Identifier
-
Mp00322:
Integer partitions
—Loehr-Warrington⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000620: Integer partitions ⟶ ℤ
Values
[4] => [1,1,1,1] => [1,1,1] => [1,1] => 1
[5] => [1,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[4,1] => [2,1,1,1] => [1,1,1] => [1,1] => 1
[6] => [1,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[5,1] => [2,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[4,2] => [2,2,1,1] => [2,1,1] => [1,1] => 1
[4,1,1] => [3,1,1,1] => [1,1,1] => [1,1] => 1
[2,2,2] => [2,2,2] => [2,2] => [2] => 0
[7] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[6,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[5,2] => [2,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[5,1,1] => [3,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[4,1,1,1] => [3,2,1,1] => [2,1,1] => [1,1] => 1
[3,2,2] => [2,2,2,1] => [2,2,1] => [2,1] => 1
[3,1,1,1,1] => [3,2,2] => [2,2] => [2] => 0
[2,2,2,1] => [4,1,1,1] => [1,1,1] => [1,1] => 1
[8] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[7,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[6,2] => [2,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[6,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[5,3] => [2,2,2,1,1] => [2,2,1,1] => [2,1,1] => 2
[5,2,1] => [4,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[5,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[3,3,2] => [2,2,2,2] => [2,2,2] => [2,2] => 1
[3,2,2,1] => [3,2,2,1] => [2,2,1] => [2,1] => 1
[3,2,1,1,1] => [3,3,1,1] => [3,1,1] => [1,1] => 1
[3,1,1,1,1,1] => [4,2,1,1] => [2,1,1] => [1,1] => 1
[2,2,2,2] => [5,1,1,1] => [1,1,1] => [1,1] => 1
[2,2,1,1,1,1] => [3,3,2] => [3,2] => [2] => 0
[2,1,1,1,1,1,1] => [4,2,2] => [2,2] => [2] => 0
[9] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[8,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[7,2] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[6,3] => [2,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 3
[6,2,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[6,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[5,3,1] => [3,2,2,1,1] => [2,2,1,1] => [2,1,1] => 2
[5,2,2] => [6,1,1,1] => [1,1,1] => [1,1] => 1
[5,2,1,1] => [3,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[5,1,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[3,3,3] => [2,2,2,2,1] => [2,2,2,1] => [2,2,1] => 3
[3,3,2,1] => [3,2,2,2] => [2,2,2] => [2,2] => 1
[3,3,1,1,1] => [5,2,1,1] => [2,1,1] => [1,1] => 1
[3,2,2,2] => [5,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[3,2,2,1,1] => [3,3,3] => [3,3] => [3] => 1
[3,2,1,1,1,1] => [5,2,2] => [2,2] => [2] => 0
[2,2,2,1,1,1] => [3,3,2,1] => [3,2,1] => [2,1] => 1
[2,2,1,1,1,1,1] => [4,2,2,1] => [2,2,1] => [2,1] => 1
[2,1,1,1,1,1,1,1] => [4,3,1,1] => [3,1,1] => [1,1] => 1
[1,1,1,1,1,1,1,1,1] => [4,3,2] => [3,2] => [2] => 0
[10] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[9,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[8,2] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[8,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[7,3] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 4
[7,2,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[6,4] => [2,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 6
[6,3,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 3
[6,2,2] => [5,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[6,2,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[6,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[5,3,2] => [7,1,1,1] => [1,1,1] => [1,1] => 1
[5,3,1,1] => [6,2,1,1] => [2,1,1] => [1,1] => 1
[5,2,2,1] => [3,3,2,1,1] => [3,2,1,1] => [2,1,1] => 2
[5,2,1,1,1] => [4,2,2,1,1] => [2,2,1,1] => [2,1,1] => 2
[5,1,1,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[4,3,3] => [2,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[4,2,2,1,1] => [3,3,2,2] => [3,2,2] => [2,2] => 1
[4,1,1,1,1,1,1] => [4,3,3] => [3,3] => [3] => 1
[3,3,3,1] => [3,2,2,2,1] => [2,2,2,1] => [2,2,1] => 3
[3,3,2,2] => [6,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[3,3,2,1,1] => [6,2,2] => [2,2] => [2] => 0
[3,2,2,2,1] => [5,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[3,2,2,1,1,1] => [4,2,2,2] => [2,2,2] => [2,2] => 1
[3,2,1,1,1,1,1] => [4,4,1,1] => [4,1,1] => [1,1] => 1
[3,1,1,1,1,1,1,1] => [4,4,2] => [4,2] => [2] => 0
[2,2,2,2,1,1] => [3,3,3,1] => [3,3,1] => [3,1] => 2
[2,2,2,1,1,1,1] => [5,2,2,1] => [2,2,1] => [2,1] => 1
[2,2,1,1,1,1,1,1] => [5,3,1,1] => [3,1,1] => [1,1] => 1
[2,1,1,1,1,1,1,1,1] => [5,3,2] => [3,2] => [2] => 0
[1,1,1,1,1,1,1,1,1,1] => [4,3,2,1] => [3,2,1] => [2,1] => 1
[11] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[10,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[9,2] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[9,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[8,3] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 5
[8,2,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[8,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[7,4] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 10
[7,3,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 4
[7,2,2] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,2,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[6,4,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 6
[6,3,2] => [7,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[6,3,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[6,2,2,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 3
[6,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 3
[6,1,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
>>> Load all 1048 entries. <<<[5,3,3] => [8,1,1,1] => [1,1,1] => [1,1] => 1
[5,3,2,1] => [7,2,1,1] => [2,1,1] => [1,1] => 1
[5,2,2,1,1] => [6,2,2,1] => [2,2,1] => [2,1] => 1
[5,2,1,1,1,1] => [6,3,1,1] => [3,1,1] => [1,1] => 1
[5,1,1,1,1,1,1] => [4,3,2,1,1] => [3,2,1,1] => [2,1,1] => 2
[4,4,3] => [2,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 9
[4,3,3,1] => [3,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[4,3,2,2] => [3,3,2,2,1] => [3,2,2,1] => [2,2,1] => 3
[4,3,2,1,1] => [7,2,2] => [2,2] => [2] => 0
[4,2,2,2,1] => [3,3,3,1,1] => [3,3,1,1] => [3,1,1] => 4
[4,2,2,1,1,1] => [5,2,2,1,1] => [2,2,1,1] => [2,1,1] => 2
[4,2,1,1,1,1,1] => [6,3,2] => [3,2] => [2] => 0
[4,1,1,1,1,1,1,1] => [4,3,2,2] => [3,2,2] => [2,2] => 1
[3,3,3,2] => [6,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[3,3,3,1,1] => [4,2,2,2,1] => [2,2,2,1] => [2,2,1] => 3
[3,3,2,2,1] => [6,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[3,3,2,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[3,3,1,1,1,1,1] => [4,4,3] => [4,3] => [3] => 1
[3,2,2,1,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[3,2,1,1,1,1,1,1] => [5,3,3] => [3,3] => [3] => 1
[3,1,1,1,1,1,1,1,1] => [4,3,3,1] => [3,3,1] => [3,1] => 2
[2,2,2,2,2,1] => [3,3,3,2] => [3,3,2] => [3,2] => 3
[2,2,2,2,1,1,1] => [5,2,2,2] => [2,2,2] => [2,2] => 1
[2,2,2,1,1,1,1,1] => [5,4,1,1] => [4,1,1] => [1,1] => 1
[2,2,1,1,1,1,1,1,1] => [5,4,2] => [4,2] => [2] => 0
[2,1,1,1,1,1,1,1,1,1] => [4,4,2,1] => [4,2,1] => [2,1] => 1
[1,1,1,1,1,1,1,1,1,1,1] => [5,3,2,1] => [3,2,1] => [2,1] => 1
[12] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[11,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[10,2] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[10,1,1] => [3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[9,3] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 6
[9,2,1] => [4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[9,1,1,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[8,4] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[8,3,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 5
[8,2,2] => [5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[8,2,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[8,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[7,5] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 19
[7,4,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 10
[7,3,2] => [6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,3,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,2,2,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 4
[7,2,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 4
[7,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[6,4,2] => [3,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 6
[6,4,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 6
[6,3,3] => [8,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[6,3,2,1] => [7,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[6,3,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[6,2,2,2] => [3,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 7
[6,2,2,1,1] => [5,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 3
[6,2,1,1,1,1] => [5,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[6,1,1,1,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 3
[5,4,3] => [9,1,1,1] => [1,1,1] => [1,1] => 1
[5,3,3,1] => [8,2,1,1] => [2,1,1] => [1,1] => 1
[5,3,1,1,1,1] => [4,4,4] => [4,4] => [4] => 0
[5,2,2,2,1] => [7,2,2,1] => [2,2,1] => [2,1] => 1
[5,2,2,1,1,1] => [5,5,1,1] => [5,1,1] => [1,1] => 1
[5,2,1,1,1,1,1] => [5,5,2] => [5,2] => [2] => 0
[5,1,1,1,1,1,1,1] => [6,3,2,1] => [3,2,1] => [2,1] => 1
[4,4,4] => [2,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 9
[4,4,3,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 9
[4,4,2,1,1] => [8,2,2] => [2,2] => [2] => 0
[4,3,3,2] => [3,3,2,2,2] => [3,2,2,2] => [2,2,2] => 3
[4,3,3,1,1] => [4,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[4,3,2,2,1] => [6,2,2,1,1] => [2,2,1,1] => [2,1,1] => 2
[4,3,2,1,1,1] => [6,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[4,3,1,1,1,1,1] => [7,3,2] => [3,2] => [2] => 0
[4,2,2,2,2] => [3,3,3,3] => [3,3,3] => [3,3] => 3
[4,2,2,2,1,1] => [6,2,2,2] => [2,2,2] => [2,2] => 1
[4,2,2,1,1,1,1] => [4,3,3,1,1] => [3,3,1,1] => [3,1,1] => 4
[4,2,1,1,1,1,1,1] => [4,4,2,1,1] => [4,2,1,1] => [2,1,1] => 2
[4,1,1,1,1,1,1,1,1] => [5,3,2,1,1] => [3,2,1,1] => [2,1,1] => 2
[3,3,3,3] => [7,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[3,3,3,2,1] => [6,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[3,3,3,1,1,1] => [4,3,2,2,1] => [3,2,2,1] => [2,2,1] => 3
[3,3,2,2,1,1] => [7,3,1,1] => [3,1,1] => [1,1] => 1
[3,3,2,1,1,1,1] => [6,3,3] => [3,3] => [3] => 1
[3,3,1,1,1,1,1,1] => [4,3,3,2] => [3,3,2] => [3,2] => 3
[3,2,2,2,1,1,1] => [6,4,1,1] => [4,1,1] => [1,1] => 1
[3,2,2,1,1,1,1,1] => [6,4,2] => [4,2] => [2] => 0
[3,2,1,1,1,1,1,1,1] => [4,4,2,2] => [4,2,2] => [2,2] => 1
[3,1,1,1,1,1,1,1,1,1] => [5,3,2,2] => [3,2,2] => [2,2] => 1
[2,2,2,2,2,2] => [3,3,3,2,1] => [3,3,2,1] => [3,2,1] => 10
[2,2,2,2,2,1,1] => [5,2,2,2,1] => [2,2,2,1] => [2,2,1] => 3
[2,2,2,2,1,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[2,2,2,1,1,1,1,1,1] => [5,4,3] => [4,3] => [3] => 1
[2,2,1,1,1,1,1,1,1,1] => [4,4,3,1] => [4,3,1] => [3,1] => 2
[2,1,1,1,1,1,1,1,1,1,1] => [5,3,3,1] => [3,3,1] => [3,1] => 2
[1,1,1,1,1,1,1,1,1,1,1,1] => [5,4,2,1] => [4,2,1] => [2,1] => 1
[13] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[12,1] => [2,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[11,2] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[11,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[10,3] => [2,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 7
[10,2,1] => [4,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[10,1,1,1] => [3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[9,4] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[9,3,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 6
[9,2,2] => [5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[9,2,1,1] => [3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[9,1,1,1,1] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[8,5] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 34
[8,4,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[8,3,2] => [6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[8,3,1,1] => [5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[8,2,2,1] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 5
[8,2,1,1,1] => [4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 5
[8,1,1,1,1,1] => [4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[7,5,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 19
[7,4,2] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 10
[7,4,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 10
[7,3,3] => [8,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[7,3,2,1] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,3,1,1,1] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,2,2,2] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 11
[7,2,2,1,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 4
[7,2,1,1,1,1] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,1,1,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 4
[6,4,3] => [9,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[6,4,2,1] => [7,2,2,1,1] => [2,2,1,1] => [2,1,1] => 2
[6,4,1,1,1] => [4,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 6
[6,3,3,1] => [8,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[6,3,2,2] => [3,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 23
[6,3,2,1,1] => [7,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[6,3,1,1,1,1] => [4,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 7
[6,2,2,2,1] => [5,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 6
[6,2,2,1,1,1] => [5,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[6,2,1,1,1,1,1] => [4,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 3
[6,1,1,1,1,1,1,1] => [5,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 3
[5,5,3] => [10,1,1,1] => [1,1,1] => [1,1] => 1
[5,4,4] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 28
[5,4,3,1] => [9,2,1,1] => [2,1,1] => [1,1] => 1
[5,4,2,1,1] => [9,2,2] => [2,2] => [2] => 0
[5,3,2,1,1,1] => [7,3,3] => [3,3] => [3] => 1
[5,3,1,1,1,1,1] => [7,4,2] => [4,2] => [2] => 0
[5,2,2,2,2] => [8,2,2,1] => [2,2,1] => [2,1] => 1
[5,2,2,2,1,1] => [7,4,1,1] => [4,1,1] => [1,1] => 1
[5,2,2,1,1,1,1] => [5,4,4] => [4,4] => [4] => 0
[5,2,1,1,1,1,1,1] => [4,4,4,1] => [4,4,1] => [4,1] => 2
[5,1,1,1,1,1,1,1,1] => [5,5,2,1] => [5,2,1] => [2,1] => 1
[4,4,4,1] => [3,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 9
[4,4,3,2] => [3,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 9
[4,4,3,1,1] => [4,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 9
[4,4,2,2,1] => [6,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 3
[4,4,2,1,1,1] => [8,3,1,1] => [3,1,1] => [1,1] => 1
[4,4,1,1,1,1,1] => [8,3,2] => [3,2] => [2] => 0
[4,3,3,3] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,3,3,2,1] => [7,2,2,2] => [2,2,2] => [2,2] => 1
[4,3,3,1,1,1] => [4,3,2,2,2] => [3,2,2,2] => [2,2,2] => 3
[4,3,2,2,2] => [3,3,3,2,2] => [3,3,2,2] => [3,2,2] => 13
[4,3,2,2,1,1] => [6,5,1,1] => [5,1,1] => [1,1] => 1
[4,3,2,1,1,1,1] => [6,3,2,1,1] => [3,2,1,1] => [2,1,1] => 2
[4,3,1,1,1,1,1,1] => [6,3,2,2] => [3,2,2] => [2,2] => 1
[4,2,2,2,2,1] => [5,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[4,2,2,2,1,1,1] => [5,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[4,2,2,1,1,1,1,1] => [7,3,2,1] => [3,2,1] => [2,1] => 1
[4,2,1,1,1,1,1,1,1] => [6,3,3,1] => [3,3,1] => [3,1] => 2
[4,1,1,1,1,1,1,1,1,1] => [6,4,2,1] => [4,2,1] => [2,1] => 1
[3,3,3,3,1] => [7,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[3,3,3,2,1,1] => [6,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[3,3,3,1,1,1,1] => [4,3,3,3] => [3,3,3] => [3,3] => 3
[3,3,2,2,1,1,1] => [6,5,2] => [5,2] => [2] => 0
[3,3,2,1,1,1,1,1] => [4,4,2,2,1] => [4,2,2,1] => [2,2,1] => 3
[3,3,1,1,1,1,1,1,1] => [5,3,2,2,1] => [3,2,2,1] => [2,2,1] => 3
[3,2,2,2,2,2] => [3,3,3,3,1] => [3,3,3,1] => [3,3,1] => 13
[3,2,2,2,2,1,1] => [4,3,3,2,1] => [3,3,2,1] => [3,2,1] => 10
[3,2,2,2,1,1,1,1] => [5,5,3] => [5,3] => [3] => 1
[3,2,2,1,1,1,1,1,1] => [4,4,3,1,1] => [4,3,1,1] => [3,1,1] => 4
[3,2,1,1,1,1,1,1,1,1] => [5,3,3,1,1] => [3,3,1,1] => [3,1,1] => 4
[3,1,1,1,1,1,1,1,1,1,1] => [5,4,2,1,1] => [4,2,1,1] => [2,1,1] => 2
[2,2,2,2,2,2,1] => [6,2,2,2,1] => [2,2,2,1] => [2,2,1] => 3
[2,2,2,2,2,1,1,1] => [6,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[2,2,2,2,1,1,1,1,1] => [6,4,3] => [4,3] => [3] => 1
[2,2,2,1,1,1,1,1,1,1] => [4,4,3,2] => [4,3,2] => [3,2] => 3
[2,2,1,1,1,1,1,1,1,1,1] => [5,3,3,2] => [3,3,2] => [3,2] => 3
[2,1,1,1,1,1,1,1,1,1,1,1] => [5,4,2,2] => [4,2,2] => [2,2] => 1
[1,1,1,1,1,1,1,1,1,1,1,1,1] => [5,4,3,1] => [4,3,1] => [3,1] => 2
[14] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
[13,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[12,2] => [2,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[12,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[11,3] => [2,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 8
[11,2,1] => [4,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[11,1,1,1] => [3,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[10,4] => [2,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 28
[10,3,1] => [3,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 7
[10,2,2] => [5,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[10,2,1,1] => [3,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[10,1,1,1,1] => [4,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[9,5] => [2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 55
[9,4,1] => [3,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[9,3,2] => [6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[9,3,1,1] => [5,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[9,2,2,1] => [3,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 6
[9,2,1,1,1] => [4,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 6
[9,1,1,1,1,1] => [4,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[8,6] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 62
[8,5,1] => [3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 34
[8,4,2] => [3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[8,4,1,1] => [4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[8,3,3] => [7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[8,3,2,1] => [6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[8,3,1,1,1] => [4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[8,2,2,2] => [3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 16
[8,2,2,1,1] => [5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 5
[8,2,1,1,1,1] => [5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[8,1,1,1,1,1,1] => [4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 5
[7,5,2] => [3,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 19
[7,5,1,1] => [4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 19
[7,4,3] => [9,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[7,4,2,1] => [6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 4
[7,4,1,1,1] => [4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 10
[7,3,3,1] => [8,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[7,3,2,2] => [3,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 44
[7,3,2,1,1] => [6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,3,1,1,1,1] => [4,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 11
[7,2,2,2,1] => [5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 10
[7,2,2,1,1,1] => [5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,2,1,1,1,1,1] => [4,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 4
[7,1,1,1,1,1,1,1] => [5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 4
[6,5,3] => [11,1,1,1] => [1,1,1] => [1,1] => 1
[6,4,4] => [10,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[6,4,3,1] => [9,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[6,4,2,2] => [8,2,2,1,1] => [2,2,1,1] => [2,1,1] => 2
[6,4,2,1,1] => [6,6,1,1] => [6,1,1] => [1,1] => 1
[6,4,1,1,1,1] => [7,3,2,1,1] => [3,2,1,1] => [2,1,1] => 2
[6,3,3,1,1] => [8,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[6,3,2,2,1] => [4,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 23
[6,3,2,1,1,1] => [4,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 6
[6,3,1,1,1,1,1] => [5,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 6
[6,2,2,2,2] => [7,2,2,2,1] => [2,2,2,1] => [2,2,1] => 3
[6,2,2,2,1,1] => [7,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[6,2,2,1,1,1,1] => [4,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 7
[6,2,1,1,1,1,1,1] => [5,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 7
[6,1,1,1,1,1,1,1,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 3
[5,5,4] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 28
[5,5,3,1] => [10,2,1,1] => [2,1,1] => [1,1] => 1
[5,5,2,1,1] => [10,2,2] => [2,2] => [2] => 0
[5,4,4,1] => [3,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 28
[5,4,2,2,1] => [9,2,2,1] => [2,2,1] => [2,1] => 1
[5,4,2,1,1,1] => [9,3,1,1] => [3,1,1] => [1,1] => 1
[5,4,1,1,1,1,1] => [9,3,2] => [3,2] => [2] => 0
[5,3,3,3] => [3,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 45
[5,3,3,1,1,1] => [8,3,3] => [3,3] => [3] => 1
[5,3,2,2,2] => [3,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 36
[5,3,2,2,1,1] => [8,4,1,1] => [4,1,1] => [1,1] => 1
[5,3,2,1,1,1,1] => [8,4,2] => [4,2] => [2] => 0
[5,3,1,1,1,1,1,1] => [7,3,3,1] => [3,3,1] => [3,1] => 2
[5,2,2,2,2,1] => [5,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[5,2,2,2,1,1,1] => [7,4,3] => [4,3] => [3] => 1
[5,2,2,1,1,1,1,1] => [4,4,3,3] => [4,3,3] => [3,3] => 3
[5,2,1,1,1,1,1,1,1] => [7,4,2,1] => [4,2,1] => [2,1] => 1
[5,1,1,1,1,1,1,1,1,1] => [5,4,4,1] => [4,4,1] => [4,1] => 2
[4,4,4,2] => [3,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 9
[4,4,4,1,1] => [4,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 9
[4,4,3,3] => [8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,4,3,2,1] => [5,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 9
[4,4,3,1,1,1] => [4,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 9
[4,4,2,2,2] => [8,2,2,2] => [2,2,2] => [2,2] => 1
[4,4,2,2,1,1] => [7,5,1,1] => [5,1,1] => [1,1] => 1
[4,4,2,1,1,1,1] => [6,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 3
[4,4,1,1,1,1,1,1] => [8,3,2,1] => [3,2,1] => [2,1] => 1
[4,3,3,3,1] => [7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,3,3,2,2] => [7,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 3
[4,3,3,2,1,1] => [6,6,2] => [6,2] => [2] => 0
[4,3,3,1,1,1,1] => [7,3,2,2] => [3,2,2] => [2,2] => 1
[4,3,2,2,2,1] => [4,3,3,2,2] => [3,3,2,2] => [3,2,2] => 13
[4,3,2,2,1,1,1] => [5,5,4] => [5,4] => [4] => 0
[4,3,2,1,1,1,1,1] => [6,5,2,1] => [5,2,1] => [2,1] => 1
[4,3,1,1,1,1,1,1,1] => [5,5,2,1,1] => [5,2,1,1] => [2,1,1] => 2
[4,2,2,2,2,2] => [6,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 6
[4,2,2,2,2,1,1] => [6,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[4,2,2,2,1,1,1,1] => [4,4,4,1,1] => [4,4,1,1] => [4,1,1] => 6
[4,2,2,1,1,1,1,1,1] => [4,4,4,2] => [4,4,2] => [4,2] => 5
[4,2,1,1,1,1,1,1,1,1] => [5,5,2,2] => [5,2,2] => [2,2] => 1
[4,1,1,1,1,1,1,1,1,1,1] => [5,5,3,1] => [5,3,1] => [3,1] => 2
[3,3,3,3,1,1] => [7,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[3,3,3,2,1,1,1] => [4,4,2,2,2] => [4,2,2,2] => [2,2,2] => 3
[3,3,3,1,1,1,1,1] => [6,3,2,2,1] => [3,2,2,1] => [2,2,1] => 3
[3,3,2,2,2,2] => [3,3,3,3,2] => [3,3,3,2] => [3,3,2] => 26
[3,3,2,2,2,1,1] => [7,5,2] => [5,2] => [2] => 0
[3,3,2,2,1,1,1,1] => [5,3,2,2,2] => [3,2,2,2] => [2,2,2] => 3
[3,3,2,1,1,1,1,1,1] => [6,3,3,1,1] => [3,3,1,1] => [3,1,1] => 4
[3,3,1,1,1,1,1,1,1,1] => [6,4,2,1,1] => [4,2,1,1] => [2,1,1] => 2
[3,2,2,2,2,2,1] => [4,3,3,3,1] => [3,3,3,1] => [3,3,1] => 13
[3,2,2,2,2,1,1,1] => [6,4,4] => [4,4] => [4] => 0
[3,2,2,2,1,1,1,1,1] => [5,3,3,3] => [3,3,3] => [3,3] => 3
[3,2,2,1,1,1,1,1,1,1] => [6,3,3,2] => [3,3,2] => [3,2] => 3
[3,2,1,1,1,1,1,1,1,1,1] => [6,4,2,2] => [4,2,2] => [2,2] => 1
[3,1,1,1,1,1,1,1,1,1,1,1] => [6,4,3,1] => [4,3,1] => [3,1] => 2
[2,2,2,2,2,2,2] => [6,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[2,2,2,2,2,2,1,1] => [6,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[2,2,2,2,2,1,1,1,1] => [6,5,3] => [5,3] => [3] => 1
[2,2,2,2,1,1,1,1,1,1] => [4,4,3,2,1] => [4,3,2,1] => [3,2,1] => 10
[2,2,2,1,1,1,1,1,1,1,1] => [5,3,3,2,1] => [3,3,2,1] => [3,2,1] => 10
[2,2,1,1,1,1,1,1,1,1,1,1] => [5,4,2,2,1] => [4,2,2,1] => [2,2,1] => 3
[2,1,1,1,1,1,1,1,1,1,1,1,1] => [5,4,3,1,1] => [4,3,1,1] => [3,1,1] => 4
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [5,4,3,2] => [4,3,2] => [3,2] => 3
[14,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
[13,2] => [2,2,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[13,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[12,3] => [2,2,2,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 9
[12,2,1] => [4,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[12,1,1,1] => [3,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[11,4] => [2,2,2,2,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 36
[11,3,1] => [3,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 8
[11,2,2] => [5,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[11,2,1,1] => [3,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[11,1,1,1,1] => [4,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[10,5] => [2,2,2,2,2,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 83
[10,4,1] => [3,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 28
[10,3,2] => [6,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[10,3,1,1] => [5,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[10,2,2,1] => [3,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 7
[10,2,1,1,1] => [4,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 7
[10,1,1,1,1,1] => [4,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[9,6] => [2,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 117
[9,5,1] => [3,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 55
[9,4,2] => [3,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[9,4,1,1] => [4,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[9,3,3] => [7,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[9,3,2,1] => [6,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[9,3,1,1,1] => [4,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[9,2,2,2] => [3,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 22
[9,2,2,1,1] => [5,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 6
[9,2,1,1,1,1] => [5,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[9,1,1,1,1,1,1] => [4,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 6
[8,6,1] => [3,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 62
[8,5,2] => [3,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => 34
[8,5,1,1] => [4,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 34
[8,4,3] => [9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[8,4,2,1] => [6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 5
[8,4,1,1,1] => [4,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[8,3,3,1] => [7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[8,3,2,2] => [3,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => 75
[8,3,2,1,1] => [6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[8,3,1,1,1,1] => [4,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 16
[8,2,2,2,1] => [5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[8,2,2,1,1,1] => [5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[8,2,1,1,1,1,1] => [4,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 5
[8,1,1,1,1,1,1,1] => [5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 5
[7,5,3] => [3,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 108
[7,5,2,1] => [5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 19
[7,5,1,1,1] => [4,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 19
[7,4,4] => [10,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[7,4,3,1] => [9,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[7,4,2,2] => [8,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 3
[7,4,2,1,1] => [5,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,4,1,1,1,1] => [6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 4
[7,3,3,2] => [3,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => 80
[7,3,3,1,1] => [8,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[7,3,2,2,1] => [4,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 44
[7,3,2,1,1,1] => [4,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 10
[7,3,1,1,1,1,1] => [5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 10
[7,2,2,2,2] => [6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 10
[7,2,2,2,1,1] => [6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,2,2,1,1,1,1] => [4,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 11
[7,2,1,1,1,1,1,1] => [5,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 11
[7,1,1,1,1,1,1,1,1] => [5,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 4
[6,6,3] => [12,1,1,1] => [1,1,1] => [1,1] => 1
[6,5,4] => [11,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[6,5,3,1] => [11,2,1,1] => [2,1,1] => [1,1] => 1
[6,5,2,1,1] => [11,2,2] => [2,2] => [2] => 0
[6,4,4,1] => [10,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[6,4,3,2] => [9,2,2,1,1] => [2,2,1,1] => [2,1,1] => 2
[6,4,3,1,1] => [9,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[6,4,2,2,1] => [8,5,1,1] => [5,1,1] => [1,1] => 1
[6,4,2,1,1,1] => [8,3,2,1,1] => [3,2,1,1] => [2,1,1] => 2
[6,4,1,1,1,1,1] => [6,6,2,1] => [6,2,1] => [2,1] => 1
[6,3,3,1,1,1] => [7,3,2,2,1] => [3,2,2,1] => [2,2,1] => 3
[6,3,2,2,2] => [8,2,2,2,1] => [2,2,2,1] => [2,2,1] => 3
[6,3,2,2,1,1] => [5,5,5] => [5,5] => [5] => 1
[6,3,2,1,1,1,1] => [7,3,3,1,1] => [3,3,1,1] => [3,1,1] => 4
[6,3,1,1,1,1,1,1] => [7,4,2,1,1] => [4,2,1,1] => [2,1,1] => 2
[6,2,2,2,2,1] => [6,6,1,1,1] => [6,1,1,1] => [1,1,1] => 1
[6,2,2,2,1,1,1] => [4,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 23
[6,2,2,1,1,1,1,1] => [5,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 23
[6,2,1,1,1,1,1,1,1] => [5,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 6
[6,1,1,1,1,1,1,1,1,1] => [5,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 7
[5,5,5] => [2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 90
[5,5,4,1] => [3,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 28
[5,5,2,2,1] => [10,2,2,1] => [2,2,1] => [2,1] => 1
[5,5,2,1,1,1] => [10,3,1,1] => [3,1,1] => [1,1] => 1
[5,5,1,1,1,1,1] => [10,3,2] => [3,2] => [2] => 0
[5,4,4,2] => [3,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 28
[5,4,4,1,1] => [4,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 28
[5,4,3,3] => [3,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => 54
[5,4,3,1,1,1] => [9,3,3] => [3,3] => [3] => 1
[5,4,2,2,2] => [9,2,2,2] => [2,2,2] => [2,2] => 1
[5,4,2,2,1,1] => [9,4,1,1] => [4,1,1] => [1,1] => 1
[5,4,2,1,1,1,1] => [9,4,2] => [4,2] => [2] => 0
[5,4,1,1,1,1,1,1] => [9,3,2,1] => [3,2,1] => [2,1] => 1
[5,3,3,3,1] => [4,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 45
[5,3,3,2,2] => [3,3,3,3,3] => [3,3,3,3] => [3,3,3] => 26
[5,3,3,2,1,1] => [8,5,2] => [5,2] => [2] => 0
[5,3,3,1,1,1,1] => [6,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 6
[5,3,2,2,2,1] => [4,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 36
[5,3,2,2,1,1,1] => [8,4,3] => [4,3] => [3] => 1
[5,3,2,1,1,1,1,1] => [8,3,3,1] => [3,3,1] => [3,1] => 2
[5,3,1,1,1,1,1,1,1] => [8,4,2,1] => [4,2,1] => [2,1] => 1
[5,2,2,2,2,2] => [7,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[5,2,2,2,2,1,1] => [6,6,3] => [6,3] => [3] => 1
[5,2,2,2,1,1,1,1] => [4,4,3,2,2] => [4,3,2,2] => [3,2,2] => 13
[5,2,2,1,1,1,1,1,1] => [5,3,3,2,2] => [3,3,2,2] => [3,2,2] => 13
[5,2,1,1,1,1,1,1,1,1] => [7,4,3,1] => [4,3,1] => [3,1] => 2
[5,1,1,1,1,1,1,1,1,1,1] => [5,4,3,3] => [4,3,3] => [3,3] => 3
[4,4,4,3] => [8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[4,4,4,2,1] => [5,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 9
[4,4,4,1,1,1] => [4,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 9
[4,4,3,3,1] => [8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,4,3,2,2] => [7,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 6
[4,4,3,2,1,1] => [4,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 9
[4,4,3,1,1,1,1] => [5,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 9
[4,4,2,2,2,1] => [8,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[4,4,2,2,1,1,1] => [4,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 13
[4,4,2,1,1,1,1,1] => [7,5,2,1] => [5,2,1] => [2,1] => 1
[4,4,1,1,1,1,1,1,1] => [5,5,4,1] => [5,4,1] => [4,1] => 2
[4,3,3,3,2] => [7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 4
[4,3,3,3,1,1] => [7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,3,3,2,2,1] => [7,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[4,3,3,2,1,1,1] => [8,3,2,2] => [3,2,2] => [2,2] => 1
[4,3,3,1,1,1,1,1] => [5,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 3
[4,3,2,2,2,2] => [7,6,1,1] => [6,1,1] => [1,1] => 1
[4,3,2,2,2,1,1] => [7,4,4] => [4,4] => [4] => 0
[4,3,2,2,1,1,1,1] => [4,4,4,3] => [4,4,3] => [4,3] => 8
[4,3,2,1,1,1,1,1,1] => [7,4,2,2] => [4,2,2] => [2,2] => 1
[4,3,1,1,1,1,1,1,1,1] => [6,4,4,1] => [4,4,1] => [4,1] => 2
[4,2,2,2,2,2,1] => [7,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[4,2,2,2,2,1,1,1] => [7,5,3] => [5,3] => [3] => 1
[4,2,2,2,1,1,1,1,1] => [6,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 3
[4,2,2,1,1,1,1,1,1,1] => [5,4,2,2,2] => [4,2,2,2] => [2,2,2] => 3
[4,2,1,1,1,1,1,1,1,1,1] => [5,4,4,1,1] => [4,4,1,1] => [4,1,1] => 6
[4,1,1,1,1,1,1,1,1,1,1,1] => [5,4,4,2] => [4,4,2] => [4,2] => 5
[3,3,3,3,1,1,1] => [7,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 3
[3,3,3,2,2,2] => [3,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 107
[3,3,3,2,2,1,1] => [7,6,2] => [6,2] => [2] => 0
[3,3,3,2,1,1,1,1] => [7,3,3,2] => [3,3,2] => [3,2] => 3
[3,3,3,1,1,1,1,1,1] => [6,5,2,1,1] => [5,2,1,1] => [2,1,1] => 2
[3,3,2,2,2,2,1] => [4,3,3,3,2] => [3,3,3,2] => [3,3,2] => 26
[3,3,2,2,2,1,1,1] => [6,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 7
[3,3,2,2,1,1,1,1,1] => [6,3,3,3] => [3,3,3] => [3,3] => 3
[3,3,2,1,1,1,1,1,1,1] => [6,5,2,2] => [5,2,2] => [2,2] => 1
[3,3,1,1,1,1,1,1,1,1,1] => [6,5,3,1] => [5,3,1] => [3,1] => 2
[3,2,2,2,2,2,2] => [6,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 9
[3,2,2,2,2,2,1,1] => [6,3,2,2,2] => [3,2,2,2] => [2,2,2] => 3
[3,2,2,2,2,1,1,1,1] => [4,4,3,3,1] => [4,3,3,1] => [3,3,1] => 13
[3,2,2,2,1,1,1,1,1,1] => [4,4,4,2,1] => [4,4,2,1] => [4,2,1] => 21
[3,2,2,1,1,1,1,1,1,1,1] => [5,5,2,2,1] => [5,2,2,1] => [2,2,1] => 3
[3,2,1,1,1,1,1,1,1,1,1,1] => [5,5,3,1,1] => [5,3,1,1] => [3,1,1] => 4
[3,1,1,1,1,1,1,1,1,1,1,1,1] => [5,5,3,2] => [5,3,2] => [3,2] => 3
[2,2,2,2,2,2,2,1] => [6,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[2,2,2,2,2,2,1,1,1] => [6,5,4] => [5,4] => [4] => 0
[2,2,2,2,2,1,1,1,1,1] => [5,3,3,3,1] => [3,3,3,1] => [3,3,1] => 13
[2,2,2,2,1,1,1,1,1,1,1] => [6,3,3,2,1] => [3,3,2,1] => [3,2,1] => 10
[2,2,2,1,1,1,1,1,1,1,1,1] => [6,4,2,2,1] => [4,2,2,1] => [2,2,1] => 3
[2,2,1,1,1,1,1,1,1,1,1,1,1] => [6,4,3,1,1] => [4,3,1,1] => [3,1,1] => 4
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [6,4,3,2] => [4,3,2] => [3,2] => 3
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [5,4,3,2,1] => [4,3,2,1] => [3,2,1] => 10
[14,2] => [2,2,1,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
[14,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
[13,3] => [2,2,2,1,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 10
[13,2,1] => [4,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[13,1,1,1] => [3,2,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[12,4] => [2,2,2,2,1,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 45
[12,3,1] => [3,2,2,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 9
[12,2,2] => [5,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[12,2,1,1] => [3,3,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[12,1,1,1,1] => [4,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[11,5] => [2,2,2,2,2,1,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 119
[11,4,1] => [3,2,2,2,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 36
[11,3,2] => [6,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[11,3,1,1] => [5,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[11,2,2,1] => [3,3,2,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 8
[11,2,1,1,1] => [4,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 8
[11,1,1,1,1,1] => [4,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[10,6] => [2,2,2,2,2,2,1,1,1,1] => [2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 200
[10,5,1] => [3,2,2,2,2,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 83
[10,4,2] => [3,3,2,2,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 28
[10,4,1,1] => [4,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 28
[10,3,3] => [7,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[10,3,2,1] => [6,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[10,3,1,1,1] => [4,4,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[10,2,2,2] => [3,3,3,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 29
[10,2,2,1,1] => [5,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 7
[10,2,1,1,1,1] => [5,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[10,1,1,1,1,1,1] => [4,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 7
[9,7] => [2,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 207
[9,6,1] => [3,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 117
[9,5,2] => [3,3,2,2,2,1,1,1,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 55
[9,5,1,1] => [4,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 55
[9,4,3] => [8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[9,4,2,1] => [6,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 6
[9,4,1,1,1] => [4,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[9,3,3,1] => [7,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[9,3,2,2] => [3,3,3,2,1,1,1,1,1] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 118
[9,3,2,1,1] => [6,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[9,3,1,1,1,1] => [4,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 22
[9,2,2,2,1] => [5,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[9,2,2,1,1,1] => [5,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[9,2,1,1,1,1,1] => [4,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 6
[9,1,1,1,1,1,1,1] => [5,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 6
[8,6,2] => [3,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => 62
[8,6,1,1] => [4,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 62
[8,5,3] => [3,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => 217
[8,5,2,1] => [5,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 34
[8,5,1,1,1] => [4,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => 34
[8,4,4] => [10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[8,4,3,1] => [9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[8,4,2,2] => [7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 5
[8,4,2,1,1] => [5,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[8,4,1,1,1,1] => [6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 5
[8,3,3,2] => [3,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => 155
[8,3,3,1,1] => [7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[8,3,2,2,1] => [4,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => 75
[8,3,2,1,1,1] => [4,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[8,3,1,1,1,1,1] => [5,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[8,2,2,2,2] => [6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[8,2,2,2,1,1] => [6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[8,2,2,1,1,1,1] => [4,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 16
[8,2,1,1,1,1,1,1] => [5,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 16
[8,1,1,1,1,1,1,1,1] => [5,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 5
[7,6,3] => [13,1,1,1] => [1,1,1] => [1,1] => 1
[7,5,4] => [11,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[7,5,3,1] => [4,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 108
[7,5,2,2] => [8,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 6
[7,5,2,1,1] => [4,4,2,2,2,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => 19
[7,5,1,1,1,1] => [5,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 19
[7,4,4,1] => [10,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[7,4,3,2] => [9,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 3
[7,4,3,1,1] => [9,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[7,4,2,2,1] => [8,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[7,4,2,1,1,1] => [8,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 3
[7,4,1,1,1,1,1] => [5,5,2,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => 4
[7,3,3,3] => [3,3,3,3,2,1,1] => [3,3,3,2,1,1] => [3,3,2,1,1] => 295
[7,3,3,2,1] => [4,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => 80
[7,3,3,1,1,1] => [6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 10
[7,3,2,2,2] => [6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 19
[7,3,2,2,1,1] => [4,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 24
[7,3,2,1,1,1,1] => [6,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 11
[7,3,1,1,1,1,1,1] => [6,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 4
[7,2,2,2,2,1] => [6,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[7,2,2,2,1,1,1] => [4,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 44
[7,2,2,1,1,1,1,1] => [5,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 44
[7,2,1,1,1,1,1,1,1] => [5,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 10
[7,1,1,1,1,1,1,1,1,1] => [5,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 11
[6,6,4] => [12,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[6,6,3,1] => [12,2,1,1] => [2,1,1] => [1,1] => 1
[6,6,2,1,1] => [12,2,2] => [2,2] => [2] => 0
[6,5,5] => [2,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => 90
[6,5,4,1] => [11,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[6,5,2,2,1] => [11,2,2,1] => [2,2,1] => [2,1] => 1
[6,5,2,1,1,1] => [11,3,1,1] => [3,1,1] => [1,1] => 1
[6,5,1,1,1,1,1] => [11,3,2] => [3,2] => [2] => 0
[6,4,4,2] => [10,2,2,1,1] => [2,2,1,1] => [2,1,1] => 2
[6,4,4,1,1] => [10,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[6,4,3,2,1] => [9,5,1,1] => [5,1,1] => [1,1] => 1
[6,4,3,1,1,1] => [9,3,2,1,1] => [3,2,1,1] => [2,1,1] => 2
[6,4,2,2,2] => [7,7,1,1] => [7,1,1] => [1,1] => 1
[6,4,2,2,1,1] => [8,4,4] => [4,4] => [4] => 0
[6,4,2,1,1,1,1] => [8,5,2,1] => [5,2,1] => [2,1] => 1
[6,4,1,1,1,1,1,1] => [5,5,5,1] => [5,5,1] => [5,1] => 3
[6,3,3,2,2] => [9,2,2,2,1] => [2,2,2,1] => [2,2,1] => 3
[6,3,3,2,1,1] => [7,7,2] => [7,2] => [2] => 0
[6,3,3,1,1,1,1] => [6,6,2,1,1] => [6,2,1,1] => [2,1,1] => 2
[6,3,2,2,2,1] => [8,3,2,2,1] => [3,2,2,1] => [2,2,1] => 3
[6,3,2,2,1,1,1] => [8,3,3,1,1] => [3,3,1,1] => [3,1,1] => 4
[6,3,2,1,1,1,1,1] => [6,6,2,2] => [6,2,2] => [2,2] => 1
[6,3,1,1,1,1,1,1,1] => [6,6,3,1] => [6,3,1] => [3,1] => 2
[6,2,2,2,2,2] => [8,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[6,2,2,2,2,1,1] => [6,5,5] => [5,5] => [5] => 1
[6,2,2,2,1,1,1,1] => [7,3,3,2,1] => [3,3,2,1] => [3,2,1] => 10
[6,2,2,1,1,1,1,1,1] => [7,4,2,2,1] => [4,2,2,1] => [2,2,1] => 3
[6,2,1,1,1,1,1,1,1,1] => [7,4,3,1,1] => [4,3,1,1] => [3,1,1] => 4
[6,1,1,1,1,1,1,1,1,1,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 23
[5,5,5,1] => [3,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 90
[5,5,4,2] => [3,3,2,2,2,2,2] => [3,2,2,2,2,2] => [2,2,2,2,2] => 28
[5,5,4,1,1] => [4,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 28
[5,5,3,1,1,1] => [10,3,3] => [3,3] => [3] => 1
[5,5,2,2,2] => [10,2,2,2] => [2,2,2] => [2,2] => 1
[5,5,2,2,1,1] => [10,4,1,1] => [4,1,1] => [1,1] => 1
[5,5,2,1,1,1,1] => [10,4,2] => [4,2] => [2] => 0
[5,5,1,1,1,1,1,1] => [10,3,2,1] => [3,2,1] => [2,1] => 1
[5,4,4,3] => [3,3,3,2,2,2,1] => [3,3,2,2,2,1] => [3,2,2,2,1] => 190
[5,4,4,2,1] => [5,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 28
[5,4,4,1,1,1] => [4,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 28
[5,4,3,3,1] => [4,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => 54
[5,4,3,2,2] => [7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 10
[5,4,3,2,1,1] => [9,5,2] => [5,2] => [2] => 0
[5,4,3,1,1,1,1] => [9,3,2,2] => [3,2,2] => [2,2] => 1
[5,4,2,2,2,1] => [9,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[5,4,2,2,1,1,1] => [9,4,3] => [4,3] => [3] => 1
[5,4,2,1,1,1,1,1] => [9,3,3,1] => [3,3,1] => [3,1] => 2
[5,4,1,1,1,1,1,1,1] => [9,4,2,1] => [4,2,1] => [2,1] => 1
[5,3,3,3,2] => [3,3,3,3,2,2] => [3,3,3,2,2] => [3,3,2,2] => 161
[5,3,3,3,1,1] => [7,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 6
[5,3,3,2,2,1] => [4,3,3,3,3] => [3,3,3,3] => [3,3,3] => 26
[5,3,3,2,1,1,1] => [7,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 7
[5,3,3,1,1,1,1,1] => [7,5,2,1,1] => [5,2,1,1] => [2,1,1] => 2
[5,3,2,2,2,2] => [6,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 9
[5,3,2,2,2,1,1] => [7,3,2,2,2] => [3,2,2,2] => [2,2,2] => 3
[5,3,2,2,1,1,1,1] => [4,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => 57
[5,3,2,1,1,1,1,1,1] => [5,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => 6
[5,3,1,1,1,1,1,1,1,1] => [8,4,3,1] => [4,3,1] => [3,1] => 2
[5,2,2,2,2,2,1] => [4,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => 36
[5,2,2,2,2,1,1,1] => [8,3,3,2] => [3,3,2] => [3,2] => 3
[5,2,2,2,1,1,1,1,1] => [6,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 23
[5,2,2,1,1,1,1,1,1,1] => [5,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => 7
[5,2,1,1,1,1,1,1,1,1,1] => [7,4,3,2] => [4,3,2] => [3,2] => 3
[5,1,1,1,1,1,1,1,1,1,1,1] => [5,4,3,2,2] => [4,3,2,2] => [3,2,2] => 13
[4,4,4,4] => [9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[4,4,4,3,1] => [8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[4,4,4,2,2] => [8,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[4,4,4,2,1,1] => [4,4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => 9
[4,4,4,1,1,1,1] => [5,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 9
[4,4,3,3,2] => [8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 4
[4,4,3,3,1,1] => [8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,4,3,2,2,1] => [4,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 45
[4,4,3,2,1,1,1] => [5,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 45
[4,4,3,1,1,1,1,1] => [5,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 9
[4,4,2,2,2,2] => [7,6,1,1,1] => [6,1,1,1] => [1,1,1] => 1
[4,4,2,2,2,1,1] => [7,6,3] => [6,3] => [3] => 1
[4,4,2,2,1,1,1,1] => [8,4,2,1,1] => [4,2,1,1] => [2,1,1] => 2
[4,4,2,1,1,1,1,1,1] => [5,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 13
[4,4,1,1,1,1,1,1,1,1] => [5,4,4,3] => [4,4,3] => [4,3] => 8
[4,3,3,3,2,1] => [7,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,3,3,3,1,1,1] => [7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 4
[4,3,3,2,2,2] => [8,6,1,1] => [6,1,1] => [1,1] => 1
[4,3,3,2,2,1,1] => [8,5,3] => [5,3] => [3] => 1
[4,3,3,2,1,1,1,1] => [5,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 36
[4,3,3,1,1,1,1,1,1] => [8,4,2,2] => [4,2,2] => [2,2] => 1
[4,3,2,2,2,2,1] => [4,4,4,4] => [4,4,4] => [4,4] => 8
[4,3,2,2,2,1,1,1] => [4,4,3,3,2] => [4,3,3,2] => [3,3,2] => 26
[4,3,2,2,1,1,1,1,1] => [7,4,4,1] => [4,4,1] => [4,1] => 2
[4,3,2,1,1,1,1,1,1,1] => [7,5,3,1] => [5,3,1] => [3,1] => 2
[4,3,1,1,1,1,1,1,1,1,1] => [5,5,3,3] => [5,3,3] => [3,3] => 3
[4,2,2,2,2,2,2] => [6,6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => 1
[4,2,2,2,2,2,1,1] => [6,6,4] => [6,4] => [4] => 0
[4,2,2,2,2,1,1,1,1] => [5,3,3,3,2] => [3,3,3,2] => [3,3,2] => 26
[4,2,2,2,1,1,1,1,1,1] => [6,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 6
[4,2,2,1,1,1,1,1,1,1,1] => [6,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 7
[4,2,1,1,1,1,1,1,1,1,1,1] => [6,4,3,3] => [4,3,3] => [3,3] => 3
[4,1,1,1,1,1,1,1,1,1,1,1,1] => [5,4,3,3,1] => [4,3,3,1] => [3,3,1] => 13
[3,3,3,3,2,2] => [3,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => 133
[3,3,3,3,2,1,1] => [8,6,2] => [6,2] => [2] => 0
[3,3,3,3,1,1,1,1] => [7,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 3
[3,3,3,2,2,2,1] => [4,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 107
[3,3,3,2,2,1,1,1] => [7,6,2,1] => [6,2,1] => [2,1] => 1
[3,3,3,2,1,1,1,1,1] => [7,5,2,2] => [5,2,2] => [2,2] => 1
[3,3,3,1,1,1,1,1,1,1] => [6,5,4,1] => [5,4,1] => [4,1] => 2
[3,3,2,2,2,2,2] => [7,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 9
[3,3,2,2,2,2,1,1] => [7,3,3,3] => [3,3,3] => [3,3] => 3
[3,3,2,2,2,1,1,1,1] => [4,4,4,2,2] => [4,4,2,2] => [4,2,2] => 34
[3,3,2,2,1,1,1,1,1,1] => [5,5,2,2,2] => [5,2,2,2] => [2,2,2] => 3
[3,3,2,1,1,1,1,1,1,1,1] => [5,5,4,1,1] => [5,4,1,1] => [4,1,1] => 6
[3,3,1,1,1,1,1,1,1,1,1,1] => [5,5,4,2] => [5,4,2] => [4,2] => 5
[3,2,2,2,2,2,2,1] => [6,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 9
[3,2,2,2,2,2,1,1,1] => [6,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 3
[3,2,2,2,2,1,1,1,1,1] => [6,3,3,2,2] => [3,3,2,2] => [3,2,2] => 13
[3,2,2,2,1,1,1,1,1,1,1] => [6,4,2,2,2] => [4,2,2,2] => [2,2,2] => 3
[3,2,2,1,1,1,1,1,1,1,1,1] => [6,4,4,1,1] => [4,4,1,1] => [4,1,1] => 6
[3,2,1,1,1,1,1,1,1,1,1,1,1] => [6,4,4,2] => [4,4,2] => [4,2] => 5
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => [5,4,4,2,1] => [4,4,2,1] => [4,2,1] => 21
[2,2,2,2,2,2,2,2] => [7,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[2,2,2,2,2,2,2,1,1] => [7,5,4] => [5,4] => [4] => 0
[2,2,2,2,2,2,1,1,1,1] => [4,4,4,3,1] => [4,4,3,1] => [4,3,1] => 42
[2,2,2,2,2,1,1,1,1,1,1] => [6,3,3,3,1] => [3,3,3,1] => [3,3,1] => 13
[2,2,2,2,1,1,1,1,1,1,1,1] => [6,5,2,2,1] => [5,2,2,1] => [2,2,1] => 3
[2,2,2,1,1,1,1,1,1,1,1,1,1] => [6,5,3,1,1] => [5,3,1,1] => [3,1,1] => 4
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => [6,5,3,2] => [5,3,2] => [3,2] => 3
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [5,5,3,2,1] => [5,3,2,1] => [3,2,1] => 10
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [6,4,3,2,1] => [4,3,2,1] => [3,2,1] => 10
[14,2,1] => [4,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
[14,1,1,1] => [3,2,1,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => 1
[13,3,1] => [3,2,2,1,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 10
[13,2,2] => [5,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[13,2,1,1] => [3,3,1,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[13,1,1,1,1] => [4,2,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[12,4,1] => [3,2,2,2,1,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 45
[12,3,2] => [6,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[12,3,1,1] => [5,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[12,2,2,1] => [3,3,2,1,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 9
[12,2,1,1,1] => [4,2,2,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 9
[12,1,1,1,1,1] => [4,3,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[11,5,1] => [3,2,2,2,2,1,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 119
[11,4,2] => [3,3,2,2,1,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 36
[11,4,1,1] => [4,2,2,2,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 36
[11,3,3] => [7,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[11,3,2,1] => [6,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[11,3,1,1,1] => [4,4,1,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[11,2,2,2] => [3,3,3,1,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => 37
[11,2,2,1,1] => [5,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 8
[11,2,1,1,1,1] => [5,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[11,1,1,1,1,1,1] => [4,3,2,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 8
[10,6,1] => [3,2,2,2,2,2,1,1,1,1] => [2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 200
[10,5,2] => [3,3,2,2,2,1,1,1,1,1] => [3,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 83
[10,5,1,1] => [4,2,2,2,2,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 83
[10,4,3] => [8,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[10,4,2,1] => [6,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 7
[10,4,1,1,1] => [4,3,2,2,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 28
[10,3,3,1] => [7,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[10,3,2,2] => [3,3,3,2,1,1,1,1,1,1] => [3,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => 175
[10,3,2,1,1] => [6,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[10,3,1,1,1,1] => [4,3,3,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 29
[10,2,2,2,1] => [5,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 28
[10,2,2,1,1,1] => [5,4,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[10,2,1,1,1,1,1] => [4,4,2,1,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 7
[10,1,1,1,1,1,1,1] => [5,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 7
[9,7,1] => [3,2,2,2,2,2,2,1,1] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 207
[9,6,2] => [3,3,2,2,2,2,1,1,1] => [3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 117
[9,6,1,1] => [4,2,2,2,2,2,1,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 117
[9,5,3] => [3,3,3,2,2,1,1,1,1] => [3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => 390
[9,5,2,1] => [5,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 55
[9,5,1,1,1] => [4,3,2,2,2,1,1,1,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 55
[9,4,4] => [10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[9,4,3,1] => [8,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[9,4,2,2] => [7,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 6
[9,4,2,1,1] => [5,5,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[9,4,1,1,1,1] => [6,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 6
[9,3,3,2] => [3,3,3,3,1,1,1,1,1] => [3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => 273
[9,3,3,1,1] => [7,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[9,3,2,2,1] => [4,3,3,2,1,1,1,1,1] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 118
[9,3,2,1,1,1] => [4,4,2,2,1,1,1,1,1] => [4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[9,3,1,1,1,1,1] => [5,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[9,2,2,2,2] => [6,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 21
[9,2,2,2,1,1] => [6,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[9,2,2,1,1,1,1] => [4,4,3,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 22
[9,2,1,1,1,1,1,1] => [5,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 22
[9,1,1,1,1,1,1,1,1] => [5,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 6
[8,6,3] => [3,3,3,2,2,2,1,1] => [3,3,2,2,2,1,1] => [3,2,2,2,1,1] => 469
[8,6,2,1] => [5,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 62
[8,6,1,1,1] => [4,3,2,2,2,2,1,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => 62
[8,5,4] => [11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
[8,5,3,1] => [4,3,3,2,2,1,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => 217
[8,5,2,2] => [7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[8,5,2,1,1] => [4,4,2,2,2,1,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => 34
[8,5,1,1,1,1] => [5,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => 34
[8,4,4,1] => [10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 1
[8,4,3,2] => [9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 4
[8,4,3,1,1] => [9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 1
[8,4,2,2,1] => [7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[8,4,2,1,1,1] => [7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 5
[8,4,1,1,1,1,1] => [5,5,2,1,1,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => 5
[8,3,3,3] => [3,3,3,3,2,1,1,1] => [3,3,3,2,1,1,1] => [3,3,2,1,1,1] => 667
[8,3,3,2,1] => [4,3,3,3,1,1,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => 155
[8,3,3,1,1,1] => [6,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[8,3,2,2,2] => [6,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 34
[8,3,2,2,1,1] => [4,4,4,1,1,1,1,1] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => 40
[8,3,2,1,1,1,1] => [6,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 16
[8,3,1,1,1,1,1,1] => [6,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 5
[8,2,2,2,2,1] => [6,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[8,2,2,2,1,1,1] => [4,4,3,2,1,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => 75
[8,2,2,1,1,1,1,1] => [5,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => 75
[8,2,1,1,1,1,1,1,1] => [5,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 15
[8,1,1,1,1,1,1,1,1,1] => [5,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 16
[7,7,3] => [14,1,1,1] => [1,1,1] => [1,1] => 1
[7,6,4] => [13,1,1,1,1] => [1,1,1,1] => [1,1,1] => 1
[7,6,3,1] => [13,2,1,1] => [2,1,1] => [1,1] => 1
[7,6,2,1,1] => [13,2,2] => [2,2] => [2] => 0
[7,5,5] => [12,1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[7,5,4,1] => [11,2,1,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[7,5,3,2] => [9,2,2,2,1,1] => [2,2,2,1,1] => [2,2,1,1] => 6
[7,5,3,1,1] => [8,3,2,2,1,1] => [3,2,2,1,1] => [2,2,1,1] => 6
[7,5,2,2,1] => [4,4,3,2,2,1,1] => [4,3,2,2,1,1] => [3,2,2,1,1] => 108
[7,5,2,1,1,1] => [5,3,3,2,2,1,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 108
[7,5,1,1,1,1,1] => [5,4,2,2,2,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => 19
[7,4,4,2] => [10,2,2,1,1,1] => [2,2,1,1,1] => [2,1,1,1] => 3
[7,4,4,1,1] => [10,3,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[7,4,3,2,1] => [9,4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[7,4,3,1,1,1] => [9,3,2,1,1,1] => [3,2,1,1,1] => [2,1,1,1] => 3
[7,4,2,2,2] => [7,7,1,1,1] => [7,1,1,1] => [1,1,1] => 1
[7,4,2,2,1,1] => [4,4,3,3,1,1,1] => [4,3,3,1,1,1] => [3,3,1,1,1] => 80
[7,4,2,1,1,1,1] => [8,4,2,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 3
[7,4,1,1,1,1,1,1] => [5,4,4,1,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 24
[7,3,3,3,1] => [4,3,3,3,2,1,1] => [3,3,3,2,1,1] => [3,3,2,1,1] => 295
[7,3,3,2,2] => [8,2,2,2,2,1] => [2,2,2,2,1] => [2,2,2,1] => 9
[7,3,3,2,1,1] => [8,3,3,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 7
[7,3,3,1,1,1,1] => [6,5,2,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => 4
[7,3,2,2,2,1] => [6,3,2,2,2,1,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 19
[7,3,2,2,1,1,1] => [5,3,3,3,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => 80
[7,3,2,1,1,1,1,1] => [5,5,2,2,1,1,1] => [5,2,2,1,1,1] => [2,2,1,1,1] => 10
[7,3,1,1,1,1,1,1,1] => [5,5,3,1,1,1,1] => [5,3,1,1,1,1] => [3,1,1,1,1] => 11
[7,2,2,2,2,2] => [8,5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[7,2,2,2,2,1,1] => [4,4,4,2,1,1,1] => [4,4,2,1,1,1] => [4,2,1,1,1] => 125
[7,2,2,2,1,1,1,1] => [6,3,3,2,1,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 44
[7,2,2,1,1,1,1,1,1] => [6,4,2,2,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 10
[7,2,1,1,1,1,1,1,1,1] => [6,4,3,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 11
[7,1,1,1,1,1,1,1,1,1,1] => [5,4,3,2,1,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 44
[6,6,4,1] => [12,2,1,1,1] => [2,1,1,1] => [1,1,1] => 1
[6,6,2,2,1] => [12,2,2,1] => [2,2,1] => [2,1] => 1
[6,6,2,1,1,1] => [12,3,1,1] => [3,1,1] => [1,1] => 1
[6,6,1,1,1,1,1] => [12,3,2] => [3,2] => [2] => 0
[6,5,5,1] => [3,2,2,2,2,2,2,2] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => 90
[6,5,4,2] => [11,2,2,1,1] => [2,2,1,1] => [2,1,1] => 2
[6,5,4,1,1] => [11,3,1,1,1] => [3,1,1,1] => [1,1,1] => 1
[6,5,3,1,1,1] => [11,3,3] => [3,3] => [3] => 1
[6,5,2,2,2] => [11,2,2,2] => [2,2,2] => [2,2] => 1
[6,5,2,2,1,1] => [11,4,1,1] => [4,1,1] => [1,1] => 1
[6,5,2,1,1,1,1] => [11,4,2] => [4,2] => [2] => 0
[6,5,1,1,1,1,1,1] => [11,3,2,1] => [3,2,1] => [2,1] => 1
[6,4,4,3] => [3,3,3,3,2,2,1] => [3,3,3,2,2,1] => [3,3,2,2,1] => 646
[6,4,4,2,1] => [10,5,1,1] => [5,1,1] => [1,1] => 1
[6,4,4,1,1,1] => [10,3,2,1,1] => [3,2,1,1] => [2,1,1] => 2
[6,4,3,2,2] => [9,6,1,1] => [6,1,1] => [1,1] => 1
[6,4,3,2,1,1] => [9,4,4] => [4,4] => [4] => 0
[6,4,3,1,1,1,1] => [9,5,2,1] => [5,2,1] => [2,1] => 1
[6,4,2,2,2,1] => [9,5,1,1,1] => [5,1,1,1] => [1,1,1] => 1
[6,4,2,2,1,1,1] => [4,4,3,3,3] => [4,3,3,3] => [3,3,3] => 26
[6,4,2,1,1,1,1,1] => [8,4,4,1] => [4,4,1] => [4,1] => 2
[6,4,1,1,1,1,1,1,1] => [8,5,3,1] => [5,3,1] => [3,1] => 2
[6,3,3,3,2] => [10,2,2,2,1] => [2,2,2,1] => [2,2,1] => 3
[6,3,3,3,1,1] => [9,6,2] => [6,2] => [2] => 0
[6,3,3,2,2,1] => [9,3,2,2,1] => [3,2,2,1] => [2,2,1] => 3
[6,3,3,2,1,1,1] => [7,7,2,1] => [7,2,1] => [2,1] => 1
[6,3,3,1,1,1,1,1] => [6,5,5,1] => [5,5,1] => [5,1] => 3
[6,3,2,2,2,2] => [6,6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => 1
[6,3,2,2,2,1,1] => [8,5,2,1,1] => [5,2,1,1] => [2,1,1] => 2
[6,3,2,2,1,1,1,1] => [8,5,2,2] => [5,2,2] => [2,2] => 1
[6,3,2,1,1,1,1,1,1] => [5,5,5,1,1] => [5,5,1,1] => [5,1,1] => 9
[6,3,1,1,1,1,1,1,1,1] => [5,5,5,2] => [5,5,2] => [5,2] => 8
[6,2,2,2,2,2,1] => [8,5,4] => [5,4] => [4] => 0
[6,2,2,2,2,1,1,1] => [8,3,3,2,1] => [3,3,2,1] => [3,2,1] => 10
[6,2,2,2,1,1,1,1,1] => [6,6,2,2,1] => [6,2,2,1] => [2,2,1] => 3
[6,2,2,1,1,1,1,1,1,1] => [6,6,3,1,1] => [6,3,1,1] => [3,1,1] => 4
[6,2,1,1,1,1,1,1,1,1,1] => [6,6,3,2] => [6,3,2] => [3,2] => 3
[6,1,1,1,1,1,1,1,1,1,1,1] => [7,4,3,2,1] => [4,3,2,1] => [3,2,1] => 10
[5,5,5,2] => [3,3,2,2,2,2,2,1] => [3,2,2,2,2,2,1] => [2,2,2,2,2,1] => 90
[5,5,5,1,1] => [4,2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 90
[5,5,4,3] => [3,3,3,2,2,2,2] => [3,3,2,2,2,2] => [3,2,2,2,2] => 218
[5,5,4,2,1] => [5,2,2,2,2,2,2] => [2,2,2,2,2,2] => [2,2,2,2,2] => 28
[5,5,4,1,1,1] => [4,3,2,2,2,2,2] => [3,2,2,2,2,2] => [2,2,2,2,2] => 28
[5,5,3,2,2] => [8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 10
[5,5,3,2,1,1] => [10,5,2] => [5,2] => [2] => 0
[5,5,3,1,1,1,1] => [10,3,2,2] => [3,2,2] => [2,2] => 1
[5,5,2,2,2,1] => [10,4,1,1,1] => [4,1,1,1] => [1,1,1] => 1
[5,5,2,2,1,1,1] => [10,4,3] => [4,3] => [3] => 1
[5,5,2,1,1,1,1,1] => [10,3,3,1] => [3,3,1] => [3,1] => 2
[5,5,1,1,1,1,1,1,1] => [10,4,2,1] => [4,2,1] => [2,1] => 1
[5,4,4,4] => [9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[5,4,4,3,1] => [4,3,3,2,2,2,1] => [3,3,2,2,2,1] => [3,2,2,2,1] => 190
[5,4,4,2,2] => [6,2,2,2,2,2,1] => [2,2,2,2,2,1] => [2,2,2,2,1] => 28
[5,4,4,2,1,1] => [4,4,2,2,2,2,1] => [4,2,2,2,2,1] => [2,2,2,2,1] => 28
[5,4,4,1,1,1,1] => [5,3,2,2,2,2,1] => [3,2,2,2,2,1] => [2,2,2,2,1] => 28
[5,4,3,3,2] => [9,2,2,2,2] => [2,2,2,2] => [2,2,2] => 3
[5,4,3,3,1,1] => [8,3,2,2,2] => [3,2,2,2] => [2,2,2] => 3
[5,4,3,2,2,1] => [7,3,2,2,1,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 10
[5,4,3,2,1,1,1] => [9,3,3,1,1] => [3,3,1,1] => [3,1,1] => 4
[5,4,3,1,1,1,1,1] => [9,4,2,1,1] => [4,2,1,1] => [2,1,1] => 2
[5,4,2,2,2,2] => [8,6,1,1,1] => [6,1,1,1] => [1,1,1] => 1
[5,4,2,2,2,1,1] => [9,5,3] => [5,3] => [3] => 1
[5,4,2,2,1,1,1,1] => [9,3,3,2] => [3,3,2] => [3,2] => 3
[5,4,2,1,1,1,1,1,1] => [9,4,2,2] => [4,2,2] => [2,2] => 1
[5,4,1,1,1,1,1,1,1,1] => [9,4,3,1] => [4,3,1] => [3,1] => 2
[5,3,3,3,3] => [3,3,3,3,3,1,1] => [3,3,3,3,1,1] => [3,3,3,1,1] => 428
[5,3,3,3,2,1] => [4,3,3,3,2,2] => [3,3,3,2,2] => [3,3,2,2] => 161
[5,3,3,3,1,1,1] => [7,6,2,1,1] => [6,2,1,1] => [2,1,1] => 2
[5,3,3,2,2,2] => [7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 19
[5,3,3,2,2,1,1] => [8,3,3,3] => [3,3,3] => [3,3] => 3
[5,3,3,2,1,1,1,1] => [7,6,2,2] => [6,2,2] => [2,2] => 1
[5,3,3,1,1,1,1,1,1] => [6,6,4,1] => [6,4,1] => [4,1] => 2
[5,3,2,2,2,2,1] => [6,3,2,2,2,2] => [3,2,2,2,2] => [2,2,2,2] => 9
[5,3,2,2,2,1,1,1] => [7,3,3,2,2] => [3,3,2,2] => [3,2,2] => 13
[5,3,2,2,1,1,1,1,1] => [8,4,2,2,1] => [4,2,2,1] => [2,2,1] => 3
[5,3,2,1,1,1,1,1,1,1] => [7,4,4,1,1] => [4,4,1,1] => [4,1,1] => 6
[5,3,1,1,1,1,1,1,1,1,1] => [5,4,4,2,1,1] => [4,4,2,1,1] => [4,2,1,1] => 57
[5,2,2,2,2,2,2] => [6,6,5] => [6,5] => [5] => 1
[5,2,2,2,2,2,1,1] => [4,4,4,4,1] => [4,4,4,1] => [4,4,1] => 50
[5,2,2,2,2,1,1,1,1] => [7,3,3,3,1] => [3,3,3,1] => [3,3,1] => 13
[5,2,2,2,1,1,1,1,1,1] => [7,5,2,2,1] => [5,2,2,1] => [2,2,1] => 3
[5,2,2,1,1,1,1,1,1,1,1] => [8,4,3,2] => [4,3,2] => [3,2] => 3
[5,2,1,1,1,1,1,1,1,1,1,1] => [5,5,3,2,1,1] => [5,3,2,1,1] => [3,2,1,1] => 23
[5,1,1,1,1,1,1,1,1,1,1,1,1] => [6,4,3,2,1,1] => [4,3,2,1,1] => [3,2,1,1] => 23
[4,4,4,4,1] => [9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[4,4,4,3,2] => [8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 5
[4,4,4,3,1,1] => [8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[4,4,4,2,2,1] => [4,4,3,2,2,2] => [4,3,2,2,2] => [3,2,2,2] => 54
[4,4,4,2,1,1,1] => [5,3,3,2,2,2] => [3,3,2,2,2] => [3,2,2,2] => 54
[4,4,4,1,1,1,1,1] => [5,4,2,2,2,2] => [4,2,2,2,2] => [2,2,2,2] => 9
[4,4,3,3,2,1] => [8,4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,4,3,3,1,1,1] => [8,3,2,1,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 4
[4,4,3,2,2,2] => [7,7,3] => [7,3] => [3] => 1
[4,4,3,2,2,1,1] => [7,3,3,2,1,1] => [3,3,2,1,1] => [3,2,1,1] => 23
[4,4,3,2,1,1,1,1] => [7,4,2,2,1,1] => [4,2,2,1,1] => [2,2,1,1] => 6
[4,4,3,1,1,1,1,1,1] => [5,4,3,2,2,1] => [4,3,2,2,1] => [3,2,2,1] => 45
[4,4,2,2,2,2,1] => [4,4,3,3,2,1] => [4,3,3,2,1] => [3,3,2,1] => 107
[4,4,2,2,2,1,1,1] => [5,3,3,3,3] => [3,3,3,3] => [3,3,3] => 26
[4,4,2,2,1,1,1,1,1] => [7,6,3,1] => [6,3,1] => [3,1] => 2
[4,4,2,1,1,1,1,1,1,1] => [8,4,3,1,1] => [4,3,1,1] => [3,1,1] => 4
[4,4,1,1,1,1,1,1,1,1,1] => [5,4,3,3,2] => [4,3,3,2] => [3,3,2] => 26
[4,3,3,3,2,2] => [8,7,1,1] => [7,1,1] => [1,1] => 1
[4,3,3,3,2,1,1] => [7,3,3,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 11
[4,3,3,3,1,1,1,1] => [7,4,2,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 4
[4,3,3,2,2,2,1] => [8,6,3] => [6,3] => [3] => 1
[4,3,3,2,2,1,1,1] => [4,4,4,2,2,1] => [4,4,2,2,1] => [4,2,2,1] => 136
[4,3,3,2,1,1,1,1,1] => [7,4,3,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 7
[4,3,3,1,1,1,1,1,1,1] => [5,4,3,3,1,1] => [4,3,3,1,1] => [3,3,1,1] => 36
[4,3,2,2,2,2,2] => [7,5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 1
[4,3,2,2,2,2,1,1] => [6,6,2,1,1,1] => [6,2,1,1,1] => [2,1,1,1] => 3
[4,3,2,2,2,1,1,1,1] => [6,3,3,2,2,1] => [3,3,2,2,1] => [3,2,2,1] => 45
[4,3,2,2,1,1,1,1,1,1] => [7,4,3,3] => [4,3,3] => [3,3] => 3
[4,3,2,1,1,1,1,1,1,1,1] => [7,4,4,2] => [4,4,2] => [4,2] => 5
[4,3,1,1,1,1,1,1,1,1,1,1] => [5,4,4,2,2] => [4,4,2,2] => [4,2,2] => 34
[4,2,2,2,2,2,2,1] => [7,5,5] => [5,5] => [5] => 1
[4,2,2,2,2,2,1,1,1] => [4,4,4,3,1,1] => [4,4,3,1,1] => [4,3,1,1] => 135
[4,2,2,2,2,1,1,1,1,1] => [5,5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => 13
[4,2,2,2,1,1,1,1,1,1,1] => [7,5,3,1,1] => [5,3,1,1] => [3,1,1] => 4
[4,2,2,1,1,1,1,1,1,1,1,1] => [7,5,3,2] => [5,3,2] => [3,2] => 3
[4,2,1,1,1,1,1,1,1,1,1,1,1] => [5,5,3,2,2] => [5,3,2,2] => [3,2,2] => 13
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => [6,4,3,2,2] => [4,3,2,2] => [3,2,2] => 13
[3,3,3,3,3,2] => [3,3,3,3,3,2] => [3,3,3,3,2] => [3,3,3,2] => 294
[3,3,3,3,3,1,1] => [8,7,2] => [7,2] => [2] => 0
[3,3,3,3,2,2,1] => [4,3,3,3,3,1] => [3,3,3,3,1] => [3,3,3,1] => 133
[3,3,3,3,2,1,1,1] => [8,6,2,1] => [6,2,1] => [2,1] => 1
[3,3,3,3,1,1,1,1,1] => [7,4,2,2,2] => [4,2,2,2] => [2,2,2] => 3
[3,3,3,2,2,2,2] => [7,2,2,2,2,2] => [2,2,2,2,2] => [2,2,2,2] => 9
[3,3,3,2,2,2,1,1] => [5,3,3,3,2,1] => [3,3,3,2,1] => [3,3,2,1] => 107
[3,3,3,2,2,1,1,1,1] => [5,4,4,4] => [4,4,4] => [4,4] => 8
[3,3,3,2,1,1,1,1,1,1] => [7,5,4,1] => [5,4,1] => [4,1] => 2
[3,3,3,1,1,1,1,1,1,1,1] => [5,5,4,3] => [5,4,3] => [4,3] => 8
[3,3,2,2,2,2,2,1] => [7,3,2,2,2,1] => [3,2,2,2,1] => [2,2,2,1] => 9
[3,3,2,2,2,2,1,1,1] => [5,5,2,2,2,1] => [5,2,2,2,1] => [2,2,2,1] => 9
[3,3,2,2,2,1,1,1,1,1] => [6,4,2,2,2,1] => [4,2,2,2,1] => [2,2,2,1] => 9
[3,3,2,2,1,1,1,1,1,1,1] => [6,4,4,1,1,1] => [4,4,1,1,1] => [4,1,1,1] => 13
[3,3,2,1,1,1,1,1,1,1,1,1] => [6,4,4,3] => [4,4,3] => [4,3] => 8
[3,3,1,1,1,1,1,1,1,1,1,1,1] => [5,4,4,3,1] => [4,4,3,1] => [4,3,1] => 42
[3,2,2,2,2,2,2,2] => [7,6,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => 1
[3,2,2,2,2,2,2,1,1] => [7,5,2,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 3
[3,2,2,2,2,2,1,1,1,1] => [6,3,3,3,1,1] => [3,3,3,1,1] => [3,3,1,1] => 36
[3,2,2,2,2,1,1,1,1,1,1] => [6,5,2,2,1,1] => [5,2,2,1,1] => [2,2,1,1] => 6
[3,2,2,2,1,1,1,1,1,1,1,1] => [6,5,3,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => 7
[3,2,2,1,1,1,1,1,1,1,1,1,1] => [6,5,3,3] => [5,3,3] => [3,3] => 3
[3,2,1,1,1,1,1,1,1,1,1,1,1,1] => [5,5,3,3,1] => [5,3,3,1] => [3,3,1] => 13
[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [6,4,3,3,1] => [4,3,3,1] => [3,3,1] => 13
[2,2,2,2,2,2,2,2,1] => [7,6,4] => [6,4] => [4] => 0
[2,2,2,2,2,2,2,1,1,1] => [4,4,4,3,2] => [4,4,3,2] => [4,3,2] => 102
[2,2,2,2,2,2,1,1,1,1,1] => [6,3,3,3,2] => [3,3,3,2] => [3,3,2] => 26
[2,2,2,2,2,1,1,1,1,1,1,1] => [6,5,2,2,2] => [5,2,2,2] => [2,2,2] => 3
[2,2,2,2,1,1,1,1,1,1,1,1,1] => [6,5,4,1,1] => [5,4,1,1] => [4,1,1] => 6
[2,2,2,1,1,1,1,1,1,1,1,1,1,1] => [6,5,4,2] => [5,4,2] => [4,2] => 5
[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [5,5,4,2,1] => [5,4,2,1] => [4,2,1] => 21
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [6,4,4,2,1] => [4,4,2,1] => [4,2,1] => 21
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [6,5,3,2,1] => [5,3,2,1] => [3,2,1] => 10
[6,5,4,3,2,1] => [11,7,3] => [7,3] => [3] => 1
[2,2,2,2,2,2,2,2,2] => [7,6,5] => [6,5] => [5] => 1
[3,3,3,3,3,3] => [3,3,3,3,3,2,1] => [3,3,3,3,2,1] => [3,3,3,2,1] => 1368
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Description
The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd.
To be precise, this is given for a partition $\lambda \vdash n$ by the number of standard tableaux $T$ of shape $\lambda$ such that $\min\big( \operatorname{Des}(T) \cup \{n\} \big)$ is odd.
The case of an even minimum is St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even..
To be precise, this is given for a partition $\lambda \vdash n$ by the number of standard tableaux $T$ of shape $\lambda$ such that $\min\big( \operatorname{Des}(T) \cup \{n\} \big)$ is odd.
The case of an even minimum is St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even..
Map
Loehr-Warrington
Description
Return a partition whose diagonal inversion number is the length of the preimage.
Map
first row removal
Description
Removes the first entry of an integer partition
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