Identifier
-
Mp00040:
Integer compositions
—to partition⟶
Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
St000157: Standard tableaux ⟶ ℤ
Values
[1] => [1] => [1,0,1,0] => [[1,3],[2,4]] => 2
[1,1] => [1,1] => [1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => 2
[2] => [2] => [1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => 2
[1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => 2
[1,2] => [2,1] => [1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => 3
[2,1] => [2,1] => [1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => 3
[3] => [3] => [1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => 2
[1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [[1,3,4,5,6],[2,7,8,9,10]] => 2
[1,1,2] => [2,1,1] => [1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => 3
[1,2,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => 3
[1,3] => [3,1] => [1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => 3
[2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => 3
[2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => 2
[3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => 3
[4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [[1,2,3,4,9],[5,6,7,8,10]] => 2
[1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[1,3,4,5,6,7],[2,8,9,10,11,12]] => 2
[1,1,1,2] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [[1,3,4,5,7],[2,6,8,9,10]] => 3
[1,1,2,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [[1,3,4,5,7],[2,6,8,9,10]] => 3
[1,1,3] => [3,1,1] => [1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => 3
[1,2,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [[1,3,4,5,7],[2,6,8,9,10]] => 3
[1,2,2] => [2,2,1] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 3
[1,3,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => 3
[1,4] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [[1,2,3,5,9],[4,6,7,8,10]] => 3
[2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [[1,3,4,5,7],[2,6,8,9,10]] => 3
[2,1,2] => [2,2,1] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 3
[2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => 3
[2,3] => [3,2] => [1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => 3
[3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => 3
[3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => 3
[4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [[1,2,3,5,9],[4,6,7,8,10]] => 3
[5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,11],[6,7,8,9,10,12]] => 2
[1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8],[2,9,10,11,12,13,14]] => 2
[1,1,1,1,2] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[1,3,4,5,6,8],[2,7,9,10,11,12]] => 3
[1,1,1,2,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[1,3,4,5,6,8],[2,7,9,10,11,12]] => 3
[1,1,1,3] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [[1,3,4,5,8],[2,6,7,9,10]] => 3
[1,1,2,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[1,3,4,5,6,8],[2,7,9,10,11,12]] => 3
[1,1,2,2] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[1,3,4,6,7],[2,5,8,9,10]] => 3
[1,1,3,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [[1,3,4,5,8],[2,6,7,9,10]] => 3
[1,1,4] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [[1,2,4,5,9],[3,6,7,8,10]] => 3
[1,2,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[1,3,4,5,6,8],[2,7,9,10,11,12]] => 3
[1,2,1,2] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[1,3,4,6,7],[2,5,8,9,10]] => 3
[1,2,2,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[1,3,4,6,7],[2,5,8,9,10]] => 3
[1,2,3] => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 4
[1,3,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [[1,3,4,5,8],[2,6,7,9,10]] => 3
[1,3,2] => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 4
[1,4,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [[1,2,4,5,9],[3,6,7,8,10]] => 3
[1,5] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,4,6,11],[5,7,8,9,10,12]] => 3
[2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[1,3,4,5,6,8],[2,7,9,10,11,12]] => 3
[2,1,1,2] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[1,3,4,6,7],[2,5,8,9,10]] => 3
[2,1,2,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[1,3,4,6,7],[2,5,8,9,10]] => 3
[2,1,3] => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 4
[2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[1,3,4,6,7],[2,5,8,9,10]] => 3
[2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [[1,2,5,6,7],[3,4,8,9,10]] => 2
[2,3,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 4
[2,4] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [[1,2,3,6,9],[4,5,7,8,10]] => 3
[3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [[1,3,4,5,8],[2,6,7,9,10]] => 3
[3,1,2] => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 4
[3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => 4
[3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [[1,2,3,7,8],[4,5,6,9,10]] => 2
[4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [[1,2,4,5,9],[3,6,7,8,10]] => 3
[4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [[1,2,3,6,9],[4,5,7,8,10]] => 3
[5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,4,6,11],[5,7,8,9,10,12]] => 3
[6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,13],[7,8,9,10,11,12,14]] => 2
[1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9],[2,10,11,12,13,14,15,16]] => 2
[1,1,1,1,1,2] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9],[2,8,10,11,12,13,14]] => 3
[1,1,1,1,2,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9],[2,8,10,11,12,13,14]] => 3
[1,1,1,1,3] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[1,3,4,5,6,9],[2,7,8,10,11,12]] => 3
[1,1,1,2,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9],[2,8,10,11,12,13,14]] => 3
[1,1,1,2,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => 3
[1,1,1,3,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[1,3,4,5,6,9],[2,7,8,10,11,12]] => 3
[1,1,1,4] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [[1,3,4,5,9],[2,6,7,8,10]] => 3
[1,1,2,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9],[2,8,10,11,12,13,14]] => 3
[1,1,2,1,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => 3
[1,1,2,2,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => 3
[1,1,2,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => 4
[1,1,3,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[1,3,4,5,6,9],[2,7,8,10,11,12]] => 3
[1,1,3,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => 4
[1,1,4,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [[1,3,4,5,9],[2,6,7,8,10]] => 3
[1,1,5] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[1,2,3,5,6,11],[4,7,8,9,10,12]] => 3
[1,2,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9],[2,8,10,11,12,13,14]] => 3
[1,2,1,1,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => 3
[1,2,1,2,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => 3
[1,2,1,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => 4
[1,2,2,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => 3
[1,2,2,2] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [[1,3,5,6,7],[2,4,8,9,10]] => 3
[1,2,3,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => 4
[1,2,4] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,9],[3,5,7,8,10]] => 4
[1,3,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[1,3,4,5,6,9],[2,7,8,10,11,12]] => 3
[1,3,1,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => 4
[1,3,2,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => 4
[1,3,3] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [[1,2,4,7,8],[3,5,6,9,10]] => 3
[1,4,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [[1,3,4,5,9],[2,6,7,8,10]] => 3
[1,4,2] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,9],[3,5,7,8,10]] => 4
[1,5,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[1,2,3,5,6,11],[4,7,8,9,10,12]] => 3
[1,6] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,7,13],[6,8,9,10,11,12,14]] => 3
[2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9],[2,8,10,11,12,13,14]] => 3
[2,1,1,1,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => 3
[2,1,1,2,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => 3
[2,1,1,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => 4
[2,1,2,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => 3
[2,1,2,2] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [[1,3,5,6,7],[2,4,8,9,10]] => 3
>>> Load all 1162 entries. <<<[2,1,3,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => 4
[2,1,4] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,9],[3,5,7,8,10]] => 4
[2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => 3
[2,2,1,2] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [[1,3,5,6,7],[2,4,8,9,10]] => 3
[2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [[1,3,5,6,7],[2,4,8,9,10]] => 3
[2,2,3] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [[1,2,5,6,8],[3,4,7,9,10]] => 3
[2,3,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => 4
[2,3,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [[1,2,5,6,8],[3,4,7,9,10]] => 3
[2,4,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,9],[3,5,7,8,10]] => 4
[2,5] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [[1,2,3,4,7,11],[5,6,8,9,10,12]] => 3
[3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[1,3,4,5,6,9],[2,7,8,10,11,12]] => 3
[3,1,1,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => 4
[3,1,2,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => 4
[3,1,3] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [[1,2,4,7,8],[3,5,6,9,10]] => 3
[3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => 4
[3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [[1,2,5,6,8],[3,4,7,9,10]] => 3
[3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [[1,2,4,7,8],[3,5,6,9,10]] => 3
[3,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [[1,2,3,7,9],[4,5,6,8,10]] => 3
[4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [[1,3,4,5,9],[2,6,7,8,10]] => 3
[4,1,2] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,9],[3,5,7,8,10]] => 4
[4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,9],[3,5,7,8,10]] => 4
[4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [[1,2,3,7,9],[4,5,6,8,10]] => 3
[5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[1,2,3,5,6,11],[4,7,8,9,10,12]] => 3
[5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [[1,2,3,4,7,11],[5,6,8,9,10,12]] => 3
[6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,7,13],[6,8,9,10,11,12,14]] => 3
[7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,15],[8,9,10,11,12,13,14,16]] => 2
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10],[2,11,12,13,14,15,16,17,18]] => 2
[1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10],[2,9,11,12,13,14,15,16]] => 3
[1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10],[2,9,11,12,13,14,15,16]] => 3
[1,1,1,1,1,3] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[1,3,4,5,6,7,10],[2,8,9,11,12,13,14]] => 3
[1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10],[2,9,11,12,13,14,15,16]] => 3
[1,1,1,1,2,2] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]] => 3
[1,1,1,1,3,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[1,3,4,5,6,7,10],[2,8,9,11,12,13,14]] => 3
[1,1,1,1,4] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[1,3,4,5,6,10],[2,7,8,9,11,12]] => 3
[1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10],[2,9,11,12,13,14,15,16]] => 3
[1,1,1,2,1,2] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]] => 3
[1,1,1,2,2,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]] => 3
[1,1,1,2,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[1,1,1,3,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[1,3,4,5,6,7,10],[2,8,9,11,12,13,14]] => 3
[1,1,1,3,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[1,1,1,4,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[1,3,4,5,6,10],[2,7,8,9,11,12]] => 3
[1,1,1,5] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[1,2,4,5,6,11],[3,7,8,9,10,12]] => 3
[1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10],[2,9,11,12,13,14,15,16]] => 3
[1,1,2,1,1,2] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]] => 3
[1,1,2,1,2,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]] => 3
[1,1,2,1,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[1,1,2,2,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]] => 3
[1,1,2,2,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => 3
[1,1,2,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[1,1,2,4] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => 4
[1,1,3,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[1,3,4,5,6,7,10],[2,8,9,11,12,13,14]] => 3
[1,1,3,1,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[1,1,3,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[1,1,3,3] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [[1,3,4,7,8],[2,5,6,9,10]] => 3
[1,1,4,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[1,3,4,5,6,10],[2,7,8,9,11,12]] => 3
[1,1,4,2] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => 4
[1,1,5,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[1,2,4,5,6,11],[3,7,8,9,10,12]] => 3
[1,1,6] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[1,2,3,4,6,7,13],[5,8,9,10,11,12,14]] => 3
[1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10],[2,9,11,12,13,14,15,16]] => 3
[1,2,1,1,1,2] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]] => 3
[1,2,1,1,2,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]] => 3
[1,2,1,1,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[1,2,1,2,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]] => 3
[1,2,1,2,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => 3
[1,2,1,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[1,2,1,4] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => 4
[1,2,2,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]] => 3
[1,2,2,1,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => 3
[1,2,2,2,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => 3
[1,2,2,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => 4
[1,2,3,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[1,2,3,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => 4
[1,2,4,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => 4
[1,2,5] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[1,2,3,5,7,11],[4,6,8,9,10,12]] => 4
[1,3,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[1,3,4,5,6,7,10],[2,8,9,11,12,13,14]] => 3
[1,3,1,1,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[1,3,1,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[1,3,1,3] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [[1,3,4,7,8],[2,5,6,9,10]] => 3
[1,3,2,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[1,3,2,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => 4
[1,3,3,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [[1,3,4,7,8],[2,5,6,9,10]] => 3
[1,3,4] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[1,2,4,7,9],[3,5,6,8,10]] => 4
[1,4,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[1,3,4,5,6,10],[2,7,8,9,11,12]] => 3
[1,4,1,2] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => 4
[1,4,2,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => 4
[1,4,3] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[1,2,4,7,9],[3,5,6,8,10]] => 4
[1,5,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[1,2,4,5,6,11],[3,7,8,9,10,12]] => 3
[1,5,2] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[1,2,3,5,7,11],[4,6,8,9,10,12]] => 4
[1,6,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[1,2,3,4,6,7,13],[5,8,9,10,11,12,14]] => 3
[1,7] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,8,15],[7,9,10,11,12,13,14,16]] => 3
[2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10],[2,9,11,12,13,14,15,16]] => 3
[2,1,1,1,1,2] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]] => 3
[2,1,1,1,2,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]] => 3
[2,1,1,1,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[2,1,1,2,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]] => 3
[2,1,1,2,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => 3
[2,1,1,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[2,1,1,4] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => 4
[2,1,2,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]] => 3
[2,1,2,1,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => 3
[2,1,2,2,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => 3
[2,1,2,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => 4
[2,1,3,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[2,1,3,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => 4
[2,1,4,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => 4
[2,1,5] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[1,2,3,5,7,11],[4,6,8,9,10,12]] => 4
[2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]] => 3
[2,2,1,1,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => 3
[2,2,1,2,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => 3
[2,2,1,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => 4
[2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => 3
[2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[1,2,5,6,7,8],[3,4,9,10,11,12]] => 2
[2,2,3,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => 4
[2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [[1,2,5,6,9],[3,4,7,8,10]] => 3
[2,3,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[2,3,1,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => 4
[2,3,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => 4
[2,3,3] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [[1,2,5,7,8],[3,4,6,9,10]] => 3
[2,4,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => 4
[2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [[1,2,5,6,9],[3,4,7,8,10]] => 3
[2,5,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[1,2,3,5,7,11],[4,6,8,9,10,12]] => 4
[2,6] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[1,2,3,4,5,8,13],[6,7,9,10,11,12,14]] => 3
[3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[1,3,4,5,6,7,10],[2,8,9,11,12,13,14]] => 3
[3,1,1,1,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[3,1,1,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[3,1,1,3] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [[1,3,4,7,8],[2,5,6,9,10]] => 3
[3,1,2,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[3,1,2,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => 4
[3,1,3,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [[1,3,4,7,8],[2,5,6,9,10]] => 3
[3,1,4] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[1,2,4,7,9],[3,5,6,8,10]] => 4
[3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 4
[3,2,1,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => 4
[3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => 4
[3,2,3] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [[1,2,5,7,8],[3,4,6,9,10]] => 3
[3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [[1,3,4,7,8],[2,5,6,9,10]] => 3
[3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [[1,2,5,7,8],[3,4,6,9,10]] => 3
[3,4,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[1,2,4,7,9],[3,5,6,8,10]] => 4
[3,5] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [[1,2,3,4,8,11],[5,6,7,9,10,12]] => 3
[4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[1,3,4,5,6,10],[2,7,8,9,11,12]] => 3
[4,1,1,2] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => 4
[4,1,2,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => 4
[4,1,3] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[1,2,4,7,9],[3,5,6,8,10]] => 4
[4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => 4
[4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [[1,2,5,6,9],[3,4,7,8,10]] => 3
[4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[1,2,4,7,9],[3,5,6,8,10]] => 4
[4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[1,2,3,4,9,10],[5,6,7,8,11,12]] => 2
[5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[1,2,4,5,6,11],[3,7,8,9,10,12]] => 3
[5,1,2] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[1,2,3,5,7,11],[4,6,8,9,10,12]] => 4
[5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[1,2,3,5,7,11],[4,6,8,9,10,12]] => 4
[5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [[1,2,3,4,8,11],[5,6,7,9,10,12]] => 3
[6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[1,2,3,4,6,7,13],[5,8,9,10,11,12,14]] => 3
[6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[1,2,3,4,5,8,13],[6,7,9,10,11,12,14]] => 3
[7,1] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,8,15],[7,9,10,11,12,13,14,16]] => 3
[8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,8,17],[9,10,11,12,13,14,15,16,18]] => 2
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10,11],[2,12,13,14,15,16,17,18,19,20]] => 2
[1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,11],[2,10,12,13,14,15,16,17,18]] => 3
[1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,11],[2,10,12,13,14,15,16,17,18]] => 3
[1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,8,11],[2,9,10,12,13,14,15,16]] => 3
[1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,11],[2,10,12,13,14,15,16,17,18]] => 3
[1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,8,11],[2,9,10,12,13,14,15,16]] => 3
[1,1,1,1,1,4] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[1,3,4,5,6,7,11],[2,8,9,10,12,13,14]] => 3
[1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,11],[2,10,12,13,14,15,16,17,18]] => 3
[1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[1,1,1,1,2,3] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,8,11],[2,9,10,12,13,14,15,16]] => 3
[1,1,1,1,3,2] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,1,1,1,4,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[1,3,4,5,6,7,11],[2,8,9,10,12,13,14]] => 3
[1,1,1,1,5] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[1,3,4,5,6,11],[2,7,8,9,10,12]] => 3
[1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,11],[2,10,12,13,14,15,16,17,18]] => 3
[1,1,1,2,1,1,2] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[1,1,1,2,1,3] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[1,1,1,2,2,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[1,1,1,2,3,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,1,1,2,4] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,8,11],[2,9,10,12,13,14,15,16]] => 3
[1,1,1,3,1,2] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,1,1,3,2,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,1,1,3,3] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => 3
[1,1,1,4,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[1,3,4,5,6,7,11],[2,8,9,10,12,13,14]] => 3
[1,1,1,4,2] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[1,1,1,5,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[1,3,4,5,6,11],[2,7,8,9,10,12]] => 3
[1,1,1,6] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[1,2,3,5,6,7,13],[4,8,9,10,11,12,14]] => 3
[1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,11],[2,10,12,13,14,15,16,17,18]] => 3
[1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[1,1,2,1,1,3] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[1,1,2,1,2,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[1,1,2,1,3,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,1,2,1,4] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[1,1,2,2,1,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[1,1,2,2,2,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[1,1,2,2,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[1,1,2,3,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,1,2,3,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[1,1,2,4,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[1,1,2,5] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => 4
[1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,8,11],[2,9,10,12,13,14,15,16]] => 3
[1,1,3,1,1,2] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,1,3,1,2,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,1,3,1,3] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => 3
[1,1,3,2,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,1,3,2,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[1,1,3,3,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => 3
[1,1,3,4] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => 4
[1,1,4,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[1,3,4,5,6,7,11],[2,8,9,10,12,13,14]] => 3
[1,1,4,1,2] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[1,1,4,2,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[1,1,4,3] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => 4
[1,1,5,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[1,3,4,5,6,11],[2,7,8,9,10,12]] => 3
[1,1,5,2] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => 4
[1,1,6,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[1,2,3,5,6,7,13],[4,8,9,10,11,12,14]] => 3
[1,1,7] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,7,8,15],[6,9,10,11,12,13,14,16]] => 3
[1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,11],[2,10,12,13,14,15,16,17,18]] => 3
[1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[1,2,1,1,1,3] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[1,2,1,1,2,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[1,2,1,1,3,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,2,1,1,4] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[1,2,1,2,1,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[1,2,1,2,2,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[1,2,1,2,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[1,2,1,3,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,2,1,3,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[1,2,1,4,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[1,2,1,5] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => 4
[1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[1,2,2,1,1,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[1,2,2,1,2,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[1,2,2,1,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[1,2,2,2,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[1,2,2,2,2] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[1,3,5,6,7,8],[2,4,9,10,11,12]] => 3
[1,2,2,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[1,2,2,4] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => 4
[1,2,3,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,2,3,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[1,2,3,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[1,2,3,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => 4
[1,2,4,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[1,2,4,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => 4
[1,2,5,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => 4
[1,2,6] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[1,2,3,4,6,8,13],[5,7,9,10,11,12,14]] => 4
[1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,8,11],[2,9,10,12,13,14,15,16]] => 3
[1,3,1,1,1,2] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,3,1,1,2,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,3,1,1,3] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => 3
[1,3,1,2,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,3,1,2,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[1,3,1,3,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => 3
[1,3,1,4] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => 4
[1,3,2,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[1,3,2,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[1,3,2,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[1,3,2,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => 4
[1,3,3,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => 3
[1,3,3,2] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => 4
[1,3,4,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => 4
[1,3,5] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[1,2,3,5,8,11],[4,6,7,9,10,12]] => 4
[1,4,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[1,3,4,5,6,7,11],[2,8,9,10,12,13,14]] => 3
[1,4,1,1,2] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[1,4,1,2,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[1,4,1,3] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => 4
[1,4,2,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[1,4,2,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => 4
[1,4,3,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => 4
[1,4,4] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [[1,2,3,5,9,10],[4,6,7,8,11,12]] => 3
[1,5,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[1,3,4,5,6,11],[2,7,8,9,10,12]] => 3
[1,5,1,2] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => 4
[1,5,2,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => 4
[1,5,3] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[1,2,3,5,8,11],[4,6,7,9,10,12]] => 4
[1,6,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[1,2,3,5,6,7,13],[4,8,9,10,11,12,14]] => 3
[1,6,2] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[1,2,3,4,6,8,13],[5,7,9,10,11,12,14]] => 4
[1,7,1] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,7,8,15],[6,9,10,11,12,13,14,16]] => 3
[1,8] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,9,17],[8,10,11,12,13,14,15,16,18]] => 3
[2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,11],[2,10,12,13,14,15,16,17,18]] => 3
[2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[2,1,1,1,1,3] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[2,1,1,1,2,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[2,1,1,1,3,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[2,1,1,1,4] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[2,1,1,2,1,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[2,1,1,2,2,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[2,1,1,2,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[2,1,1,3,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[2,1,1,3,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[2,1,1,4,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[2,1,1,5] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => 4
[2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[2,1,2,1,1,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[2,1,2,1,2,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[2,1,2,1,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[2,1,2,2,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[2,1,2,2,2] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[1,3,5,6,7,8],[2,4,9,10,11,12]] => 3
[2,1,2,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[2,1,2,4] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => 4
[2,1,3,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[2,1,3,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[2,1,3,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[2,1,3,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => 4
[2,1,4,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[2,1,4,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => 4
[2,1,5,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => 4
[2,1,6] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[1,2,3,4,6,8,13],[5,7,9,10,11,12,14]] => 4
[2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => 3
[2,2,1,1,1,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[2,2,1,1,2,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[2,2,1,1,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[2,2,1,2,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[2,2,1,2,2] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[1,3,5,6,7,8],[2,4,9,10,11,12]] => 3
[2,2,1,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[2,2,1,4] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => 4
[2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => 3
[2,2,2,1,2] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[1,3,5,6,7,8],[2,4,9,10,11,12]] => 3
[2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[1,3,5,6,7,8],[2,4,9,10,11,12]] => 3
[2,2,2,3] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[1,2,5,6,7,9],[3,4,8,10,11,12]] => 3
[2,2,3,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[2,2,3,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[1,2,5,6,7,9],[3,4,8,10,11,12]] => 3
[2,2,4,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => 4
[2,2,5] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[1,2,3,6,7,11],[4,5,8,9,10,12]] => 3
[2,3,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[2,3,1,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[2,3,1,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[2,3,1,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => 4
[2,3,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[2,3,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[1,2,5,6,7,9],[3,4,8,10,11,12]] => 3
[2,3,3,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => 4
[2,3,4] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[1,2,5,7,9],[3,4,6,8,10]] => 4
[2,4,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[2,4,1,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => 4
[2,4,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => 4
[2,4,3] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[1,2,5,7,9],[3,4,6,8,10]] => 4
[2,5,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => 4
[2,5,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[1,2,3,6,7,11],[4,5,8,9,10,12]] => 3
[2,6,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[1,2,3,4,6,8,13],[5,7,9,10,11,12,14]] => 4
[2,7] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,9,15],[7,8,10,11,12,13,14,16]] => 3
[3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,8,11],[2,9,10,12,13,14,15,16]] => 3
[3,1,1,1,1,2] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[3,1,1,1,2,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[3,1,1,1,3] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => 3
[3,1,1,2,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[3,1,1,2,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[3,1,1,3,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => 3
[3,1,1,4] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => 4
[3,1,2,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[3,1,2,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[3,1,2,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[3,1,2,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => 4
[3,1,3,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => 3
[3,1,3,2] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => 4
[3,1,4,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => 4
[3,1,5] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[1,2,3,5,8,11],[4,6,7,9,10,12]] => 4
[3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => 4
[3,2,1,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[3,2,1,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[3,2,1,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => 4
[3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 4
[3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[1,2,5,6,7,9],[3,4,8,10,11,12]] => 3
[3,2,3,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => 4
[3,2,4] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[1,2,5,7,9],[3,4,6,8,10]] => 4
[3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => 3
[3,3,1,2] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => 4
[3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => 4
[3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[1,2,3,7,8,9],[4,5,6,10,11,12]] => 2
[3,4,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => 4
[3,4,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[1,2,5,7,9],[3,4,6,8,10]] => 4
[3,5,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[1,2,3,5,8,11],[4,6,7,9,10,12]] => 4
[3,6] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[1,2,3,4,5,9,13],[6,7,8,10,11,12,14]] => 3
[4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[1,3,4,5,6,7,11],[2,8,9,10,12,13,14]] => 3
[4,1,1,1,2] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[4,1,1,2,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[4,1,1,3] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => 4
[4,1,2,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[4,1,2,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => 4
[4,1,3,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => 4
[4,1,4] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [[1,2,3,5,9,10],[4,6,7,8,11,12]] => 3
[4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 4
[4,2,1,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => 4
[4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => 4
[4,2,3] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[1,2,5,7,9],[3,4,6,8,10]] => 4
[4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => 4
[4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[1,2,5,7,9],[3,4,6,8,10]] => 4
[4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [[1,2,3,5,9,10],[4,6,7,8,11,12]] => 3
[4,5] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[1,2,3,4,9,11],[5,6,7,8,10,12]] => 3
[5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[1,3,4,5,6,11],[2,7,8,9,10,12]] => 3
[5,1,1,2] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => 4
[5,1,2,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => 4
[5,1,3] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[1,2,3,5,8,11],[4,6,7,9,10,12]] => 4
[5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => 4
[5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[1,2,3,6,7,11],[4,5,8,9,10,12]] => 3
[5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[1,2,3,5,8,11],[4,6,7,9,10,12]] => 4
[5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[1,2,3,4,9,11],[5,6,7,8,10,12]] => 3
[6,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[1,2,3,5,6,7,13],[4,8,9,10,11,12,14]] => 3
[6,1,2] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[1,2,3,4,6,8,13],[5,7,9,10,11,12,14]] => 4
[6,2,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[1,2,3,4,6,8,13],[5,7,9,10,11,12,14]] => 4
[6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[1,2,3,4,5,9,13],[6,7,8,10,11,12,14]] => 3
[7,1,1] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,7,8,15],[6,9,10,11,12,13,14,16]] => 3
[7,2] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,9,15],[7,8,10,11,12,13,14,16]] => 3
[8,1] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,9,17],[8,10,11,12,13,14,15,16,18]] => 3
[9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,8,9,19],[10,11,12,13,14,15,16,17,18,20]] => 2
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10,11,12],[2,13,14,15,16,17,18,19,20,21,22]] => 2
[1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10,12],[2,11,13,14,15,16,17,18,19,20]] => 3
[1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10,12],[2,11,13,14,15,16,17,18,19,20]] => 3
[1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,12],[2,10,11,13,14,15,16,17,18]] => 3
[1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10,12],[2,11,13,14,15,16,17,18,19,20]] => 3
[1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,12],[2,10,11,13,14,15,16,17,18]] => 3
[1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[1,3,4,5,6,7,8,12],[2,9,10,11,13,14,15,16]] => 3
[1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10,12],[2,11,13,14,15,16,17,18,19,20]] => 3
[1,1,1,1,1,2,1,2] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,1,1,1,1,2,3] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,12],[2,10,11,13,14,15,16,17,18]] => 3
[1,1,1,1,1,3,2] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[1,3,4,5,6,7,8,12],[2,9,10,11,13,14,15,16]] => 3
[1,1,1,1,1,5] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[1,3,4,5,6,7,12],[2,8,9,10,11,13,14]] => 3
[1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10,12],[2,11,13,14,15,16,17,18,19,20]] => 3
[1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,1,1,1,2,1,3] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[1,1,1,1,2,3,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,1,1,2,4] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,12],[2,10,11,13,14,15,16,17,18]] => 3
[1,1,1,1,3,1,2] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,1,1,3,2,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,1,1,3,3] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]] => 3
[1,1,1,1,4,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[1,3,4,5,6,7,8,12],[2,9,10,11,13,14,15,16]] => 3
[1,1,1,1,4,2] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,1,1,1,5,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[1,3,4,5,6,7,12],[2,8,9,10,11,13,14]] => 3
[1,1,1,1,6] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[1,2,4,5,6,7,13],[3,8,9,10,11,12,14]] => 3
[1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10,12],[2,11,13,14,15,16,17,18,19,20]] => 3
[1,1,1,2,1,1,1,2] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,1,1,2,1,1,3] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,1,2,1,2,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,1,1,2,1,2,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[1,1,1,2,1,3,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,1,2,1,4] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,1,1,2,2,1,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[1,1,1,2,2,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,1,1,2,3,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,1,2,3,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,1,1,2,4,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,1,1,2,5] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,12],[2,10,11,13,14,15,16,17,18]] => 3
[1,1,1,3,1,1,2] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,1,3,1,2,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,1,3,1,3] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]] => 3
[1,1,1,3,2,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,1,3,2,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,1,1,3,3,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]] => 3
[1,1,1,3,4] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[1,1,1,4,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[1,3,4,5,6,7,8,12],[2,9,10,11,13,14,15,16]] => 3
[1,1,1,4,1,2] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,1,1,4,2,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,1,1,4,3] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[1,1,1,5,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[1,3,4,5,6,7,12],[2,8,9,10,11,13,14]] => 3
[1,1,1,5,2] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[1,1,1,6,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[1,2,4,5,6,7,13],[3,8,9,10,11,12,14]] => 3
[1,1,1,7] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,6,7,8,15],[5,9,10,11,12,13,14,16]] => 3
[1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10,12],[2,11,13,14,15,16,17,18,19,20]] => 3
[1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,1,2,1,1,1,3] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,1,2,1,1,2,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[1,1,2,1,1,3,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,2,1,1,4] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,1,2,1,2,1,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[1,1,2,1,2,2,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[1,1,2,1,2,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,1,2,1,3,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,2,1,3,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,1,2,1,4,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,1,2,1,5] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,1,2,2,1,1,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[1,1,2,2,1,2,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[1,1,2,2,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,1,2,2,2,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[1,1,2,2,2,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]] => 3
[1,1,2,2,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,1,2,2,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[1,1,2,3,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,2,3,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,1,2,3,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,1,2,3,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[1,1,2,4,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,1,2,4,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[1,1,2,5,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[1,1,2,6] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,5,6,8,13],[4,7,9,10,11,12,14]] => 4
[1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,12],[2,10,11,13,14,15,16,17,18]] => 3
[1,1,3,1,1,1,2] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,3,1,1,2,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,3,1,1,3] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]] => 3
[1,1,3,1,2,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,3,1,2,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,1,3,1,3,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]] => 3
[1,1,3,1,4] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[1,1,3,2,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,1,3,2,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,1,3,2,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,1,3,2,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[1,1,3,3,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]] => 3
[1,1,3,3,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[1,1,3,4,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[1,1,3,5] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => 4
[1,1,4,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[1,3,4,5,6,7,8,12],[2,9,10,11,13,14,15,16]] => 3
[1,1,4,1,1,2] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,1,4,1,2,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,1,4,1,3] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[1,1,4,2,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,1,4,2,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[1,1,4,3,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[1,1,4,4] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[1,2,4,5,9,10],[3,6,7,8,11,12]] => 3
[1,1,5,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[1,3,4,5,6,7,12],[2,8,9,10,11,13,14]] => 3
[1,1,5,1,2] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[1,1,5,2,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[1,1,5,3] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => 4
[1,1,6,1,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[1,2,4,5,6,7,13],[3,8,9,10,11,12,14]] => 3
[1,1,6,2] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,5,6,8,13],[4,7,9,10,11,12,14]] => 4
[1,1,7,1] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,6,7,8,15],[5,9,10,11,12,13,14,16]] => 3
[1,1,8] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,8,9,17],[7,10,11,12,13,14,15,16,18]] => 3
[1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10,12],[2,11,13,14,15,16,17,18,19,20]] => 3
[1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[1,2,1,1,1,3,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,2,1,1,1,4] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,2,1,1,2,1,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[1,2,1,1,2,2,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[1,2,1,1,2,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,2,1,1,3,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,2,1,1,3,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,2,1,1,4,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,2,1,1,5] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,2,1,2,1,1,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[1,2,1,2,1,2,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[1,2,1,2,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,2,1,2,2,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[1,2,1,2,2,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]] => 3
[1,2,1,2,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,2,1,2,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[1,2,1,3,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,2,1,3,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,2,1,3,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,2,1,3,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[1,2,1,4,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,2,1,4,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[1,2,1,5,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[1,2,1,6] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,5,6,8,13],[4,7,9,10,11,12,14]] => 4
[1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[1,2,2,1,1,1,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[1,2,2,1,1,2,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[1,2,2,1,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,2,2,1,2,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[1,2,2,1,2,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]] => 3
[1,2,2,1,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,2,2,1,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[1,2,2,2,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[1,2,2,2,1,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]] => 3
[1,2,2,2,2,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]] => 3
[1,2,2,2,3] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[1,2,2,3,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,2,2,3,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[1,2,2,4,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[1,2,2,5] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => 4
[1,2,3,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,2,3,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,2,3,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,2,3,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[1,2,3,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,2,3,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[1,2,3,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[1,2,3,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[1,2,4,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,2,4,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[1,2,4,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[1,2,4,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[1,2,5,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[1,2,5,2] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => 4
[1,2,6,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,5,6,8,13],[4,7,9,10,11,12,14]] => 4
[1,2,7] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,7,9,15],[6,8,10,11,12,13,14,16]] => 4
[1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,12],[2,10,11,13,14,15,16,17,18]] => 3
[1,3,1,1,1,1,2] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,3,1,1,1,2,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,3,1,1,1,3] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]] => 3
[1,3,1,1,2,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,3,1,1,2,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,3,1,1,3,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]] => 3
[1,3,1,1,4] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[1,3,1,2,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,3,1,2,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,3,1,2,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,3,1,2,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[1,3,1,3,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]] => 3
[1,3,1,3,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[1,3,1,4,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[1,3,1,5] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => 4
[1,3,2,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[1,3,2,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,3,2,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,3,2,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[1,3,2,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[1,3,2,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[1,3,2,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[1,3,2,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[1,3,3,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]] => 3
[1,3,3,1,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[1,3,3,2,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[1,3,3,3] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[1,2,4,7,8,9],[3,5,6,10,11,12]] => 3
[1,3,4,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[1,3,4,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[1,3,5,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => 4
[1,3,6] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[1,2,3,4,6,9,13],[5,7,8,10,11,12,14]] => 4
[1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[1,3,4,5,6,7,8,12],[2,9,10,11,13,14,15,16]] => 3
[1,4,1,1,1,2] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,4,1,1,2,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,4,1,1,3] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[1,4,1,2,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,4,1,2,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[1,4,1,3,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[1,4,1,4] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[1,2,4,5,9,10],[3,6,7,8,11,12]] => 3
[1,4,2,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[1,4,2,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[1,4,2,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[1,4,2,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[1,4,3,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[1,4,3,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[1,4,4,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[1,2,4,5,9,10],[3,6,7,8,11,12]] => 3
[1,4,5] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[1,2,3,5,9,11],[4,6,7,8,10,12]] => 4
[1,5,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[1,3,4,5,6,7,12],[2,8,9,10,11,13,14]] => 3
[1,5,1,1,2] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[1,5,1,2,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[1,5,1,3] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => 4
[1,5,2,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[1,5,2,2] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => 4
[1,5,3,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => 4
[1,5,4] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[1,2,3,5,9,11],[4,6,7,8,10,12]] => 4
[1,6,1,1,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[1,2,4,5,6,7,13],[3,8,9,10,11,12,14]] => 3
[1,6,1,2] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,5,6,8,13],[4,7,9,10,11,12,14]] => 4
[1,6,2,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,5,6,8,13],[4,7,9,10,11,12,14]] => 4
[1,6,3] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[1,2,3,4,6,9,13],[5,7,8,10,11,12,14]] => 4
[1,7,1,1] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,6,7,8,15],[5,9,10,11,12,13,14,16]] => 3
[1,7,2] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,7,9,15],[6,8,10,11,12,13,14,16]] => 4
[1,8,1] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,8,9,17],[7,10,11,12,13,14,15,16,18]] => 3
[1,9] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,8,10,19],[9,11,12,13,14,15,16,17,18,20]] => 3
[2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10,12],[2,11,13,14,15,16,17,18,19,20]] => 3
[2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[2,1,1,1,1,1,3] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[2,1,1,1,1,4] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[2,1,1,1,2,1,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[2,1,1,1,2,2,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[2,1,1,1,2,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[2,1,1,1,3,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[2,1,1,1,3,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[2,1,1,1,4,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[2,1,1,1,5] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[2,1,1,2,1,1,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[2,1,1,2,1,2,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[2,1,1,2,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[2,1,1,2,2,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[2,1,1,2,2,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]] => 3
[2,1,1,2,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[2,1,1,2,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[2,1,1,3,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[2,1,1,3,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[2,1,1,3,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[2,1,1,4,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[2,1,1,4,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[2,1,1,5,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[2,1,1,6] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,5,6,8,13],[4,7,9,10,11,12,14]] => 4
[2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[2,1,2,1,1,1,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[2,1,2,1,1,2,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[2,1,2,1,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[2,1,2,1,2,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[2,1,2,1,2,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]] => 3
[2,1,2,1,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[2,1,2,1,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[2,1,2,2,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[2,1,2,2,1,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]] => 3
[2,1,2,2,2,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]] => 3
[2,1,2,2,3] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[2,1,2,3,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[2,1,2,3,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[2,1,2,4,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[2,1,2,5] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => 4
[2,1,3,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[2,1,3,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[2,1,3,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[2,1,3,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[2,1,3,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[2,1,3,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[2,1,3,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[2,1,3,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[2,1,4,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[2,1,4,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[2,1,4,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[2,1,4,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[2,1,5,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[2,1,5,2] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => 4
[2,1,6,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,5,6,8,13],[4,7,9,10,11,12,14]] => 4
[2,1,7] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,7,9,15],[6,8,10,11,12,13,14,16]] => 4
[2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => 3
[2,2,1,1,1,1,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[2,2,1,1,1,2,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[2,2,1,1,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[2,2,1,1,2,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[2,2,1,1,2,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]] => 3
[2,2,1,1,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[2,2,1,1,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[2,2,1,2,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[2,2,1,2,1,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]] => 3
[2,2,1,2,2,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]] => 3
[2,2,1,2,3] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[2,2,1,3,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[2,2,1,3,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[2,2,1,4,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[2,2,1,5] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => 4
[2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => 3
[2,2,2,1,1,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]] => 3
[2,2,2,1,2,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]] => 3
[2,2,2,1,3] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]] => 3
[2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[1,2,5,6,7,8,9],[3,4,10,11,12,13,14]] => 2
[2,2,2,3,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[2,2,2,4] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[1,2,5,6,7,10],[3,4,8,9,11,12]] => 3
[2,2,3,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[2,2,3,1,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[2,2,3,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[2,2,3,3] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[1,2,5,6,8,9],[3,4,7,10,11,12]] => 3
[2,2,4,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[2,2,4,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[1,2,5,6,7,10],[3,4,8,9,11,12]] => 3
[2,2,5,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => 4
[2,2,6] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[1,2,3,4,7,8,13],[5,6,9,10,11,12,14]] => 3
[2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[2,3,1,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[2,3,1,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[2,3,1,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[2,3,1,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[2,3,1,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[2,3,1,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[2,3,1,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[2,3,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[2,3,2,1,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[2,3,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[2,3,2,3] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[1,2,5,6,8,9],[3,4,7,10,11,12]] => 3
[2,3,3,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[2,3,3,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[1,2,5,6,8,9],[3,4,7,10,11,12]] => 3
[2,3,4,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[2,3,5] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[1,2,3,6,8,11],[4,5,7,9,10,12]] => 4
[2,4,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[2,4,1,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[2,4,1,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[2,4,1,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[2,4,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[2,4,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[1,2,5,6,7,10],[3,4,8,9,11,12]] => 3
[2,4,3,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[2,4,4] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[1,2,3,6,9,10],[4,5,7,8,11,12]] => 3
[2,5,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[2,5,1,2] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => 4
[2,5,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => 4
[2,5,3] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[1,2,3,6,8,11],[4,5,7,9,10,12]] => 4
[2,6,1,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,5,6,8,13],[4,7,9,10,11,12,14]] => 4
[2,6,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[1,2,3,4,7,8,13],[5,6,9,10,11,12,14]] => 3
[2,7,1] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,7,9,15],[6,8,10,11,12,13,14,16]] => 4
[2,8] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,10,17],[8,9,11,12,13,14,15,16,18]] => 3
[3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,12],[2,10,11,13,14,15,16,17,18]] => 3
[3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[3,1,1,1,1,3] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]] => 3
[3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[3,1,1,1,2,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[3,1,1,1,3,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]] => 3
[3,1,1,1,4] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[3,1,1,2,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[3,1,1,2,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[3,1,1,2,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[3,1,1,2,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[3,1,1,3,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]] => 3
[3,1,1,3,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[3,1,1,4,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[3,1,1,5] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => 4
[3,1,2,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[3,1,2,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[3,1,2,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[3,1,2,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[3,1,2,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[3,1,2,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[3,1,2,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[3,1,2,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[3,1,3,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]] => 3
[3,1,3,1,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[3,1,3,2,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[3,1,3,3] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[1,2,4,7,8,9],[3,5,6,10,11,12]] => 3
[3,1,4,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[3,1,4,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[3,1,5,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => 4
[3,1,6] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[1,2,3,4,6,9,13],[5,7,8,10,11,12,14]] => 4
[3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => 4
[3,2,1,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[3,2,1,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[3,2,1,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[3,2,1,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[3,2,1,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[3,2,1,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[3,2,1,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => 4
[3,2,2,1,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 4
[3,2,2,3] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[1,2,5,6,8,9],[3,4,7,10,11,12]] => 3
[3,2,3,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[3,2,3,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[1,2,5,6,8,9],[3,4,7,10,11,12]] => 3
[3,2,4,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[3,2,5] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[1,2,3,6,8,11],[4,5,7,9,10,12]] => 4
[3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]] => 3
[3,3,1,1,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[3,3,1,2,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[3,3,1,3] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[1,2,4,7,8,9],[3,5,6,10,11,12]] => 3
[3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 4
[3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[1,2,5,6,8,9],[3,4,7,10,11,12]] => 3
[3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[1,2,4,7,8,9],[3,5,6,10,11,12]] => 3
[3,3,4] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[1,2,3,7,8,10],[4,5,6,9,11,12]] => 3
[3,4,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[3,4,1,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[3,4,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[3,4,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[1,2,3,7,8,10],[4,5,6,9,11,12]] => 3
[3,5,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => 4
[3,5,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[1,2,3,6,8,11],[4,5,7,9,10,12]] => 4
[3,6,1] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[1,2,3,4,6,9,13],[5,7,8,10,11,12,14]] => 4
[3,7] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[1,2,3,4,5,6,10,15],[7,8,9,11,12,13,14,16]] => 3
[4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[1,3,4,5,6,7,8,12],[2,9,10,11,13,14,15,16]] => 3
[4,1,1,1,1,2] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[4,1,1,1,2,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[4,1,1,1,3] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[4,1,1,2,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[4,1,1,2,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[4,1,1,3,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[4,1,1,4] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[1,2,4,5,9,10],[3,6,7,8,11,12]] => 3
[4,1,2,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[4,1,2,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[4,1,2,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[4,1,2,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[4,1,3,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[4,1,3,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[4,1,4,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[1,2,4,5,9,10],[3,6,7,8,11,12]] => 3
[4,1,5] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[1,2,3,5,9,11],[4,6,7,8,10,12]] => 4
[4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => 4
[4,2,1,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[4,2,1,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[4,2,1,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 4
[4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[1,2,5,6,7,10],[3,4,8,9,11,12]] => 3
[4,2,3,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[4,2,4] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[1,2,3,6,9,10],[4,5,7,8,11,12]] => 3
[4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 4
[4,3,1,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[1,2,3,7,8,10],[4,5,6,9,11,12]] => 3
[4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[1,2,4,5,9,10],[3,6,7,8,11,12]] => 3
[4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[1,2,3,6,9,10],[4,5,7,8,11,12]] => 3
[4,5,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[1,2,3,5,9,11],[4,6,7,8,10,12]] => 4
[4,6] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[1,2,3,4,5,10,13],[6,7,8,9,11,12,14]] => 3
[5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[1,3,4,5,6,7,12],[2,8,9,10,11,13,14]] => 3
[5,1,1,1,2] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[5,1,1,2,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[5,1,1,3] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => 4
[5,1,2,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[5,1,2,2] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => 4
[5,1,3,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => 4
[5,1,4] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[1,2,3,5,9,11],[4,6,7,8,10,12]] => 4
[5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 4
[5,2,1,2] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => 4
[5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => 4
[5,2,3] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[1,2,3,6,8,11],[4,5,7,9,10,12]] => 4
[5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => 4
[5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[1,2,3,6,8,11],[4,5,7,9,10,12]] => 4
[5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[1,2,3,5,9,11],[4,6,7,8,10,12]] => 4
[5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[1,2,3,4,5,11,12],[6,7,8,9,10,13,14]] => 2
[6,1,1,1,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[1,2,4,5,6,7,13],[3,8,9,10,11,12,14]] => 3
[6,1,1,2] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,5,6,8,13],[4,7,9,10,11,12,14]] => 4
[6,1,2,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,5,6,8,13],[4,7,9,10,11,12,14]] => 4
[6,1,3] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[1,2,3,4,6,9,13],[5,7,8,10,11,12,14]] => 4
[6,2,1,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,5,6,8,13],[4,7,9,10,11,12,14]] => 4
[6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[1,2,3,4,7,8,13],[5,6,9,10,11,12,14]] => 3
[6,3,1] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[1,2,3,4,6,9,13],[5,7,8,10,11,12,14]] => 4
[6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[1,2,3,4,5,10,13],[6,7,8,9,11,12,14]] => 3
[7,1,1,1] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,6,7,8,15],[5,9,10,11,12,13,14,16]] => 3
[7,1,2] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,7,9,15],[6,8,10,11,12,13,14,16]] => 4
[7,2,1] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,7,9,15],[6,8,10,11,12,13,14,16]] => 4
[7,3] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[1,2,3,4,5,6,10,15],[7,8,9,11,12,13,14,16]] => 3
[8,1,1] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,8,9,17],[7,10,11,12,13,14,15,16,18]] => 3
[8,2] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,10,17],[8,9,11,12,13,14,15,16,18]] => 3
[9,1] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,8,10,19],[9,11,12,13,14,15,16,17,18,20]] => 3
[10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,8,9,10,21],[11,12,13,14,15,16,17,18,19,20,22]] => 2
[1,5,4,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[1,2,4,5,9,11],[3,6,7,8,10,12]] => 4
[1,4,5,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[1,2,4,5,9,11],[3,6,7,8,10,12]] => 4
[2,2,4,4] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[1,2,5,6,9,10],[3,4,7,8,11,12]] => 3
[2,1,4,5] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => 5
[3,2,3,4] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => 4
[3,1,3,5] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[1,2,4,7,8,11],[3,5,6,9,10,12]] => 4
[4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[1,2,5,6,9,10],[3,4,7,8,11,12]] => 3
[4,3,2,3] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => 4
[4,2,2,4] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[1,2,5,6,9,10],[3,4,7,8,11,12]] => 3
[4,1,2,5] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => 5
[5,4,1,2] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => 5
[5,3,1,3] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[1,2,4,7,8,11],[3,5,6,9,10,12]] => 4
[5,2,1,4] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => 5
[1,2,2,4,3] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[1,2,3,4,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[1,2,3,3,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => 4
[1,2,4,4,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [[1,3,4,6,9,10],[2,5,7,8,11,12]] => 4
[1,2,4,3,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[1,2,4,2,3] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[1,2,5,4] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => 5
[1,3,3,3,2] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => 4
[1,3,4,3,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[1,3,4,7,8,10],[2,5,6,9,11,12]] => 4
[1,3,4,2,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[1,3,5,3] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[1,2,4,7,8,11],[3,5,6,9,10,12]] => 4
[1,3,2,4,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[1,3,2,3,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => 4
[1,3,3,4,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[1,3,4,7,8,10],[2,5,6,9,11,12]] => 4
[1,3,3,2,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => 4
[1,3,4,4] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[1,2,4,7,9,10],[3,5,6,8,11,12]] => 4
[1,4,4,2,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [[1,3,4,6,9,10],[2,5,7,8,11,12]] => 4
[1,4,5,2] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => 5
[1,4,3,3,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[1,3,4,7,8,10],[2,5,6,9,11,12]] => 4
[1,4,3,2,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[1,4,4,3] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[1,2,4,7,9,10],[3,5,6,8,11,12]] => 4
[1,4,2,4,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [[1,3,4,6,9,10],[2,5,7,8,11,12]] => 4
[1,4,2,3,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[1,4,2,2,3] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[1,4,3,4] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[1,2,4,7,9,10],[3,5,6,8,11,12]] => 4
[1,5,4,2] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => 5
[1,5,3,3] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[1,2,4,7,8,11],[3,5,6,9,10,12]] => 4
[1,5,2,4] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => 5
[2,3,3,3,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => 4
[2,3,4,3] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => 4
[2,4,3,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[2,4,4,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[1,2,5,6,9,10],[3,4,7,8,11,12]] => 3
[2,4,2,3,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[2,4,3,3] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => 4
[2,5,4,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => 5
[2,5,3,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => 4
[2,5,2,3] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => 4
[2,2,4,3,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[2,2,5,3] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => 4
[2,2,3,4,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[2,3,4,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[2,3,5,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => 4
[2,3,2,4,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[2,3,3,4] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => 4
[2,4,5,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => 5
[2,4,2,4] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[1,2,5,6,9,10],[3,4,7,8,11,12]] => 3
[3,4,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[3,4,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => 4
[3,5,3,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[1,2,4,7,8,11],[3,5,6,9,10,12]] => 4
[3,5,2,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => 4
[3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => 4
[3,3,4,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => 4
[3,3,2,3,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => 4
[3,4,4,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[1,2,4,7,9,10],[3,5,6,8,11,12]] => 4
[3,4,2,3] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => 4
[3,5,4] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[1,2,3,7,9,11],[4,5,6,8,10,12]] => 4
[3,2,4,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[3,2,5,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => 4
[3,2,3,3,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => 4
[3,2,4,3] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => 4
[3,2,2,4,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[3,3,5,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[1,2,4,7,8,11],[3,5,6,9,10,12]] => 4
[3,3,2,4] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => 4
[3,4,5] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[1,2,3,7,9,11],[4,5,6,8,10,12]] => 4
[4,5,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => 5
[4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[1,2,4,7,9,10],[3,5,6,8,11,12]] => 4
[4,5,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[1,2,3,7,9,11],[4,5,6,8,10,12]] => 4
[4,3,4,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[1,2,4,7,9,10],[3,5,6,8,11,12]] => 4
[4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => 4
[4,2,5,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => 5
[4,2,4,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[1,2,5,6,9,10],[3,4,7,8,11,12]] => 3
[4,2,3,3] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => 4
[4,3,5] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[1,2,3,7,9,11],[4,5,6,8,10,12]] => 4
[5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[1,2,3,7,9,11],[4,5,6,8,10,12]] => 4
[5,3,4] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[1,2,3,7,9,11],[4,5,6,8,10,12]] => 4
[1,5,2,1,2] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [[1,3,4,6,7,11],[2,5,8,9,10,12]] => 4
[1,2,2,2,5] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[1,3,5,6,7,11],[2,4,8,9,10,12]] => 4
[1,1,2,3,5] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => 5
[3,1,2,1,5] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => 5
[1,3,2,1,5] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => 5
[1,1,4,1,5] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[1,3,4,5,9,11],[2,6,7,8,10,12]] => 4
[1,1,2,5,3] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => 5
[3,1,2,3,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => 4
[1,1,4,3,3] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[1,3,4,7,8,10],[2,5,6,9,11,12]] => 4
[5,1,2,1,3] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => 5
[3,3,2,1,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => 4
[1,5,2,1,3] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => 5
[3,1,4,1,3] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[1,3,4,7,8,10],[2,5,6,9,11,12]] => 4
[1,3,4,1,3] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[1,3,4,7,8,10],[2,5,6,9,11,12]] => 4
[5,2,2,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[1,3,5,6,7,11],[2,4,8,9,10,12]] => 4
[3,1,2,5,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => 5
[1,3,2,5,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => 5
[1,1,4,5,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[1,3,4,5,9,11],[2,6,7,8,10,12]] => 4
[5,1,2,3,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => 5
[1,5,2,3,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => 5
[3,1,4,3,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[1,3,4,7,8,10],[2,5,6,9,11,12]] => 4
[5,3,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => 5
[3,5,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => 5
[5,1,4,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[1,3,4,5,9,11],[2,6,7,8,10,12]] => 4
[3,3,4,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[1,3,4,7,8,10],[2,5,6,9,11,12]] => 4
[1,5,4,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[1,3,4,5,9,11],[2,6,7,8,10,12]] => 4
[4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[4,2,3,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[4,2,2,3,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 5
[5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => 5
[5,3,3,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[1,2,4,7,8,11],[3,5,6,9,10,12]] => 4
[5,3,2,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => 4
[5,2,4,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => 5
[5,2,3,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => 4
[5,2,2,3] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => 4
[2,1,2,5,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [[1,3,4,6,7,11],[2,5,8,9,10,12]] => 4
[1,2,5,2,2] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[1,3,5,6,7,11],[2,4,8,9,10,12]] => 4
[1,3,5,2,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => 5
[1,5,2,2,2] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[1,3,5,6,7,11],[2,4,8,9,10,12]] => 4
[1,5,3,2,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => 5
[2,5,2,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[1,3,5,6,7,11],[2,4,8,9,10,12]] => 4
[2,2,5,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[1,3,5,6,7,11],[2,4,8,9,10,12]] => 4
[1,3,1,5,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [[1,3,4,5,8,11],[2,6,7,9,10,12]] => 4
[1,5,1,3,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [[1,3,4,5,8,11],[2,6,7,9,10,12]] => 4
[1,4,1,4,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[1,3,4,5,9,10],[2,6,7,8,11,12]] => 3
[1,4,3,2,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10],[2,5,7,9,11,12]] => 5
[1,2,3,4,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10],[2,5,7,9,11,12]] => 5
[1,2,5,2,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [[1,3,4,6,7,11],[2,5,8,9,10,12]] => 4
[1,4,3,4,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[1,3,4,7,9,10],[2,5,6,8,11,12]] => 4
[1,4,5,2,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [[1,3,4,6,9,11],[2,5,7,8,10,12]] => 5
[1,2,5,4,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [[1,3,4,6,9,11],[2,5,7,8,10,12]] => 5
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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:
2,2 3,5 2,14 4,22,6 2,44,18 4,68,56 3,107,146 4,172,312,24
$F_{1} = q^{2}$
$F_{2} = 2\ q^{2}$
$F_{3} = 2\ q^{2} + 2\ q^{3}$
$F_{4} = 3\ q^{2} + 5\ q^{3}$
$F_{5} = 2\ q^{2} + 14\ q^{3}$
$F_{6} = 4\ q^{2} + 22\ q^{3} + 6\ q^{4}$
$F_{7} = 2\ q^{2} + 44\ q^{3} + 18\ q^{4}$
$F_{8} = 4\ q^{2} + 68\ q^{3} + 56\ q^{4}$
$F_{9} = 3\ q^{2} + 107\ q^{3} + 146\ q^{4}$
$F_{10} = 4\ q^{2} + 172\ q^{3} + 312\ q^{4} + 24\ q^{5}$
Description
The number of descents of a standard tableau.
Entry $i$ of a standard Young tableau is a descent if $i+1$ appears in a row below the row of $i$.
Entry $i$ of a standard Young tableau is a descent if $i+1$ appears in a row below the row of $i$.
Map
to two-row standard tableau
Description
Return a standard tableau of shape $(n,n)$ where $n$ is the semilength of the Dyck path.
Given a Dyck path $D$, its image is given by recording the positions of the up-steps in the first row and the positions of the down-steps in the second row.
Given a Dyck path $D$, its image is given by recording the positions of the up-steps in the first row and the positions of the down-steps in the second row.
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
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