Identifier
-
Mp00044:
Integer partitions
—conjugate⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001039: Dyck paths ⟶ ℤ
Values
[3] => [1,1,1] => [1,1] => [1,1,0,0] => 1
[4] => [1,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1
[3,1] => [2,1,1] => [1,1] => [1,1,0,0] => 1
[2,2] => [2,2] => [2] => [1,0,1,0] => 2
[5] => [1,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[4,1] => [2,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1
[3,2] => [2,2,1] => [2,1] => [1,0,1,1,0,0] => 2
[3,1,1] => [3,1,1] => [1,1] => [1,1,0,0] => 1
[2,2,1] => [3,2] => [2] => [1,0,1,0] => 2
[6] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[5,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[4,2] => [2,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[4,1,1] => [3,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1
[3,3] => [2,2,2] => [2,2] => [1,1,1,0,0,0] => 2
[3,2,1] => [3,2,1] => [2,1] => [1,0,1,1,0,0] => 2
[3,1,1,1] => [4,1,1] => [1,1] => [1,1,0,0] => 1
[2,2,2] => [3,3] => [3] => [1,0,1,0,1,0] => 3
[2,2,1,1] => [4,2] => [2] => [1,0,1,0] => 2
[7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[6,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[5,2] => [2,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[5,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[4,3] => [2,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[4,2,1] => [3,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[4,1,1,1] => [4,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1
[3,3,1] => [3,2,2] => [2,2] => [1,1,1,0,0,0] => 2
[3,2,2] => [3,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[3,2,1,1] => [4,2,1] => [2,1] => [1,0,1,1,0,0] => 2
[3,1,1,1,1] => [5,1,1] => [1,1] => [1,1,0,0] => 1
[2,2,2,1] => [4,3] => [3] => [1,0,1,0,1,0] => 3
[2,2,1,1,1] => [5,2] => [2] => [1,0,1,0] => 2
[8] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[7,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[6,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[6,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[5,3] => [2,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[5,2,1] => [3,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[5,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[4,4] => [2,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[4,3,1] => [3,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[4,2,2] => [3,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[4,2,1,1] => [4,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[4,1,1,1,1] => [5,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1
[3,3,2] => [3,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 3
[3,3,1,1] => [4,2,2] => [2,2] => [1,1,1,0,0,0] => 2
[3,2,2,1] => [4,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[3,2,1,1,1] => [5,2,1] => [2,1] => [1,0,1,1,0,0] => 2
[3,1,1,1,1,1] => [6,1,1] => [1,1] => [1,1,0,0] => 1
[2,2,2,2] => [4,4] => [4] => [1,0,1,0,1,0,1,0] => 4
[2,2,2,1,1] => [5,3] => [3] => [1,0,1,0,1,0] => 3
[2,2,1,1,1,1] => [6,2] => [2] => [1,0,1,0] => 2
[8,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[7,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[7,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[6,3] => [2,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[6,2,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[6,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[5,4] => [2,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[5,3,1] => [3,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[5,2,2] => [3,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[5,2,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[4,4,1] => [3,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[4,3,2] => [3,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[4,3,1,1] => [4,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[4,2,2,1] => [4,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[4,2,1,1,1] => [5,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[4,1,1,1,1,1] => [6,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1
[3,3,3] => [3,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[3,3,2,1] => [4,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 3
[3,3,1,1,1] => [5,2,2] => [2,2] => [1,1,1,0,0,0] => 2
[3,2,2,2] => [4,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[3,2,2,1,1] => [5,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[3,2,1,1,1,1] => [6,2,1] => [2,1] => [1,0,1,1,0,0] => 2
[3,1,1,1,1,1,1] => [7,1,1] => [1,1] => [1,1,0,0] => 1
[2,2,2,2,1] => [5,4] => [4] => [1,0,1,0,1,0,1,0] => 4
[2,2,2,1,1,1] => [6,3] => [3] => [1,0,1,0,1,0] => 3
[2,2,1,1,1,1,1] => [7,2] => [2] => [1,0,1,0] => 2
[8,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[8,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[7,3] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[7,2,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[7,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[6,4] => [2,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[6,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[6,2,2] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[6,2,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[6,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[5,5] => [2,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 2
[5,4,1] => [3,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[5,3,2] => [3,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[5,3,1,1] => [4,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[5,2,2,1] => [4,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[5,1,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[4,4,2] => [3,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[4,4,1,1] => [4,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[4,3,3] => [3,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[4,3,2,1] => [4,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[4,3,1,1,1] => [5,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[4,2,2,2] => [4,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
>>> Load all 866 entries. <<<[4,2,2,1,1] => [5,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[4,2,1,1,1,1] => [6,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[4,1,1,1,1,1,1] => [7,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1
[3,3,3,1] => [4,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[3,3,2,2] => [4,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 4
[3,3,2,1,1] => [5,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 3
[3,3,1,1,1,1] => [6,2,2] => [2,2] => [1,1,1,0,0,0] => 2
[3,2,2,2,1] => [5,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[3,2,2,1,1,1] => [6,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[3,2,1,1,1,1,1] => [7,2,1] => [2,1] => [1,0,1,1,0,0] => 2
[3,1,1,1,1,1,1,1] => [8,1,1] => [1,1] => [1,1,0,0] => 1
[2,2,2,2,2] => [5,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
[2,2,2,2,1,1] => [6,4] => [4] => [1,0,1,0,1,0,1,0] => 4
[2,2,2,1,1,1,1] => [7,3] => [3] => [1,0,1,0,1,0] => 3
[2,2,1,1,1,1,1,1] => [8,2] => [2] => [1,0,1,0] => 2
[8,2,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[8,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[7,4] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[7,3,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[7,2,2] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[7,2,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[7,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[6,5] => [2,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[6,4,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[6,3,2] => [3,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[6,3,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[6,2,2,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[6,2,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[5,5,1] => [3,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 2
[5,4,2] => [3,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[5,4,1,1] => [4,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[5,3,3] => [3,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[5,3,2,1] => [4,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[5,3,1,1,1] => [5,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[5,2,2,2] => [4,4,1,1,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[5,2,2,1,1] => [5,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[5,2,1,1,1,1] => [6,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[5,1,1,1,1,1,1] => [7,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[4,4,3] => [3,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 3
[4,4,2,1] => [4,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[4,4,1,1,1] => [5,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[4,3,3,1] => [4,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[4,3,2,2] => [4,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[4,3,2,1,1] => [5,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[4,3,1,1,1,1] => [6,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[4,2,2,2,1] => [5,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[4,2,2,1,1,1] => [6,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[4,2,1,1,1,1,1] => [7,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[4,1,1,1,1,1,1,1] => [8,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1
[3,3,3,2] => [4,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 4
[3,3,3,1,1] => [5,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[3,3,2,2,1] => [5,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 4
[3,3,2,1,1,1] => [6,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 3
[3,3,1,1,1,1,1] => [7,2,2] => [2,2] => [1,1,1,0,0,0] => 2
[3,2,2,2,2] => [5,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[3,2,2,2,1,1] => [6,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[3,2,2,1,1,1,1] => [7,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[3,2,1,1,1,1,1,1] => [8,2,1] => [2,1] => [1,0,1,1,0,0] => 2
[3,1,1,1,1,1,1,1,1] => [9,1,1] => [1,1] => [1,1,0,0] => 1
[2,2,2,2,2,1] => [6,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
[2,2,2,2,1,1,1] => [7,4] => [4] => [1,0,1,0,1,0,1,0] => 4
[2,2,2,1,1,1,1,1] => [8,3] => [3] => [1,0,1,0,1,0] => 3
[2,2,1,1,1,1,1,1,1] => [9,2] => [2] => [1,0,1,0] => 2
[8,2,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[8,1,1,1,1] => [5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[7,5] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[7,4,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[7,3,2] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[7,3,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[7,2,2,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[7,2,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[7,1,1,1,1,1] => [6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[6,6] => [2,2,2,2,2,2] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[6,5,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[6,4,2] => [3,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[6,4,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[6,3,3] => [3,3,3,1,1,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[6,3,2,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[6,3,1,1,1] => [5,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[6,2,2,2] => [4,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[6,2,2,1,1] => [5,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[6,2,1,1,1,1] => [6,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[6,1,1,1,1,1,1] => [7,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[5,5,2] => [3,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[5,5,1,1] => [4,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 2
[5,4,3] => [3,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[5,4,2,1] => [4,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[5,4,1,1,1] => [5,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[5,3,3,1] => [4,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[5,3,2,2] => [4,4,2,1,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[5,3,1,1,1,1] => [6,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[5,2,2,2,1] => [5,4,1,1,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[5,2,2,1,1,1] => [6,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[5,2,1,1,1,1,1] => [7,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[5,1,1,1,1,1,1,1] => [8,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[4,4,4] => [3,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 3
[4,4,3,1] => [4,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 3
[4,4,2,2] => [4,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[4,4,2,1,1] => [5,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[4,4,1,1,1,1] => [6,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[4,3,3,2] => [4,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[4,3,3,1,1] => [5,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[4,3,2,2,1] => [5,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[4,3,2,1,1,1] => [6,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[4,3,1,1,1,1,1] => [7,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[4,2,2,2,2] => [5,5,1,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[4,2,2,2,1,1] => [6,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[4,2,2,1,1,1,1] => [7,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[4,2,1,1,1,1,1,1] => [8,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[4,1,1,1,1,1,1,1,1] => [9,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1
[3,3,3,3] => [4,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 4
[3,3,3,2,1] => [5,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 4
[3,3,3,1,1,1] => [6,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[3,3,2,2,2] => [5,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[3,3,2,2,1,1] => [6,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 4
[3,3,2,1,1,1,1] => [7,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 3
[3,3,1,1,1,1,1,1] => [8,2,2] => [2,2] => [1,1,1,0,0,0] => 2
[3,2,2,2,2,1] => [6,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[3,2,2,2,1,1,1] => [7,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[3,2,2,1,1,1,1,1] => [8,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[3,2,1,1,1,1,1,1,1] => [9,2,1] => [2,1] => [1,0,1,1,0,0] => 2
[3,1,1,1,1,1,1,1,1,1] => [10,1,1] => [1,1] => [1,1,0,0] => 1
[2,2,2,2,2,2] => [6,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[2,2,2,2,2,1,1] => [7,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
[2,2,2,2,1,1,1,1] => [8,4] => [4] => [1,0,1,0,1,0,1,0] => 4
[2,2,2,1,1,1,1,1,1] => [9,3] => [3] => [1,0,1,0,1,0] => 3
[2,2,1,1,1,1,1,1,1,1] => [10,2] => [2] => [1,0,1,0] => 2
[8,2,1,1,1] => [5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[8,1,1,1,1,1] => [6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[7,6] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2
[7,5,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[7,4,2] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[7,4,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[7,3,2,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[7,3,1,1,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[7,2,2,1,1] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[7,2,1,1,1,1] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[7,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[6,6,1] => [3,2,2,2,2,2] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[6,5,2] => [3,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[6,5,1,1] => [4,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[6,4,3] => [3,3,3,2,1,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[6,4,2,1] => [4,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[6,4,1,1,1] => [5,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[6,3,3,1] => [4,3,3,1,1,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[6,3,2,2] => [4,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[6,3,2,1,1] => [5,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[6,3,1,1,1,1] => [6,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[6,2,2,2,1] => [5,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[6,2,2,1,1,1] => [6,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[6,2,1,1,1,1,1] => [7,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[6,1,1,1,1,1,1,1] => [8,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[5,5,3] => [3,3,3,2,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[5,5,2,1] => [4,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[5,5,1,1,1] => [5,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 2
[5,4,4] => [3,3,3,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 3
[5,4,3,1] => [4,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[5,4,2,2] => [4,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[5,4,2,1,1] => [5,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[5,4,1,1,1,1] => [6,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[5,3,3,2] => [4,4,3,1,1] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[5,3,3,1,1] => [5,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[5,3,2,2,1] => [5,4,2,1,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[5,3,2,1,1,1] => [6,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[5,3,1,1,1,1,1] => [7,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[5,2,2,2,2] => [5,5,1,1,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[5,2,2,2,1,1] => [6,4,1,1,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[5,2,2,1,1,1,1] => [7,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[5,2,1,1,1,1,1,1] => [8,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[5,1,1,1,1,1,1,1,1] => [9,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[4,4,4,1] => [4,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 3
[4,4,3,2] => [4,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 4
[4,4,3,1,1] => [5,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 3
[4,4,2,2,1] => [5,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[4,4,2,1,1,1] => [6,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[4,4,1,1,1,1,1] => [7,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[4,3,3,3] => [4,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[4,3,3,2,1] => [5,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[4,3,3,1,1,1] => [6,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[4,3,2,2,2] => [5,5,2,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[4,3,2,2,1,1] => [6,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[4,3,2,1,1,1,1] => [7,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[4,3,1,1,1,1,1,1] => [8,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[4,2,2,2,2,1] => [6,5,1,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[4,2,2,2,1,1,1] => [7,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[4,2,2,1,1,1,1,1] => [8,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[4,2,1,1,1,1,1,1,1] => [9,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[4,1,1,1,1,1,1,1,1,1] => [10,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1
[3,3,3,3,1] => [5,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 4
[3,3,3,2,2] => [5,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 5
[3,3,3,2,1,1] => [6,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 4
[3,3,3,1,1,1,1] => [7,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[3,3,2,2,2,1] => [6,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[3,3,2,2,1,1,1] => [7,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 4
[3,3,2,1,1,1,1,1] => [8,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 3
[3,3,1,1,1,1,1,1,1] => [9,2,2] => [2,2] => [1,1,1,0,0,0] => 2
[3,2,2,2,2,2] => [6,6,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[3,2,2,2,2,1,1] => [7,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[3,2,2,2,1,1,1,1] => [8,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[3,2,2,1,1,1,1,1,1] => [9,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[3,2,1,1,1,1,1,1,1,1] => [10,2,1] => [2,1] => [1,0,1,1,0,0] => 2
[3,1,1,1,1,1,1,1,1,1,1] => [11,1,1] => [1,1] => [1,1,0,0] => 1
[2,2,2,2,2,2,1] => [7,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[2,2,2,2,2,1,1,1] => [8,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
[2,2,2,2,1,1,1,1,1] => [9,4] => [4] => [1,0,1,0,1,0,1,0] => 4
[2,2,2,1,1,1,1,1,1,1] => [10,3] => [3] => [1,0,1,0,1,0] => 3
[2,2,1,1,1,1,1,1,1,1,1] => [11,2] => [2] => [1,0,1,0] => 2
[8,2,1,1,1,1] => [6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[8,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[7,7] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[7,6,1] => [3,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2
[7,5,2] => [3,3,2,2,2,1,1] => [3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[7,5,1,1] => [4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[7,4,2,1] => [4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[7,4,1,1,1] => [5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[7,3,2,1,1] => [5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[7,3,1,1,1,1] => [6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[7,2,2,1,1,1] => [6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[7,2,1,1,1,1,1] => [7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[7,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[6,6,2] => [3,3,2,2,2,2] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[6,6,1,1] => [4,2,2,2,2,2] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[6,5,3] => [3,3,3,2,2,1] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[6,5,2,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[6,5,1,1,1] => [5,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[6,4,4] => [3,3,3,3,1,1] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3
[6,4,3,1] => [4,3,3,2,1,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[6,4,2,2] => [4,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[6,4,2,1,1] => [5,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[6,4,1,1,1,1] => [6,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[6,3,3,2] => [4,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[6,3,3,1,1] => [5,3,3,1,1,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[6,3,2,2,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[6,3,2,1,1,1] => [6,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[6,3,1,1,1,1,1] => [7,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[6,2,2,2,1,1] => [6,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[6,2,2,1,1,1,1] => [7,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[6,2,1,1,1,1,1,1] => [8,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[6,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[5,5,4] => [3,3,3,3,2] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[5,5,3,1] => [4,3,3,2,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[5,5,2,2] => [4,4,2,2,2] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[5,5,2,1,1] => [5,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[5,5,1,1,1,1] => [6,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 2
[5,4,4,1] => [4,3,3,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 3
[5,4,3,2] => [4,4,3,2,1] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[5,4,3,1,1] => [5,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[5,4,2,2,1] => [5,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[5,4,2,1,1,1] => [6,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[5,4,1,1,1,1,1] => [7,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[5,3,3,3] => [4,4,4,1,1] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 4
[5,3,3,2,1] => [5,4,3,1,1] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[5,3,3,1,1,1] => [6,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[5,3,2,2,2] => [5,5,2,1,1] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[5,3,2,2,1,1] => [6,4,2,1,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[5,3,2,1,1,1,1] => [7,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[5,3,1,1,1,1,1,1] => [8,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[5,2,2,2,2,1] => [6,5,1,1,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[5,2,2,2,1,1,1] => [7,4,1,1,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[5,2,2,1,1,1,1,1] => [8,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[5,2,1,1,1,1,1,1,1] => [9,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[5,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[4,4,4,2] => [4,4,3,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 4
[4,4,4,1,1] => [5,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 3
[4,4,3,3] => [4,4,4,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 4
[4,4,3,2,1] => [5,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 4
[4,4,3,1,1,1] => [6,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 3
[4,4,2,2,2] => [5,5,2,2] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 5
[4,4,2,2,1,1] => [6,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[4,4,2,1,1,1,1] => [7,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[4,4,1,1,1,1,1,1] => [8,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[4,3,3,3,1] => [5,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[4,3,3,2,2] => [5,5,3,1] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[4,3,3,2,1,1] => [6,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[4,3,3,1,1,1,1] => [7,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[4,3,2,2,2,1] => [6,5,2,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[4,3,2,2,1,1,1] => [7,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[4,3,2,1,1,1,1,1] => [8,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[4,3,1,1,1,1,1,1,1] => [9,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[4,2,2,2,2,2] => [6,6,1,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[4,2,2,2,2,1,1] => [7,5,1,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[4,2,2,2,1,1,1,1] => [8,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[4,2,2,1,1,1,1,1,1] => [9,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[4,2,1,1,1,1,1,1,1,1] => [10,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[4,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1
[3,3,3,3,2] => [5,5,4] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 5
[3,3,3,3,1,1] => [6,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 4
[3,3,3,2,2,1] => [6,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 5
[3,3,3,2,1,1,1] => [7,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 4
[3,3,3,1,1,1,1,1] => [8,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[3,3,2,2,2,2] => [6,6,2] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[3,3,2,2,2,1,1] => [7,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[3,3,2,2,1,1,1,1] => [8,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 4
[3,3,2,1,1,1,1,1,1] => [9,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 3
[3,3,1,1,1,1,1,1,1,1] => [10,2,2] => [2,2] => [1,1,1,0,0,0] => 2
[3,2,2,2,2,2,1] => [7,6,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[3,2,2,2,2,1,1,1] => [8,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[3,2,2,2,1,1,1,1,1] => [9,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[3,2,2,1,1,1,1,1,1,1] => [10,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[3,2,1,1,1,1,1,1,1,1,1] => [11,2,1] => [2,1] => [1,0,1,1,0,0] => 2
[3,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1] => [1,1] => [1,1,0,0] => 1
[2,2,2,2,2,2,2] => [7,7] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[2,2,2,2,2,2,1,1] => [8,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[2,2,2,2,2,1,1,1,1] => [9,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
[2,2,2,2,1,1,1,1,1,1] => [10,4] => [4] => [1,0,1,0,1,0,1,0] => 4
[2,2,2,1,1,1,1,1,1,1,1] => [11,3] => [3] => [1,0,1,0,1,0] => 3
[2,2,1,1,1,1,1,1,1,1,1,1] => [12,2] => [2] => [1,0,1,0] => 2
[8,2,1,1,1,1,1] => [7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[8,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[7,7,1] => [3,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[7,6,2] => [3,3,2,2,2,2,1] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[7,6,1,1] => [4,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2
[7,5,2,1] => [4,3,2,2,2,1,1] => [3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[7,5,1,1,1] => [5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[7,4,2,1,1] => [5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[7,4,1,1,1,1] => [6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[7,3,2,1,1,1] => [6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[7,3,1,1,1,1,1] => [7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[7,2,2,1,1,1,1] => [7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[7,2,1,1,1,1,1,1] => [8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[7,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[6,6,3] => [3,3,3,2,2,2] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[6,6,2,1] => [4,3,2,2,2,2] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[6,6,1,1,1] => [5,2,2,2,2,2] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[6,5,4] => [3,3,3,3,2,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[6,5,3,1] => [4,3,3,2,2,1] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[6,5,2,2] => [4,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 4
[6,5,2,1,1] => [5,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[6,5,1,1,1,1] => [6,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[6,4,4,1] => [4,3,3,3,1,1] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3
[6,4,3,2] => [4,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 4
[6,4,3,1,1] => [5,3,3,2,1,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[6,4,2,2,1] => [5,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[6,4,2,1,1,1] => [6,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[6,4,1,1,1,1,1] => [7,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[6,3,3,2,1] => [5,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[6,3,3,1,1,1] => [6,3,3,1,1,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[6,3,2,2,1,1] => [6,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[6,3,2,1,1,1,1] => [7,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[6,3,1,1,1,1,1,1] => [8,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[6,2,2,2,1,1,1] => [7,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[6,2,2,1,1,1,1,1] => [8,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[6,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[6,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[5,5,5] => [3,3,3,3,3] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 3
[5,5,4,1] => [4,3,3,3,2] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[5,5,3,2] => [4,4,3,2,2] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[5,5,3,1,1] => [5,3,3,2,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[5,5,2,2,1] => [5,4,2,2,2] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[5,5,2,1,1,1] => [6,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[5,5,1,1,1,1,1] => [7,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 2
[5,4,4,2] => [4,4,3,3,1] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 4
[5,4,4,1,1] => [5,3,3,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 3
[5,4,3,3] => [4,4,4,2,1] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 4
[5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[5,4,3,1,1,1] => [6,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[5,4,2,2,2] => [5,5,2,2,1] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[5,4,2,2,1,1] => [6,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[5,4,2,1,1,1,1] => [7,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[5,4,1,1,1,1,1,1] => [8,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[5,3,3,3,1] => [5,4,4,1,1] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 4
[5,3,3,2,2] => [5,5,3,1,1] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 5
[5,3,3,2,1,1] => [6,4,3,1,1] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[5,3,3,1,1,1,1] => [7,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[5,3,2,2,2,1] => [6,5,2,1,1] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[5,3,2,2,1,1,1] => [7,4,2,1,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[5,3,2,1,1,1,1,1] => [8,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[5,3,1,1,1,1,1,1,1] => [9,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[5,2,2,2,2,1,1] => [7,5,1,1,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[5,2,2,2,1,1,1,1] => [8,4,1,1,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[5,2,2,1,1,1,1,1,1] => [9,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[5,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[5,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[4,4,4,3] => [4,4,4,3] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 4
[4,4,4,2,1] => [5,4,3,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 4
[4,4,4,1,1,1] => [6,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 3
[4,4,3,3,1] => [5,4,4,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 4
[4,4,3,2,2] => [5,5,3,2] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 5
[4,4,3,2,1,1] => [6,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 4
[4,4,3,1,1,1,1] => [7,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 3
[4,4,2,2,2,1] => [6,5,2,2] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 5
[4,4,2,2,1,1,1] => [7,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[4,4,2,1,1,1,1,1] => [8,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[4,4,1,1,1,1,1,1,1] => [9,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[4,3,3,3,2] => [5,5,4,1] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 5
[4,3,3,3,1,1] => [6,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[4,3,3,2,2,1] => [6,5,3,1] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[4,3,3,2,1,1,1] => [7,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[4,3,3,1,1,1,1,1] => [8,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[4,3,2,2,2,2] => [6,6,2,1] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[4,3,2,2,2,1,1] => [7,5,2,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[4,3,2,2,1,1,1,1] => [8,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[4,3,2,1,1,1,1,1,1] => [9,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[4,3,1,1,1,1,1,1,1,1] => [10,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[4,2,2,2,2,2,1] => [7,6,1,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[4,2,2,2,2,1,1,1] => [8,5,1,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[4,2,2,2,1,1,1,1,1] => [9,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[4,2,2,1,1,1,1,1,1,1] => [10,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[4,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[4,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1
[3,3,3,3,3] => [5,5,5] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 5
[3,3,3,3,2,1] => [6,5,4] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 5
[3,3,3,3,1,1,1] => [7,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 4
[3,3,3,2,2,2] => [6,6,3] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 6
[3,3,3,2,2,1,1] => [7,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 5
[3,3,3,2,1,1,1,1] => [8,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 4
[3,3,3,1,1,1,1,1,1] => [9,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[3,3,2,2,2,2,1] => [7,6,2] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[3,3,2,2,2,1,1,1] => [8,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[3,3,2,2,1,1,1,1,1] => [9,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 4
[3,3,2,1,1,1,1,1,1,1] => [10,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 3
[3,3,1,1,1,1,1,1,1,1,1] => [11,2,2] => [2,2] => [1,1,1,0,0,0] => 2
[3,2,2,2,2,2,2] => [7,7,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[3,2,2,2,2,2,1,1] => [8,6,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[3,2,2,2,2,1,1,1,1] => [9,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[3,2,2,2,1,1,1,1,1,1] => [10,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[3,2,2,1,1,1,1,1,1,1,1] => [11,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[3,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1] => [2,1] => [1,0,1,1,0,0] => 2
[3,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1] => [1,1] => [1,1,0,0] => 1
[2,2,2,2,2,2,2,1] => [8,7] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[2,2,2,2,2,2,1,1,1] => [9,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[2,2,2,2,2,1,1,1,1,1] => [10,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
[2,2,2,2,1,1,1,1,1,1,1] => [11,4] => [4] => [1,0,1,0,1,0,1,0] => 4
[2,2,2,1,1,1,1,1,1,1,1,1] => [12,3] => [3] => [1,0,1,0,1,0] => 3
[2,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2] => [2] => [1,0,1,0] => 2
[8,2,1,1,1,1,1,1] => [8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[8,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[7,7,2] => [3,3,2,2,2,2,2] => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 3
[7,7,1,1] => [4,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[7,6,2,1] => [4,3,2,2,2,2,1] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[7,6,1,1,1] => [5,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2
[7,5,2,1,1] => [5,3,2,2,2,1,1] => [3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[7,5,1,1,1,1] => [6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[7,4,2,1,1,1] => [6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[7,4,1,1,1,1,1] => [7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[7,3,2,1,1,1,1] => [7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[7,3,1,1,1,1,1,1] => [8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[7,2,2,1,1,1,1,1] => [8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[7,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[7,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[6,6,4] => [3,3,3,3,2,2] => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3
[6,6,3,1] => [4,3,3,2,2,2] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[6,6,2,2] => [4,4,2,2,2,2] => [4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 4
[6,6,2,1,1] => [5,3,2,2,2,2] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[6,6,1,1,1,1] => [6,2,2,2,2,2] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[6,5,5] => [3,3,3,3,3,1] => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 3
[6,5,4,1] => [4,3,3,3,2,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[6,5,3,2] => [4,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[6,5,3,1,1] => [5,3,3,2,2,1] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[6,5,2,2,1] => [5,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 4
[6,5,2,1,1,1] => [6,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[6,5,1,1,1,1,1] => [7,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[6,4,4,2] => [4,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 4
[6,4,4,1,1] => [5,3,3,3,1,1] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3
[6,4,3,2,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 4
[6,4,3,1,1,1] => [6,3,3,2,1,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[6,4,2,2,1,1] => [6,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[6,4,2,1,1,1,1] => [7,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[6,4,1,1,1,1,1,1] => [8,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[6,3,3,2,1,1] => [6,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[6,3,3,1,1,1,1] => [7,3,3,1,1,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[6,3,2,2,1,1,1] => [7,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[6,3,2,1,1,1,1,1] => [8,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[6,3,1,1,1,1,1,1,1] => [9,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[6,2,2,2,1,1,1,1] => [8,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[6,2,2,1,1,1,1,1,1] => [9,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[6,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[6,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[5,5,5,1] => [4,3,3,3,3] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 3
[5,5,4,2] => [4,4,3,3,2] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[5,5,4,1,1] => [5,3,3,3,2] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[5,5,3,3] => [4,4,4,2,2] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 4
[5,5,3,2,1] => [5,4,3,2,2] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[5,5,3,1,1,1] => [6,3,3,2,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[5,5,2,2,2] => [5,5,2,2,2] => [5,2,2,2] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 5
[5,5,2,2,1,1] => [6,4,2,2,2] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[5,5,2,1,1,1,1] => [7,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[5,5,1,1,1,1,1,1] => [8,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 2
[5,4,4,3] => [4,4,4,3,1] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 4
[5,4,4,2,1] => [5,4,3,3,1] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 4
[5,4,4,1,1,1] => [6,3,3,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 3
[5,4,3,3,1] => [5,4,4,2,1] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 4
[5,4,3,2,2] => [5,5,3,2,1] => [5,3,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 5
[5,4,3,2,1,1] => [6,4,3,2,1] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[5,4,3,1,1,1,1] => [7,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[5,4,2,2,2,1] => [6,5,2,2,1] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[5,4,2,2,1,1,1] => [7,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[5,4,2,1,1,1,1,1] => [8,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[5,4,1,1,1,1,1,1,1] => [9,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[5,3,3,3,2] => [5,5,4,1,1] => [5,4,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 5
[5,3,3,3,1,1] => [6,4,4,1,1] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 4
[5,3,3,2,2,1] => [6,5,3,1,1] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 5
[5,3,3,2,1,1,1] => [7,4,3,1,1] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[5,3,3,1,1,1,1,1] => [8,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[5,3,2,2,2,1,1] => [7,5,2,1,1] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[5,3,2,2,1,1,1,1] => [8,4,2,1,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[5,3,2,1,1,1,1,1,1] => [9,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[5,3,1,1,1,1,1,1,1,1] => [10,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[5,2,2,2,2,1,1,1] => [8,5,1,1,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[5,2,2,2,1,1,1,1,1] => [9,4,1,1,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[5,2,2,1,1,1,1,1,1,1] => [10,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[5,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[5,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[4,4,4,4] => [4,4,4,4] => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 4
[4,4,4,3,1] => [5,4,4,3] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 4
[4,4,4,2,2] => [5,5,3,3] => [5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
[4,4,4,2,1,1] => [6,4,3,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 4
[4,4,4,1,1,1,1] => [7,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 3
[4,4,3,3,2] => [5,5,4,2] => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 5
[4,4,3,3,1,1] => [6,4,4,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 4
[4,4,3,2,2,1] => [6,5,3,2] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 5
[4,4,3,2,1,1,1] => [7,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 4
[4,4,3,1,1,1,1,1] => [8,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 3
[4,4,2,2,2,2] => [6,6,2,2] => [6,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[4,4,2,2,2,1,1] => [7,5,2,2] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 5
[4,4,2,2,1,1,1,1] => [8,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[4,4,2,1,1,1,1,1,1] => [9,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[4,4,1,1,1,1,1,1,1,1] => [10,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[4,3,3,3,3] => [5,5,5,1] => [5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 5
[4,3,3,3,2,1] => [6,5,4,1] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 5
[4,3,3,3,1,1,1] => [7,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[4,3,3,2,2,2] => [6,6,3,1] => [6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6
[4,3,3,2,2,1,1] => [7,5,3,1] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[4,3,3,2,1,1,1,1] => [8,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[4,3,3,1,1,1,1,1,1] => [9,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[4,3,2,2,2,2,1] => [7,6,2,1] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[4,3,2,2,2,1,1,1] => [8,5,2,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[4,3,2,2,1,1,1,1,1] => [9,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[4,3,2,1,1,1,1,1,1,1] => [10,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[4,3,1,1,1,1,1,1,1,1,1] => [11,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[4,2,2,2,2,2,1,1] => [8,6,1,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[4,2,2,2,2,1,1,1,1] => [9,5,1,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[4,2,2,2,1,1,1,1,1,1] => [10,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[4,2,2,1,1,1,1,1,1,1,1] => [11,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[4,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[4,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1
[3,3,3,3,3,1] => [6,5,5] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 5
[3,3,3,3,2,2] => [6,6,4] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 6
[3,3,3,3,2,1,1] => [7,5,4] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 5
[3,3,3,3,1,1,1,1] => [8,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 4
[3,3,3,2,2,2,1] => [7,6,3] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 6
[3,3,3,2,2,1,1,1] => [8,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 5
[3,3,3,2,1,1,1,1,1] => [9,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 4
[3,3,3,1,1,1,1,1,1,1] => [10,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[3,3,2,2,2,2,2] => [7,7,2] => [7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 7
[3,3,2,2,2,2,1,1] => [8,6,2] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[3,3,2,2,2,1,1,1,1] => [9,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[3,3,2,2,1,1,1,1,1,1] => [10,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 4
[3,3,2,1,1,1,1,1,1,1,1] => [11,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 3
[3,3,1,1,1,1,1,1,1,1,1,1] => [12,2,2] => [2,2] => [1,1,1,0,0,0] => 2
[3,2,2,2,2,2,2,1] => [8,7,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[3,2,2,2,2,2,1,1,1] => [9,6,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[3,2,2,2,2,1,1,1,1,1] => [10,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[3,2,2,2,1,1,1,1,1,1,1] => [11,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[3,2,2,1,1,1,1,1,1,1,1,1] => [12,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[3,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2,1] => [2,1] => [1,0,1,1,0,0] => 2
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1,1] => [1,1] => [1,1,0,0] => 1
[2,2,2,2,2,2,2,2] => [8,8] => [8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[2,2,2,2,2,2,2,1,1] => [9,7] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[2,2,2,2,2,2,1,1,1,1] => [10,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[2,2,2,2,2,1,1,1,1,1,1] => [11,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
[2,2,2,2,1,1,1,1,1,1,1,1] => [12,4] => [4] => [1,0,1,0,1,0,1,0] => 4
[2,2,2,1,1,1,1,1,1,1,1,1,1] => [13,3] => [3] => [1,0,1,0,1,0] => 3
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => [14,2] => [2] => [1,0,1,0] => 2
[8,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[8,1,1,1,1,1,1,1,1,1] => [10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[7,7,2,1] => [4,3,2,2,2,2,2] => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 3
[7,7,1,1,1] => [5,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[7,6,2,1,1] => [5,3,2,2,2,2,1] => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[7,6,1,1,1,1] => [6,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2
[7,5,2,1,1,1] => [6,3,2,2,2,1,1] => [3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[7,5,1,1,1,1,1] => [7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 2
[7,4,2,1,1,1,1] => [7,3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[7,4,1,1,1,1,1,1] => [8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 2
[7,3,2,1,1,1,1,1] => [8,3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[7,3,1,1,1,1,1,1,1] => [9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[7,2,2,1,1,1,1,1,1] => [9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[7,2,1,1,1,1,1,1,1,1] => [10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[7,1,1,1,1,1,1,1,1,1,1] => [11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[6,6,5] => [3,3,3,3,3,2] => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 3
[6,6,4,1] => [4,3,3,3,2,2] => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 3
[6,6,3,2] => [4,4,3,2,2,2] => [4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 4
[6,6,3,1,1] => [5,3,3,2,2,2] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[6,6,2,2,1] => [5,4,2,2,2,2] => [4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 4
[6,6,2,1,1,1] => [6,3,2,2,2,2] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[6,6,1,1,1,1,1] => [7,2,2,2,2,2] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[6,5,5,1] => [4,3,3,3,3,1] => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 3
[6,5,4,2] => [4,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 4
[6,5,4,1,1] => [5,3,3,3,2,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[6,5,3,2,1] => [5,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[6,5,3,1,1,1] => [6,3,3,2,2,1] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[6,5,2,2,1,1] => [6,4,2,2,2,1] => [4,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 4
[6,5,2,1,1,1,1] => [7,3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[6,5,1,1,1,1,1,1] => [8,2,2,2,2,1] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[6,4,4,2,1] => [5,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 4
[6,4,4,1,1,1] => [6,3,3,3,1,1] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 3
[6,4,3,2,1,1] => [6,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 4
[6,4,3,1,1,1,1] => [7,3,3,2,1,1] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[6,4,2,2,1,1,1] => [7,4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 4
[6,4,2,1,1,1,1,1] => [8,3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[6,4,1,1,1,1,1,1,1] => [9,2,2,2,1,1] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[6,3,3,2,1,1,1] => [7,4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[6,3,3,1,1,1,1,1] => [8,3,3,1,1,1] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[6,3,2,2,1,1,1,1] => [8,4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[6,3,2,1,1,1,1,1,1] => [9,3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[6,3,1,1,1,1,1,1,1,1] => [10,2,2,1,1,1] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[6,2,2,2,1,1,1,1,1] => [9,4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[6,2,2,1,1,1,1,1,1,1] => [10,3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[6,2,1,1,1,1,1,1,1,1,1] => [11,2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[6,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
[5,5,5,2] => [4,4,3,3,3] => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[5,5,5,1,1] => [5,3,3,3,3] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 3
[5,5,4,3] => [4,4,4,3,2] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 4
[5,5,4,2,1] => [5,4,3,3,2] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[5,5,4,1,1,1] => [6,3,3,3,2] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 3
[5,5,3,3,1] => [5,4,4,2,2] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 4
[5,5,3,2,2] => [5,5,3,2,2] => [5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 5
[5,5,3,2,1,1] => [6,4,3,2,2] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[5,5,3,1,1,1,1] => [7,3,3,2,2] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[5,5,2,2,2,1] => [6,5,2,2,2] => [5,2,2,2] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 5
[5,5,2,2,1,1,1] => [7,4,2,2,2] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[5,5,2,1,1,1,1,1] => [8,3,2,2,2] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[5,5,1,1,1,1,1,1,1] => [9,2,2,2,2] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 2
[5,4,4,4] => [4,4,4,4,1] => [4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 4
[5,4,4,3,1] => [5,4,4,3,1] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 4
[5,4,4,2,2] => [5,5,3,3,1] => [5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 5
[5,4,4,2,1,1] => [6,4,3,3,1] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 4
[5,4,4,1,1,1,1] => [7,3,3,3,1] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 3
[5,4,3,3,2] => [5,5,4,2,1] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 5
[5,4,3,3,1,1] => [6,4,4,2,1] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 4
[5,4,3,2,2,1] => [6,5,3,2,1] => [5,3,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 5
[5,4,3,2,1,1,1] => [7,4,3,2,1] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[5,4,3,1,1,1,1,1] => [8,3,3,2,1] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[5,4,2,2,2,1,1] => [7,5,2,2,1] => [5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[5,4,2,2,1,1,1,1] => [8,4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 4
[5,4,2,1,1,1,1,1,1] => [9,3,2,2,1] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[5,4,1,1,1,1,1,1,1,1] => [10,2,2,2,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[5,3,3,3,2,1] => [6,5,4,1,1] => [5,4,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 5
[5,3,3,3,1,1,1] => [7,4,4,1,1] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 4
[5,3,3,2,2,1,1] => [7,5,3,1,1] => [5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 5
[5,3,3,2,1,1,1,1] => [8,4,3,1,1] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[5,3,3,1,1,1,1,1,1] => [9,3,3,1,1] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[5,3,2,2,2,1,1,1] => [8,5,2,1,1] => [5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 5
[5,3,2,2,1,1,1,1,1] => [9,4,2,1,1] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[5,3,2,1,1,1,1,1,1,1] => [10,3,2,1,1] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[5,3,1,1,1,1,1,1,1,1,1] => [11,2,2,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 2
[5,2,2,2,2,1,1,1,1] => [9,5,1,1,1] => [5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[5,2,2,2,1,1,1,1,1,1] => [10,4,1,1,1] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[5,2,2,1,1,1,1,1,1,1,1] => [11,3,1,1,1] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[5,2,1,1,1,1,1,1,1,1,1,1] => [12,2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 2
[5,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1,1,1,1] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
[4,4,4,4,1] => [5,4,4,4] => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 4
[4,4,4,3,2] => [5,5,4,3] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 5
[4,4,4,3,1,1] => [6,4,4,3] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 4
[4,4,4,2,2,1] => [6,5,3,3] => [5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
[4,4,4,2,1,1,1] => [7,4,3,3] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 4
[4,4,4,1,1,1,1,1] => [8,3,3,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 3
[4,4,3,3,3] => [5,5,5,2] => [5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 5
[4,4,3,3,2,1] => [6,5,4,2] => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 5
[4,4,3,3,1,1,1] => [7,4,4,2] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 4
[4,4,3,2,2,2] => [6,6,3,2] => [6,3,2] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 6
[4,4,3,2,2,1,1] => [7,5,3,2] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 5
[4,4,3,2,1,1,1,1] => [8,4,3,2] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 4
[4,4,3,1,1,1,1,1,1] => [9,3,3,2] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 3
[4,4,2,2,2,2,1] => [7,6,2,2] => [6,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[4,4,2,2,2,1,1,1] => [8,5,2,2] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 5
[4,4,2,2,1,1,1,1,1] => [9,4,2,2] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
[4,4,2,1,1,1,1,1,1,1] => [10,3,2,2] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 3
[4,4,1,1,1,1,1,1,1,1,1] => [11,2,2,2] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[4,3,3,3,3,1] => [6,5,5,1] => [5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 5
[4,3,3,3,2,2] => [6,6,4,1] => [6,4,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 6
[4,3,3,3,2,1,1] => [7,5,4,1] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 5
[4,3,3,3,1,1,1,1] => [8,4,4,1] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[4,3,3,2,2,2,1] => [7,6,3,1] => [6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 6
[4,3,3,2,2,1,1,1] => [8,5,3,1] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 5
[4,3,3,2,1,1,1,1,1] => [9,4,3,1] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 4
[4,3,3,1,1,1,1,1,1,1] => [10,3,3,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[4,3,2,2,2,2,1,1] => [8,6,2,1] => [6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[4,3,2,2,2,1,1,1,1] => [9,5,2,1] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 5
[4,3,2,2,1,1,1,1,1,1] => [10,4,2,1] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 4
[4,3,2,1,1,1,1,1,1,1,1] => [11,3,2,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[4,3,1,1,1,1,1,1,1,1,1,1] => [12,2,2,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[4,2,2,2,2,2,1,1,1] => [9,6,1,1] => [6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[4,2,2,2,2,1,1,1,1,1] => [10,5,1,1] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[4,2,2,2,1,1,1,1,1,1,1] => [11,4,1,1] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[4,2,2,1,1,1,1,1,1,1,1,1] => [12,3,1,1] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[4,2,1,1,1,1,1,1,1,1,1,1,1] => [13,2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1,1,1] => [1,1,1] => [1,1,0,1,0,0] => 1
[3,3,3,3,3,2] => [6,6,5] => [6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 6
[3,3,3,3,3,1,1] => [7,5,5] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 5
[3,3,3,3,2,2,1] => [7,6,4] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 6
[3,3,3,3,2,1,1,1] => [8,5,4] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 5
[3,3,3,3,1,1,1,1,1] => [9,4,4] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 4
[3,3,3,2,2,2,2] => [7,7,3] => [7,3] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 7
[3,3,3,2,2,2,1,1] => [8,6,3] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 6
[3,3,3,2,2,1,1,1,1] => [9,5,3] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 5
[3,3,3,2,1,1,1,1,1,1] => [10,4,3] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 4
[3,3,3,1,1,1,1,1,1,1,1] => [11,3,3] => [3,3] => [1,1,1,0,1,0,0,0] => 3
[3,3,2,2,2,2,2,1] => [8,7,2] => [7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 7
[3,3,2,2,2,2,1,1,1] => [9,6,2] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[3,3,2,2,2,1,1,1,1,1] => [10,5,2] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 5
[3,3,2,2,1,1,1,1,1,1,1] => [11,4,2] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 4
[3,3,2,1,1,1,1,1,1,1,1,1] => [12,3,2] => [3,2] => [1,0,1,1,1,0,0,0] => 3
[3,3,1,1,1,1,1,1,1,1,1,1,1] => [13,2,2] => [2,2] => [1,1,1,0,0,0] => 2
[3,2,2,2,2,2,2,1,1] => [9,7,1] => [7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[3,2,2,2,2,2,1,1,1,1] => [10,6,1] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[3,2,2,2,2,1,1,1,1,1,1] => [11,5,1] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 5
[3,2,2,2,1,1,1,1,1,1,1,1] => [12,4,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 4
[3,2,2,1,1,1,1,1,1,1,1,1,1] => [13,3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[3,2,1,1,1,1,1,1,1,1,1,1,1,1] => [14,2,1] => [2,1] => [1,0,1,1,0,0] => 2
[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1,1] => [1,1] => [1,1,0,0] => 1
[2,2,2,2,2,2,2,2,1] => [9,8] => [8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[2,2,2,2,2,2,2,1,1,1] => [10,7] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[2,2,2,2,2,2,1,1,1,1,1] => [11,6] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[2,2,2,2,2,1,1,1,1,1,1,1] => [12,5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 5
[2,2,2,2,1,1,1,1,1,1,1,1,1] => [13,4] => [4] => [1,0,1,0,1,0,1,0] => 4
[2,2,2,1,1,1,1,1,1,1,1,1,1,1] => [14,3] => [3] => [1,0,1,0,1,0] => 3
[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,2] => [2] => [1,0,1,0] => 2
[5,5,4,3,2,1] => [6,5,4,3,2] => [5,4,3,2] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 5
[5,4,4,3,2,1] => [6,5,4,3,1] => [5,4,3,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 5
[4,4,4,3,2,1] => [6,5,4,3] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 5
[5,5,3,3,2,1] => [6,5,4,2,2] => [5,4,2,2] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 5
[5,4,3,3,2,1] => [6,5,4,2,1] => [5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 5
[5,5,4,2,2,1] => [6,5,3,3,2] => [5,3,3,2] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 5
[5,4,4,2,2,1] => [6,5,3,3,1] => [5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 5
[5,5,3,2,2,1] => [6,5,3,2,2] => [5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 5
[5,5,4,3,1,1] => [6,4,4,3,2] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 4
[5,4,4,3,1,1] => [6,4,4,3,1] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 4
[5,5,3,3,1,1] => [6,4,4,2,2] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 4
[6,5,4,2,1,1] => [6,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 4
[5,5,4,2,1,1] => [6,4,3,3,2] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 4
[6,4,4,2,1,1] => [6,4,3,3,1,1] => [4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 4
[6,5,3,2,1,1] => [6,4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 4
[6,5,4,1,1,1] => [6,3,3,3,2,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[5,5,4,3,2] => [5,5,4,3,2] => [5,4,3,2] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 5
[5,4,4,3,2] => [5,5,4,3,1] => [5,4,3,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 5
[5,5,3,3,2] => [5,5,4,2,2] => [5,4,2,2] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 5
[5,5,4,2,2] => [5,5,3,3,2] => [5,3,3,2] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 5
[5,5,4,3,1] => [5,4,4,3,2] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 4
[6,5,4,2,1] => [5,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 4
[4,4,4,4,3,2,1] => [7,6,5,4] => [6,5,4] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 6
[3,3,3,3,3,2,1] => [7,6,5] => [6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 6
[5,5,4,3,2,1,1] => [7,5,4,3,2] => [5,4,3,2] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 5
[6,5,4,2,1,1,1] => [7,4,3,3,2,1] => [4,3,3,2,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 4
[6,4,3,2,1,1,1] => [7,4,3,2,1,1] => [4,3,2,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 4
[5,5,5,1,1,1,1] => [7,3,3,3,3] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 3
[6,5,4,1,1,1,1] => [7,3,3,3,2,1] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[7,6,1,1,1,1,1] => [7,2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2
[4,4,4,4,3,1] => [6,5,5,4] => [5,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 5
[6,6,3,2,1] => [5,4,3,2,2,2] => [4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 4
[5,5,4,4] => [4,4,4,4,2] => [4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 4
[3,3,3,3,3,3] => [6,6,6] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 6
[3,3,3,3,3,3,1] => [7,6,6] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 6
[4,4,4,4,4] => [5,5,5,5] => [5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 5
[5,5,5,5] => [4,4,4,4,4] => [4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 4
[6,6,6] => [3,3,3,3,3,3] => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 3
[7,7,1,1,1,1] => [6,2,2,2,2,2,2] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[4,4,4,4,4,1] => [6,5,5,5] => [5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 5
[5,5,5,5,1] => [5,4,4,4,4] => [4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 4
[6,6,6,1] => [4,3,3,3,3,3] => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 3
[3,3,3,3,2,2,1,1,1,1] => [10,6,4] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 6
[4,4,3,3,2,2,1,1] => [8,6,4,2] => [6,4,2] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 6
[3,3,3,3,3,3,2,1] => [8,7,6] => [7,6] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 7
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Description
The maximal height of a column in the parallelogram polyomino associated with a Dyck path.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition λ of n is the partition λ∗ whose Ferrers diagram is obtained from the diagram of λ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
The conjugate partition of the partition λ of n is the partition λ∗ whose Ferrers diagram is obtained from the diagram of λ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
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