3,4,1,7] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,5,2,3,4,7,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[6,5,2,3,7,1,4] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,5,2,3,7,4,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[6,5,2,4,1,3,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,5,2,4,1,7,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,5,2,4,3,1,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,5,2,4,3,7,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,5,2,4,7,1,3] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,5,2,4,7,3,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[6,5,2,7,1,3,4] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,5,2,7,1,4,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,5,2,7,3,1,4] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,5,2,7,3,4,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,5,2,7,4,1,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,5,2,7,4,3,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[6,5,3,1,2,4,7] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 15
[6,5,3,1,2,7,4] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[6,5,3,1,4,2,7] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[6,5,3,1,4,7,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[6,5,3,1,7,2,4] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[6,5,3,1,7,4,2] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[6,5,3,2,1,4,7] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 18
[6,5,3,2,1,7,4] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 19
[6,5,3,2,4,1,7] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[6,5,3,2,4,7,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[6,5,3,2,7,1,4] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[6,5,3,2,7,4,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[6,5,3,4,1,2,7] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,5,3,4,1,7,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,5,3,4,2,1,7] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,5,3,4,2,7,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,5,3,4,7,1,2] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[6,5,3,4,7,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[6,5,3,7,1,2,4] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,5,3,7,1,4,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,5,3,7,2,1,4] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,5,3,7,2,4,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,5,3,7,4,1,2] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,5,3,7,4,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[6,5,4,1,2,3,7] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 15
[6,5,4,1,2,7,3] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[6,5,4,1,3,2,7] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[6,5,4,1,3,7,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[6,5,4,1,7,2,3] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[6,5,4,1,7,3,2] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[6,5,4,2,1,3,7] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 18
[6,5,4,2,1,7,3] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 19
[6,5,4,2,3,1,7] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[6,5,4,2,3,7,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[6,5,4,2,7,1,3] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[6,5,4,2,7,3,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[6,5,4,3,1,2,7] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 18
[6,5,4,3,1,7,2] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 19
[6,5,4,3,2,1,7] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => 20
[6,5,4,3,2,7,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 19
[6,5,4,3,7,1,2] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[6,5,4,3,7,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[6,5,4,7,1,2,3] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[6,5,4,7,1,3,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,5,4,7,2,1,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,5,4,7,2,3,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[6,5,4,7,3,1,2] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[6,5,4,7,3,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[6,5,7,1,2,3,4] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[6,5,7,1,2,4,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,5,7,1,3,2,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,5,7,1,3,4,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,5,7,1,4,2,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,5,7,1,4,3,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,5,7,2,1,3,4] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,5,7,2,1,4,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,5,7,2,3,1,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,5,7,2,3,4,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[6,5,7,2,4,1,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,5,7,2,4,3,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,5,7,3,1,2,4] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,5,7,3,1,4,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,5,7,3,2,1,4] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[6,5,7,3,2,4,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,5,7,3,4,1,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[6,5,7,3,4,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[6,5,7,4,1,2,3] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[6,5,7,4,1,3,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,5,7,4,2,1,3] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[6,5,7,4,2,3,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[6,5,7,4,3,1,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[6,5,7,4,3,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 16
[6,7,1,2,3,4,5] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => {{1,2},{3,4,5,6,7}} => 5
[6,7,1,2,3,5,4] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[6,7,1,2,4,3,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[6,7,1,2,4,5,3] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[6,7,1,2,5,3,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[6,7,1,2,5,4,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[6,7,1,3,2,4,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[6,7,1,3,2,5,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[6,7,1,3,4,2,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[6,7,1,3,4,5,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[6,7,1,3,5,2,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[6,7,1,3,5,4,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[6,7,1,4,2,3,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[6,7,1,4,2,5,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[6,7,1,4,3,2,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[6,7,1,4,3,5,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[6,7,1,4,5,2,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[6,7,1,4,5,3,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[6,7,1,5,2,3,4] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[6,7,1,5,2,4,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[6,7,1,5,3,2,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[6,7,1,5,3,4,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[6,7,1,5,4,2,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[6,7,1,5,4,3,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[6,7,2,1,3,4,5] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[6,7,2,1,3,5,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[6,7,2,1,4,3,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[6,7,2,1,4,5,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[6,7,2,1,5,3,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[6,7,2,1,5,4,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[6,7,2,3,1,4,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[6,7,2,3,1,5,4] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[6,7,2,3,4,1,5] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[6,7,2,3,4,5,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => {{1,2},{3,4,5,6},{7}} => 6
[6,7,2,3,5,1,4] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[6,7,2,3,5,4,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[6,7,2,4,1,3,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[6,7,2,4,1,5,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[6,7,2,4,3,1,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[6,7,2,4,3,5,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[6,7,2,4,5,1,3] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[6,7,2,4,5,3,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[6,7,2,5,1,3,4] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[6,7,2,5,1,4,3] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[6,7,2,5,3,1,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[6,7,2,5,3,4,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[6,7,2,5,4,1,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[6,7,2,5,4,3,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[6,7,3,1,2,4,5] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[6,7,3,1,2,5,4] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[6,7,3,1,4,2,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[6,7,3,1,4,5,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[6,7,3,1,5,2,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[6,7,3,1,5,4,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[6,7,3,2,1,4,5] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[6,7,3,2,1,5,4] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[6,7,3,2,4,1,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[6,7,3,2,4,5,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[6,7,3,2,5,1,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[6,7,3,2,5,4,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[6,7,3,4,1,2,5] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[6,7,3,4,1,5,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[6,7,3,4,2,1,5] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[6,7,3,4,2,5,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[6,7,3,4,5,1,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => {{1,2},{3,4,5},{6,7}} => 7
[6,7,3,4,5,2,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => {{1,2},{3,4,5},{6},{7}} => 8
[6,7,3,5,1,2,4] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[6,7,3,5,1,4,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[6,7,3,5,2,1,4] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[6,7,3,5,2,4,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[6,7,3,5,4,1,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[6,7,3,5,4,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[6,7,4,1,2,3,5] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[6,7,4,1,2,5,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[6,7,4,1,3,2,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[6,7,4,1,3,5,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[6,7,4,1,5,2,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[6,7,4,1,5,3,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[6,7,4,2,1,3,5] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[6,7,4,2,1,5,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[6,7,4,2,3,1,5] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[6,7,4,2,3,5,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[6,7,4,2,5,1,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[6,7,4,2,5,3,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[6,7,4,3,1,2,5] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[6,7,4,3,1,5,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[6,7,4,3,2,1,5] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[6,7,4,3,2,5,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[6,7,4,3,5,1,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[6,7,4,3,5,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[6,7,4,5,1,2,3] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => {{1,2},{3,4},{5,6,7}} => 8
[6,7,4,5,1,3,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[6,7,4,5,2,1,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[6,7,4,5,2,3,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => {{1,2},{3,4},{5,6},{7}} => 9
[6,7,4,5,3,1,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => {{1,2},{3,4},{5},{6,7}} => 10
[6,7,4,5,3,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => {{1,2},{3,4},{5},{6},{7}} => 11
[6,7,5,1,2,3,4] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => {{1,2},{3},{4,5,6,7}} => 9
[6,7,5,1,2,4,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[6,7,5,1,3,2,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[6,7,5,1,3,4,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[6,7,5,1,4,2,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[6,7,5,1,4,3,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[6,7,5,2,1,3,4] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[6,7,5,2,1,4,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[6,7,5,2,3,1,4] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[6,7,5,2,3,4,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => {{1,2},{3},{4,5,6},{7}} => 10
[6,7,5,2,4,1,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[6,7,5,2,4,3,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[6,7,5,3,1,2,4] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[6,7,5,3,1,4,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[6,7,5,3,2,1,4] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[6,7,5,3,2,4,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[6,7,5,3,4,1,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => {{1,2},{3},{4,5},{6,7}} => 11
[6,7,5,3,4,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => {{1,2},{3},{4,5},{6},{7}} => 12
[6,7,5,4,1,2,3] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => {{1,2},{3},{4},{5,6,7}} => 12
[6,7,5,4,1,3,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[6,7,5,4,2,1,3] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[6,7,5,4,2,3,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => {{1,2},{3},{4},{5,6},{7}} => 13
[6,7,5,4,3,1,2] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => {{1,2},{3},{4},{5},{6,7}} => 14
[6,7,5,4,3,2,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => {{1,2},{3},{4},{5},{6},{7}} => 15
[7,1,2,3,4,5,6] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7}} => 6
[7,1,2,3,4,6,5] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[7,1,2,3,5,4,6] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[7,1,2,3,5,6,4] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[7,1,2,3,6,4,5] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[7,1,2,3,6,5,4] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[7,1,2,4,3,5,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[7,1,2,4,3,6,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,1,2,4,5,3,6] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[7,1,2,4,5,6,3] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[7,1,2,4,6,3,5] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[7,1,2,4,6,5,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[7,1,2,5,3,4,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[7,1,2,5,3,6,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,1,2,5,4,3,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,1,2,5,4,6,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,1,2,5,6,3,4] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[7,1,2,5,6,4,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[7,1,2,6,3,4,5] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[7,1,2,6,3,5,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,1,2,6,4,3,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,1,2,6,4,5,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,1,2,6,5,3,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,1,2,6,5,4,3] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[7,1,3,2,4,5,6] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[7,1,3,2,4,6,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,1,3,2,5,4,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,1,3,2,5,6,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,1,3,2,6,4,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,1,3,2,6,5,4] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,1,3,4,2,5,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[7,1,3,4,2,6,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,1,3,4,5,2,6] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[7,1,3,4,5,6,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[7,1,3,4,6,2,5] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[7,1,3,4,6,5,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[7,1,3,5,2,4,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[7,1,3,5,2,6,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,1,3,5,4,2,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,1,3,5,4,6,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,1,3,5,6,2,4] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[7,1,3,5,6,4,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[7,1,3,6,2,4,5] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[7,1,3,6,2,5,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,1,3,6,4,2,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,1,3,6,4,5,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,1,3,6,5,2,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,1,3,6,5,4,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[7,1,4,2,3,5,6] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[7,1,4,2,3,6,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,1,4,2,5,3,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,1,4,2,5,6,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,1,4,2,6,3,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,1,4,2,6,5,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,1,4,3,2,5,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,1,4,3,2,6,5] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,1,4,3,5,2,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,1,4,3,5,6,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,1,4,3,6,2,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,1,4,3,6,5,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,1,4,5,2,3,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[7,1,4,5,2,6,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,1,4,5,3,2,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,1,4,5,3,6,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,1,4,5,6,2,3] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[7,1,4,5,6,3,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[7,1,4,6,2,3,5] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[7,1,4,6,2,5,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,1,4,6,3,2,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,1,4,6,3,5,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,1,4,6,5,2,3] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,1,4,6,5,3,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[7,1,5,2,3,4,6] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[7,1,5,2,3,6,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,1,5,2,4,3,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,1,5,2,4,6,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,1,5,2,6,3,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,1,5,2,6,4,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,1,5,3,2,4,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,1,5,3,2,6,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,1,5,3,4,2,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,1,5,3,4,6,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,1,5,3,6,2,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,1,5,3,6,4,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,1,5,4,2,3,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,1,5,4,2,6,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,1,5,4,3,2,6] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[7,1,5,4,3,6,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,1,5,4,6,2,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,1,5,4,6,3,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,1,5,6,2,3,4] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[7,1,5,6,2,4,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,1,5,6,3,2,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,1,5,6,3,4,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,1,5,6,4,2,3] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,1,5,6,4,3,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[7,1,6,2,3,4,5] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[7,1,6,2,3,5,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,1,6,2,4,3,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,1,6,2,4,5,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,1,6,2,5,3,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,1,6,2,5,4,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,1,6,3,2,4,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,1,6,3,2,5,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,1,6,3,4,2,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,1,6,3,4,5,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,1,6,3,5,2,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,1,6,3,5,4,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,1,6,4,2,3,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,1,6,4,2,5,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,1,6,4,3,2,5] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[7,1,6,4,3,5,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,1,6,4,5,2,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,1,6,4,5,3,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,1,6,5,2,3,4] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,1,6,5,2,4,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,1,6,5,3,2,4] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[7,1,6,5,3,4,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,1,6,5,4,2,3] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[7,1,6,5,4,3,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 16
[7,2,1,3,4,5,6] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 11
[7,2,1,3,4,6,5] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[7,2,1,3,5,4,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,2,1,3,5,6,4] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[7,2,1,3,6,4,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,2,1,3,6,5,4] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,2,1,4,3,5,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,2,1,4,3,6,5] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,2,1,4,5,3,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,2,1,4,5,6,3] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[7,2,1,4,6,3,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,2,1,4,6,5,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,2,1,5,3,4,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,2,1,5,3,6,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,2,1,5,4,3,6] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,2,1,5,4,6,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,2,1,5,6,3,4] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,2,1,5,6,4,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,2,1,6,3,4,5] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,2,1,6,3,5,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,2,1,6,4,3,5] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,2,1,6,4,5,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,2,1,6,5,3,4] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,2,1,6,5,4,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[7,2,3,1,4,5,6] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[7,2,3,1,4,6,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,2,3,1,5,4,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,2,3,1,5,6,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,2,3,1,6,4,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,2,3,1,6,5,4] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,2,3,4,1,5,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[7,2,3,4,1,6,5] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,2,3,4,5,1,6] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[7,2,3,4,5,6,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6},{7}} => 7
[7,2,3,4,6,1,5] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[7,2,3,4,6,5,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[7,2,3,5,1,4,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[7,2,3,5,1,6,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,2,3,5,4,1,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,2,3,5,4,6,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,2,3,5,6,1,4] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[7,2,3,5,6,4,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[7,2,3,6,1,4,5] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[7,2,3,6,1,5,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,2,3,6,4,1,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,2,3,6,4,5,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,2,3,6,5,1,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,2,3,6,5,4,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[7,2,4,1,3,5,6] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[7,2,4,1,3,6,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,2,4,1,5,3,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,2,4,1,5,6,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,2,4,1,6,3,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,2,4,1,6,5,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,2,4,3,1,5,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,2,4,3,1,6,5] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,2,4,3,5,1,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,2,4,3,5,6,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,2,4,3,6,1,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,2,4,3,6,5,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,2,4,5,1,3,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[7,2,4,5,1,6,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,2,4,5,3,1,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,2,4,5,3,6,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,2,4,5,6,1,3] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[7,2,4,5,6,3,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[7,2,4,6,1,3,5] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[7,2,4,6,1,5,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,2,4,6,3,1,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,2,4,6,3,5,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,2,4,6,5,1,3] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,2,4,6,5,3,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[7,2,5,1,3,4,6] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[7,2,5,1,3,6,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,2,5,1,4,3,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,2,5,1,4,6,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,2,5,1,6,3,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,2,5,1,6,4,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,2,5,3,1,4,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,2,5,3,1,6,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,2,5,3,4,1,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,2,5,3,4,6,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,2,5,3,6,1,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,2,5,3,6,4,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,2,5,4,1,3,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,2,5,4,1,6,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,2,5,4,3,1,6] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[7,2,5,4,3,6,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,2,5,4,6,1,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,2,5,4,6,3,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,2,5,6,1,3,4] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[7,2,5,6,1,4,3] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,2,5,6,3,1,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,2,5,6,3,4,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,2,5,6,4,1,3] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,2,5,6,4,3,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[7,2,6,1,3,4,5] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[7,2,6,1,3,5,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,2,6,1,4,3,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,2,6,1,4,5,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,2,6,1,5,3,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,2,6,1,5,4,3] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,2,6,3,1,4,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,2,6,3,1,5,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,2,6,3,4,1,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,2,6,3,4,5,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,2,6,3,5,1,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,2,6,3,5,4,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,2,6,4,1,3,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,2,6,4,1,5,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,2,6,4,3,1,5] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[7,2,6,4,3,5,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,2,6,4,5,1,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,2,6,4,5,3,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,2,6,5,1,3,4] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,2,6,5,1,4,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,2,6,5,3,1,4] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[7,2,6,5,3,4,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,2,6,5,4,1,3] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[7,2,6,5,4,3,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 16
[7,3,1,2,4,5,6] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 11
[7,3,1,2,4,6,5] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[7,3,1,2,5,4,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,3,1,2,5,6,4] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[7,3,1,2,6,4,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,3,1,2,6,5,4] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,3,1,4,2,5,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,3,1,4,2,6,5] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,3,1,4,5,2,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,3,1,4,5,6,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[7,3,1,4,6,2,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,3,1,4,6,5,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,3,1,5,2,4,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,3,1,5,2,6,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,3,1,5,4,2,6] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,3,1,5,4,6,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,3,1,5,6,2,4] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,3,1,5,6,4,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,3,1,6,2,4,5] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,3,1,6,2,5,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,3,1,6,4,2,5] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,3,1,6,4,5,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,3,1,6,5,2,4] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,3,1,6,5,4,2] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[7,3,2,1,4,5,6] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 15
[7,3,2,1,4,6,5] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,3,2,1,5,4,6] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,3,2,1,5,6,4] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,3,2,1,6,4,5] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,3,2,1,6,5,4] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[7,3,2,4,1,5,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,3,2,4,1,6,5] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,3,2,4,5,1,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,3,2,4,5,6,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[7,3,2,4,6,1,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,3,2,4,6,5,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,3,2,5,1,4,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,3,2,5,1,6,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,3,2,5,4,1,6] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,3,2,5,4,6,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,3,2,5,6,1,4] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,3,2,5,6,4,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,3,2,6,1,4,5] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,3,2,6,1,5,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,3,2,6,4,1,5] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,3,2,6,4,5,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,3,2,6,5,1,4] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,3,2,6,5,4,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[7,3,4,1,2,5,6] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[7,3,4,1,2,6,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,3,4,1,5,2,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,3,4,1,5,6,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,3,4,1,6,2,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,3,4,1,6,5,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,3,4,2,1,5,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,3,4,2,1,6,5] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,3,4,2,5,1,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,3,4,2,5,6,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,3,4,2,6,1,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,3,4,2,6,5,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,3,4,5,1,2,6] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[7,3,4,5,1,6,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,3,4,5,2,1,6] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,3,4,5,2,6,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,3,4,5,6,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => {{1},{2,3,4,5},{6,7}} => 8
[7,3,4,5,6,2,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => {{1},{2,3,4,5},{6},{7}} => 9
[7,3,4,6,1,2,5] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[7,3,4,6,1,5,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,3,4,6,2,1,5] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,3,4,6,2,5,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,3,4,6,5,1,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,3,4,6,5,2,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[7,3,5,1,2,4,6] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[7,3,5,1,2,6,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,3,5,1,4,2,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,3,5,1,4,6,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,3,5,1,6,2,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,3,5,1,6,4,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,3,5,2,1,4,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,3,5,2,1,6,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,3,5,2,4,1,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,3,5,2,4,6,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,3,5,2,6,1,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,3,5,2,6,4,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,3,5,4,1,2,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,3,5,4,1,6,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,3,5,4,2,1,6] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[7,3,5,4,2,6,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,3,5,4,6,1,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,3,5,4,6,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,3,5,6,1,2,4] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[7,3,5,6,1,4,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,3,5,6,2,1,4] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,3,5,6,2,4,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,3,5,6,4,1,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,3,5,6,4,2,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[7,3,6,1,2,4,5] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[7,3,6,1,2,5,4] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,3,6,1,4,2,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,3,6,1,4,5,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,3,6,1,5,2,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,3,6,1,5,4,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,3,6,2,1,4,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,3,6,2,1,5,4] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,3,6,2,4,1,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,3,6,2,4,5,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,3,6,2,5,1,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,3,6,2,5,4,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,3,6,4,1,2,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,3,6,4,1,5,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,3,6,4,2,1,5] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[7,3,6,4,2,5,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,3,6,4,5,1,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,3,6,4,5,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,3,6,5,1,2,4] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,3,6,5,1,4,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,3,6,5,2,1,4] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[7,3,6,5,2,4,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,3,6,5,4,1,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[7,3,6,5,4,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 16
[7,4,1,2,3,5,6] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 11
[7,4,1,2,3,6,5] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[7,4,1,2,5,3,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,4,1,2,5,6,3] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[7,4,1,2,6,3,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,4,1,2,6,5,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,4,1,3,2,5,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,4,1,3,2,6,5] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,4,1,3,5,2,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,4,1,3,5,6,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[7,4,1,3,6,2,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,4,1,3,6,5,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,4,1,5,2,3,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,4,1,5,2,6,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,4,1,5,3,2,6] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,4,1,5,3,6,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,4,1,5,6,2,3] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,4,1,5,6,3,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,4,1,6,2,3,5] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,4,1,6,2,5,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,4,1,6,3,2,5] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,4,1,6,3,5,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,4,1,6,5,2,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,4,1,6,5,3,2] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[7,4,2,1,3,5,6] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 15
[7,4,2,1,3,6,5] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,4,2,1,5,3,6] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,4,2,1,5,6,3] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,4,2,1,6,3,5] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,4,2,1,6,5,3] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[7,4,2,3,1,5,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,4,2,3,1,6,5] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,4,2,3,5,1,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,4,2,3,5,6,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[7,4,2,3,6,1,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,4,2,3,6,5,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,4,2,5,1,3,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,4,2,5,1,6,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,4,2,5,3,1,6] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,4,2,5,3,6,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,4,2,5,6,1,3] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,4,2,5,6,3,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,4,2,6,1,3,5] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,4,2,6,1,5,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,4,2,6,3,1,5] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,4,2,6,3,5,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,4,2,6,5,1,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,4,2,6,5,3,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[7,4,3,1,2,5,6] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 15
[7,4,3,1,2,6,5] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,4,3,1,5,2,6] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,4,3,1,5,6,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,4,3,1,6,2,5] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,4,3,1,6,5,2] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[7,4,3,2,1,5,6] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 18
[7,4,3,2,1,6,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 19
[7,4,3,2,5,1,6] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,4,3,2,5,6,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,4,3,2,6,1,5] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,4,3,2,6,5,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[7,4,3,5,1,2,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,4,3,5,1,6,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,4,3,5,2,1,6] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,4,3,5,2,6,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,4,3,5,6,1,2] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,4,3,5,6,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,4,3,6,1,2,5] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,4,3,6,1,5,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,4,3,6,2,1,5] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,4,3,6,2,5,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,4,3,6,5,1,2] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,4,3,6,5,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[7,4,5,1,2,3,6] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[7,4,5,1,2,6,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,4,5,1,3,2,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,4,5,1,3,6,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,4,5,1,6,2,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,4,5,1,6,3,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,4,5,2,1,3,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,4,5,2,1,6,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,4,5,2,3,1,6] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,4,5,2,3,6,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,4,5,2,6,1,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,4,5,2,6,3,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,4,5,3,1,2,6] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,4,5,3,1,6,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,4,5,3,2,1,6] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[7,4,5,3,2,6,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,4,5,3,6,1,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,4,5,3,6,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,4,5,6,1,2,3] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => {{1},{2,3,4},{5,6,7}} => 9
[7,4,5,6,1,3,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,4,5,6,2,1,3] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,4,5,6,2,3,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => {{1},{2,3,4},{5,6},{7}} => 10
[7,4,5,6,3,1,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => {{1},{2,3,4},{5},{6,7}} => 11
[7,4,5,6,3,2,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => {{1},{2,3,4},{5},{6},{7}} => 12
[7,4,6,1,2,3,5] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[7,4,6,1,2,5,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,4,6,1,3,2,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,4,6,1,3,5,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,4,6,1,5,2,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,4,6,1,5,3,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,4,6,2,1,3,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,4,6,2,1,5,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,4,6,2,3,1,5] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,4,6,2,3,5,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,4,6,2,5,1,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,4,6,2,5,3,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,4,6,3,1,2,5] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,4,6,3,1,5,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,4,6,3,2,1,5] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[7,4,6,3,2,5,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,4,6,3,5,1,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,4,6,3,5,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,4,6,5,1,2,3] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,4,6,5,1,3,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,4,6,5,2,1,3] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[7,4,6,5,2,3,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,4,6,5,3,1,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[7,4,6,5,3,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 16
[7,5,1,2,3,4,6] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 11
[7,5,1,2,3,6,4] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[7,5,1,2,4,3,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,5,1,2,4,6,3] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[7,5,1,2,6,3,4] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,5,1,2,6,4,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,5,1,3,2,4,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,5,1,3,2,6,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,5,1,3,4,2,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,5,1,3,4,6,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[7,5,1,3,6,2,4] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,5,1,3,6,4,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,5,1,4,2,3,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,5,1,4,2,6,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,5,1,4,3,2,6] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,5,1,4,3,6,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,5,1,4,6,2,3] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,5,1,4,6,3,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,5,1,6,2,3,4] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,5,1,6,2,4,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,5,1,6,3,2,4] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,5,1,6,3,4,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,5,1,6,4,2,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,5,1,6,4,3,2] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[7,5,2,1,3,4,6] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 15
[7,5,2,1,3,6,4] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,5,2,1,4,3,6] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,5,2,1,4,6,3] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,5,2,1,6,3,4] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,5,2,1,6,4,3] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[7,5,2,3,1,4,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,5,2,3,1,6,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,5,2,3,4,1,6] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,5,2,3,4,6,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[7,5,2,3,6,1,4] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,5,2,3,6,4,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,5,2,4,1,3,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,5,2,4,1,6,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,5,2,4,3,1,6] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,5,2,4,3,6,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,5,2,4,6,1,3] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,5,2,4,6,3,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,5,2,6,1,3,4] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,5,2,6,1,4,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,5,2,6,3,1,4] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,5,2,6,3,4,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,5,2,6,4,1,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,5,2,6,4,3,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[7,5,3,1,2,4,6] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 15
[7,5,3,1,2,6,4] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,5,3,1,4,2,6] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,5,3,1,4,6,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,5,3,1,6,2,4] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,5,3,1,6,4,2] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[7,5,3,2,1,4,6] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 18
[7,5,3,2,1,6,4] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 19
[7,5,3,2,4,1,6] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,5,3,2,4,6,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,5,3,2,6,1,4] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,5,3,2,6,4,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[7,5,3,4,1,2,6] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,5,3,4,1,6,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,5,3,4,2,1,6] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,5,3,4,2,6,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,5,3,4,6,1,2] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,5,3,4,6,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,5,3,6,1,2,4] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,5,3,6,1,4,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,5,3,6,2,1,4] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,5,3,6,2,4,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,5,3,6,4,1,2] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,5,3,6,4,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[7,5,4,1,2,3,6] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 15
[7,5,4,1,2,6,3] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,5,4,1,3,2,6] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,5,4,1,3,6,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,5,4,1,6,2,3] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,5,4,1,6,3,2] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[7,5,4,2,1,3,6] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 18
[7,5,4,2,1,6,3] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 19
[7,5,4,2,3,1,6] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,5,4,2,3,6,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,5,4,2,6,1,3] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,5,4,2,6,3,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[7,5,4,3,1,2,6] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 18
[7,5,4,3,1,6,2] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 19
[7,5,4,3,2,1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => 20
[7,5,4,3,2,6,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 19
[7,5,4,3,6,1,2] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,5,4,3,6,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[7,5,4,6,1,2,3] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,5,4,6,1,3,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,5,4,6,2,1,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,5,4,6,2,3,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,5,4,6,3,1,2] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,5,4,6,3,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[7,5,6,1,2,3,4] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => {{1},{2,3},{4,5,6,7}} => 10
[7,5,6,1,2,4,3] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,5,6,1,3,2,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,5,6,1,3,4,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,5,6,1,4,2,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,5,6,1,4,3,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,5,6,2,1,3,4] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,5,6,2,1,4,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,5,6,2,3,1,4] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,5,6,2,3,4,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => {{1},{2,3},{4,5,6},{7}} => 11
[7,5,6,2,4,1,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,5,6,2,4,3,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,5,6,3,1,2,4] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,5,6,3,1,4,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,5,6,3,2,1,4] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[7,5,6,3,2,4,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,5,6,3,4,1,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => {{1},{2,3},{4,5},{6,7}} => 12
[7,5,6,3,4,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => {{1},{2,3},{4,5},{6},{7}} => 13
[7,5,6,4,1,2,3] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => {{1},{2,3},{4},{5,6,7}} => 13
[7,5,6,4,1,3,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,5,6,4,2,1,3] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[7,5,6,4,2,3,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => {{1},{2,3},{4},{5,6},{7}} => 14
[7,5,6,4,3,1,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => {{1},{2,3},{4},{5},{6,7}} => 15
[7,5,6,4,3,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => {{1},{2,3},{4},{5},{6},{7}} => 16
[7,6,1,2,3,4,5] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => {{1},{2},{3,4,5,6,7}} => 11
[7,6,1,2,3,5,4] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[7,6,1,2,4,3,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,6,1,2,4,5,3] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[7,6,1,2,5,3,4] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,6,1,2,5,4,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,6,1,3,2,4,5] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,6,1,3,2,5,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,6,1,3,4,2,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,6,1,3,4,5,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[7,6,1,3,5,2,4] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,6,1,3,5,4,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,6,1,4,2,3,5] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,6,1,4,2,5,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,6,1,4,3,2,5] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,6,1,4,3,5,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,6,1,4,5,2,3] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,6,1,4,5,3,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,6,1,5,2,3,4] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,6,1,5,2,4,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,6,1,5,3,2,4] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,6,1,5,3,4,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,6,1,5,4,2,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,6,1,5,4,3,2] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[7,6,2,1,3,4,5] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 15
[7,6,2,1,3,5,4] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,6,2,1,4,3,5] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,6,2,1,4,5,3] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,6,2,1,5,3,4] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,6,2,1,5,4,3] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[7,6,2,3,1,4,5] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,6,2,3,1,5,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,6,2,3,4,1,5] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,6,2,3,4,5,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => {{1},{2},{3,4,5,6},{7}} => 12
[7,6,2,3,5,1,4] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,6,2,3,5,4,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,6,2,4,1,3,5] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,6,2,4,1,5,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,6,2,4,3,1,5] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,6,2,4,3,5,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,6,2,4,5,1,3] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,6,2,4,5,3,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,6,2,5,1,3,4] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,6,2,5,1,4,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,6,2,5,3,1,4] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,6,2,5,3,4,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,6,2,5,4,1,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,6,2,5,4,3,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[7,6,3,1,2,4,5] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 15
[7,6,3,1,2,5,4] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,6,3,1,4,2,5] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,6,3,1,4,5,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,6,3,1,5,2,4] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,6,3,1,5,4,2] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[7,6,3,2,1,4,5] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 18
[7,6,3,2,1,5,4] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 19
[7,6,3,2,4,1,5] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,6,3,2,4,5,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,6,3,2,5,1,4] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,6,3,2,5,4,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[7,6,3,4,1,2,5] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,6,3,4,1,5,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,6,3,4,2,1,5] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,6,3,4,2,5,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,6,3,4,5,1,2] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => {{1},{2},{3,4,5},{6,7}} => 13
[7,6,3,4,5,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => {{1},{2},{3,4,5},{6},{7}} => 14
[7,6,3,5,1,2,4] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,6,3,5,1,4,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,6,3,5,2,1,4] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,6,3,5,2,4,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,6,3,5,4,1,2] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,6,3,5,4,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[7,6,4,1,2,3,5] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 15
[7,6,4,1,2,5,3] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,6,4,1,3,2,5] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,6,4,1,3,5,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,6,4,1,5,2,3] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,6,4,1,5,3,2] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[7,6,4,2,1,3,5] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 18
[7,6,4,2,1,5,3] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 19
[7,6,4,2,3,1,5] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,6,4,2,3,5,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,6,4,2,5,1,3] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,6,4,2,5,3,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[7,6,4,3,1,2,5] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 18
[7,6,4,3,1,5,2] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 19
[7,6,4,3,2,1,5] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => 20
[7,6,4,3,2,5,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 19
[7,6,4,3,5,1,2] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,6,4,3,5,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[7,6,4,5,1,2,3] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => {{1},{2},{3,4},{5,6,7}} => 14
[7,6,4,5,1,3,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,6,4,5,2,1,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,6,4,5,2,3,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => {{1},{2},{3,4},{5,6},{7}} => 15
[7,6,4,5,3,1,2] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => {{1},{2},{3,4},{5},{6,7}} => 16
[7,6,4,5,3,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => {{1},{2},{3,4},{5},{6},{7}} => 17
[7,6,5,1,2,3,4] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => {{1},{2},{3},{4,5,6,7}} => 15
[7,6,5,1,2,4,3] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,6,5,1,3,2,4] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,6,5,1,3,4,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,6,5,1,4,2,3] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,6,5,1,4,3,2] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[7,6,5,2,1,3,4] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 18
[7,6,5,2,1,4,3] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 19
[7,6,5,2,3,1,4] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,6,5,2,3,4,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => {{1},{2},{3},{4,5,6},{7}} => 16
[7,6,5,2,4,1,3] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,6,5,2,4,3,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[7,6,5,3,1,2,4] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 18
[7,6,5,3,1,4,2] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 19
[7,6,5,3,2,1,4] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => 20
[7,6,5,3,2,4,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 19
[7,6,5,3,4,1,2] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => {{1},{2},{3},{4,5},{6,7}} => 17
[7,6,5,3,4,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => {{1},{2},{3},{4,5},{6},{7}} => 18
[7,6,5,4,1,2,3] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => {{1},{2},{3},{4},{5,6,7}} => 18
[7,6,5,4,1,3,2] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 19
[7,6,5,4,2,1,3] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => 20
[7,6,5,4,2,3,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => {{1},{2},{3},{4},{5,6},{7}} => 19
[7,6,5,4,3,1,2] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => {{1},{2},{3},{4},{5},{6,7}} => 20
[7,6,5,4,3,2,1] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => {{1},{2},{3},{4},{5},{6},{7}} => 21
[8,2,3,4,5,6,7,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[7,2,3,4,5,6,8,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[6,2,3,4,5,7,8,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[5,2,3,4,6,7,8,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[4,2,3,5,6,7,8,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[3,2,4,5,6,7,8,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[2,3,4,5,6,7,8,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => {{1,2,3,4,5,6,7},{8}} => 1
[3,4,5,6,7,8,1,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[8,7,1,2,3,4,5,6] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[7,8,1,2,3,4,5,6] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[8,6,1,2,3,4,5,7] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[8,5,1,2,3,4,6,7] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[8,4,1,2,3,5,6,7] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[8,3,1,2,4,5,6,7] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[8,2,1,3,4,5,6,7] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[8,1,2,3,4,5,6,7] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => 7
[2,3,4,5,6,7,1,8] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[7,6,1,2,3,4,5,8] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[6,7,1,2,3,4,5,8] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[7,5,1,2,3,4,6,8] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[7,4,1,2,3,5,6,8] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[7,3,1,2,4,5,6,8] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[7,2,1,3,4,5,6,8] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[7,1,2,3,4,5,6,8] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => 7
[6,5,1,2,3,4,7,8] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[5,6,1,2,3,4,7,8] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[6,4,1,2,3,5,7,8] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[6,3,1,2,4,5,7,8] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[6,2,1,3,4,5,7,8] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[6,1,2,3,4,5,7,8] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => 7
[5,4,1,2,3,6,7,8] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[4,5,1,2,3,6,7,8] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[5,3,1,2,4,6,7,8] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[5,2,1,3,4,6,7,8] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[5,1,2,3,4,6,7,8] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => 7
[4,3,1,2,5,6,7,8] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[3,4,1,2,5,6,7,8] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[4,2,1,3,5,6,7,8] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[4,1,2,3,5,6,7,8] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => 7
[3,2,1,4,5,6,7,8] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1},{2},{3,4,5,6,7,8}} => 13
[2,3,1,4,5,6,7,8] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[3,1,2,4,5,6,7,8] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => 7
[2,1,3,4,5,6,7,8] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => {{1},{2,3,4,5,6,7,8}} => 7
[1,2,3,4,5,6,7,8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => {{1,2,3,4,5,6,7,8}} => 0
[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] => {{1,2,3,4,5,6,7},{8}} => 1
[2,1,4,5,6,7,8,3] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[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] => {{1,2,3,4,5,6,7},{8}} => 1
[2,1,3,5,6,7,8,4] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[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] => {{1,2,3,4,5,6,7},{8}} => 1
[2,1,3,4,6,7,8,5] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[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] => {{1,2,3,4,5,6,7},{8}} => 1
[2,1,3,4,5,7,8,6] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[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] => {{1,2,3,4,5,6,7},{8}} => 1
[2,1,3,4,5,6,8,7] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[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] => {{1,2,3,4,5,6,7},{8}} => 1
[1,3,4,5,6,7,2,8] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[1,2,4,5,6,7,3,8] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[1,2,3,5,6,7,4,8] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[1,2,3,4,6,7,5,8] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[1,2,3,4,5,7,6,8] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 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] => {{1,2},{3,4,5,6,7,8}} => 6
[2,4,1,3,5,6,7,8] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[2,4,5,6,7,8,1,3] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[2,5,1,3,4,6,7,8] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[2,3,5,6,7,8,1,4] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[2,6,1,3,4,5,7,8] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[2,3,4,6,7,8,1,5] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[2,7,1,3,4,5,6,8] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[2,3,4,5,7,8,1,6] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[2,8,1,3,4,5,6,7] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[2,3,4,5,6,8,1,7] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[3,1,4,5,6,7,8,2] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[3,5,1,2,4,6,7,8] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[3,1,2,5,6,7,8,4] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[1,3,5,6,7,8,2,4] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[3,6,1,2,4,5,7,8] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[3,1,2,4,6,7,8,5] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[1,3,4,6,7,8,2,5] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[3,7,1,2,4,5,6,8] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[3,1,2,4,5,7,8,6] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[1,3,4,5,7,8,2,6] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[3,8,1,2,4,5,6,7] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[3,1,2,4,5,6,8,7] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[1,3,4,5,6,8,2,7] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[4,1,2,5,6,7,8,3] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[1,4,5,6,7,8,2,3] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[4,6,1,2,3,5,7,8] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[4,1,2,3,6,7,8,5] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[1,2,4,6,7,8,3,5] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[4,7,1,2,3,5,6,8] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[4,1,2,3,5,7,8,6] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[1,2,4,5,7,8,3,6] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[4,8,1,2,3,5,6,7] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[4,1,2,3,5,6,8,7] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[1,2,4,5,6,8,3,7] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 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] => {{1,2},{3,4,5,6,7,8}} => 6
[5,1,2,3,6,7,8,4] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[1,2,5,6,7,8,3,4] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[5,7,1,2,3,4,6,8] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[5,1,2,3,4,7,8,6] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[1,2,3,5,7,8,4,6] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[5,8,1,2,3,4,6,7] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[5,1,2,3,4,6,8,7] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[1,2,3,5,6,8,4,7] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 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] => {{1,2},{3,4,5,6,7,8}} => 6
[6,1,2,3,4,7,8,5] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[1,2,3,6,7,8,4,5] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[6,8,1,2,3,4,5,7] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => {{1,2},{3,4,5,6,7,8}} => 6
[6,1,2,3,4,5,8,7] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[1,2,3,4,6,8,5,7] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[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] => {{1,2},{3,4,5,6,7,8}} => 6
[7,1,2,3,4,5,8,6] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[1,2,3,4,7,8,5,6] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[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] => {{1,2},{3,4,5,6,7,8}} => 6
[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] => {{1,2},{3,4,5,6,7,8}} => 6
[1,2,3,4,5,8,6,7] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => {{1,2,3,4,5,6},{7,8}} => 2
[8,1,2,3,5,6,7,4] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[8,1,2,3,4,5,7,6] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[8,1,3,4,5,6,7,2] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[6,1,3,4,5,7,8,2] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[7,1,2,3,5,6,8,4] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[6,1,2,3,5,7,8,4] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[5,1,3,4,6,7,8,2] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[7,1,2,3,4,6,8,5] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[8,1,2,3,4,6,7,5] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[8,1,2,4,5,6,7,3] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[4,1,3,5,6,7,8,2] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[5,1,2,4,6,7,8,3] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[7,1,3,4,5,6,8,2] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[6,1,2,4,5,7,8,3] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
[7,1,2,4,5,6,8,3] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => {{1},{2,3,4,5,6,7},{8}} => 8
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,2,2,1 1,3,5,6,5,3,1 1,4,9,15,20,22,20,15,9,4,1 1,5,14,29,49,71,90,101,101,90,71,49,29,14,5,1 1,6,20,49,98,169,259,359,455,531,573,573,531,455,359,259,169,98,49,20,6,1
$F_{2} = 1 + q$
$F_{3} = 1 + 2\ q + 2\ q^{2} + q^{3}$
$F_{4} = 1 + 3\ q + 5\ q^{2} + 6\ q^{3} + 5\ q^{4} + 3\ q^{5} + q^{6}$
$F_{5} = 1 + 4\ q + 9\ q^{2} + 15\ q^{3} + 20\ q^{4} + 22\ q^{5} + 20\ q^{6} + 15\ q^{7} + 9\ q^{8} + 4\ q^{9} + q^{10}$
$F_{6} = 1 + 5\ q + 14\ q^{2} + 29\ q^{3} + 49\ q^{4} + 71\ q^{5} + 90\ q^{6} + 101\ q^{7} + 101\ q^{8} + 90\ q^{9} + 71\ q^{10} + 49\ q^{11} + 29\ q^{12} + 14\ q^{13} + 5\ q^{14} + q^{15}$
$F_{7} = 1 + 6\ q + 20\ q^{2} + 49\ q^{3} + 98\ q^{4} + 169\ q^{5} + 259\ q^{6} + 359\ q^{7} + 455\ q^{8} + 531\ q^{9} + 573\ q^{10} + 573\ q^{11} + 531\ q^{12} + 455\ q^{13} + 359\ q^{14} + 259\ q^{15} + 169\ q^{16} + 98\ q^{17} + 49\ q^{18} + 20\ q^{19} + 6\ q^{20} + q^{21}$
Description
The los statistic of a set partition.
Let $S = B_1,\ldots,B_k$ be a set partition with ordered blocks $B_i$ and with $\operatorname{min} B_a < \operatorname{min} B_b$ for $a < b$.
According to [1, Definition 3], a los (left-opener-smaller) of $S$ is given by a pair $i > j$ such that $j = \operatorname{min} B_b$ and $i \in B_a$ for $a > b$.
This is also the dual major index of [2].
Let $S = B_1,\ldots,B_k$ be a set partition with ordered blocks $B_i$ and with $\operatorname{min} B_a < \operatorname{min} B_b$ for $a < b$.
According to [1, Definition 3], a los (left-opener-smaller) of $S$ is given by a pair $i > j$ such that $j = \operatorname{min} B_b$ and $i \in B_a$ for $a > b$.
This is also the dual major index of [2].
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
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