Identifier
-
Mp00040:
Integer compositions
—to partition⟶
Integer partitions
St000913: Integer partitions ⟶ ℤ
Values
[1] => [1] => 1
[1,1] => [1,1] => 1
[2] => [2] => 1
[1,1,1] => [1,1,1] => 1
[1,2] => [2,1] => 1
[2,1] => [2,1] => 1
[3] => [3] => 1
[1,1,1,1] => [1,1,1,1] => 1
[1,1,2] => [2,1,1] => 1
[1,2,1] => [2,1,1] => 1
[1,3] => [3,1] => 1
[2,1,1] => [2,1,1] => 1
[2,2] => [2,2] => 1
[3,1] => [3,1] => 1
[4] => [4] => 2
[1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,2] => [2,1,1,1] => 1
[1,1,2,1] => [2,1,1,1] => 1
[1,1,3] => [3,1,1] => 1
[1,2,1,1] => [2,1,1,1] => 1
[1,2,2] => [2,2,1] => 1
[1,3,1] => [3,1,1] => 1
[1,4] => [4,1] => 2
[2,1,1,1] => [2,1,1,1] => 1
[2,1,2] => [2,2,1] => 1
[2,2,1] => [2,2,1] => 1
[2,3] => [3,2] => 2
[3,1,1] => [3,1,1] => 1
[3,2] => [3,2] => 2
[4,1] => [4,1] => 2
[5] => [5] => 4
[1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,2] => [2,1,1,1,1] => 1
[1,1,1,2,1] => [2,1,1,1,1] => 1
[1,1,1,3] => [3,1,1,1] => 1
[1,1,2,1,1] => [2,1,1,1,1] => 1
[1,1,2,2] => [2,2,1,1] => 1
[1,1,3,1] => [3,1,1,1] => 1
[1,1,4] => [4,1,1] => 2
[1,2,1,1,1] => [2,1,1,1,1] => 1
[1,2,1,2] => [2,2,1,1] => 1
[1,2,2,1] => [2,2,1,1] => 1
[1,2,3] => [3,2,1] => 2
[1,3,1,1] => [3,1,1,1] => 1
[1,3,2] => [3,2,1] => 2
[1,4,1] => [4,1,1] => 2
[1,5] => [5,1] => 4
[2,1,1,1,1] => [2,1,1,1,1] => 1
[2,1,1,2] => [2,2,1,1] => 1
[2,1,2,1] => [2,2,1,1] => 1
[2,1,3] => [3,2,1] => 2
[2,2,1,1] => [2,2,1,1] => 1
[2,2,2] => [2,2,2] => 1
[2,3,1] => [3,2,1] => 2
[2,4] => [4,2] => 5
[3,1,1,1] => [3,1,1,1] => 1
[3,1,2] => [3,2,1] => 2
[3,2,1] => [3,2,1] => 2
[3,3] => [3,3] => 2
[4,1,1] => [4,1,1] => 2
[4,2] => [4,2] => 5
[5,1] => [5,1] => 4
[6] => [6] => 11
[1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,2] => [2,1,1,1,1,1] => 1
[1,1,1,1,2,1] => [2,1,1,1,1,1] => 1
[1,1,1,1,3] => [3,1,1,1,1] => 1
[1,1,1,2,1,1] => [2,1,1,1,1,1] => 1
[1,1,1,2,2] => [2,2,1,1,1] => 1
[1,1,1,3,1] => [3,1,1,1,1] => 1
[1,1,1,4] => [4,1,1,1] => 2
[1,1,2,1,1,1] => [2,1,1,1,1,1] => 1
[1,1,2,1,2] => [2,2,1,1,1] => 1
[1,1,2,2,1] => [2,2,1,1,1] => 1
[1,1,2,3] => [3,2,1,1] => 2
[1,1,3,1,1] => [3,1,1,1,1] => 1
[1,1,3,2] => [3,2,1,1] => 2
[1,1,4,1] => [4,1,1,1] => 2
[1,1,5] => [5,1,1] => 4
[1,2,1,1,1,1] => [2,1,1,1,1,1] => 1
[1,2,1,1,2] => [2,2,1,1,1] => 1
[1,2,1,2,1] => [2,2,1,1,1] => 1
[1,2,1,3] => [3,2,1,1] => 2
[1,2,2,1,1] => [2,2,1,1,1] => 1
[1,2,2,2] => [2,2,2,1] => 1
[1,2,3,1] => [3,2,1,1] => 2
[1,2,4] => [4,2,1] => 5
[1,3,1,1,1] => [3,1,1,1,1] => 1
[1,3,1,2] => [3,2,1,1] => 2
[1,3,2,1] => [3,2,1,1] => 2
[1,3,3] => [3,3,1] => 2
[1,4,1,1] => [4,1,1,1] => 2
[1,4,2] => [4,2,1] => 5
[1,5,1] => [5,1,1] => 4
[1,6] => [6,1] => 11
[2,1,1,1,1,1] => [2,1,1,1,1,1] => 1
[2,1,1,1,2] => [2,2,1,1,1] => 1
[2,1,1,2,1] => [2,2,1,1,1] => 1
[2,1,1,3] => [3,2,1,1] => 2
[2,1,2,1,1] => [2,2,1,1,1] => 1
[2,1,2,2] => [2,2,2,1] => 1
>>> Load all 1887 entries. <<<[2,1,3,1] => [3,2,1,1] => 2
[2,1,4] => [4,2,1] => 5
[2,2,1,1,1] => [2,2,1,1,1] => 1
[2,2,1,2] => [2,2,2,1] => 1
[2,2,2,1] => [2,2,2,1] => 1
[2,2,3] => [3,2,2] => 3
[2,3,1,1] => [3,2,1,1] => 2
[2,3,2] => [3,2,2] => 3
[2,4,1] => [4,2,1] => 5
[2,5] => [5,2] => 12
[3,1,1,1,1] => [3,1,1,1,1] => 1
[3,1,1,2] => [3,2,1,1] => 2
[3,1,2,1] => [3,2,1,1] => 2
[3,1,3] => [3,3,1] => 2
[3,2,1,1] => [3,2,1,1] => 2
[3,2,2] => [3,2,2] => 3
[3,3,1] => [3,3,1] => 2
[3,4] => [4,3] => 10
[4,1,1,1] => [4,1,1,1] => 2
[4,1,2] => [4,2,1] => 5
[4,2,1] => [4,2,1] => 5
[4,3] => [4,3] => 10
[5,1,1] => [5,1,1] => 4
[5,2] => [5,2] => 12
[6,1] => [6,1] => 11
[7] => [7] => 33
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,1,3] => [3,1,1,1,1,1] => 1
[1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,1,2,2] => [2,2,1,1,1,1] => 1
[1,1,1,1,3,1] => [3,1,1,1,1,1] => 1
[1,1,1,1,4] => [4,1,1,1,1] => 2
[1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,1,2,1,2] => [2,2,1,1,1,1] => 1
[1,1,1,2,2,1] => [2,2,1,1,1,1] => 1
[1,1,1,2,3] => [3,2,1,1,1] => 2
[1,1,1,3,1,1] => [3,1,1,1,1,1] => 1
[1,1,1,3,2] => [3,2,1,1,1] => 2
[1,1,1,4,1] => [4,1,1,1,1] => 2
[1,1,1,5] => [5,1,1,1] => 4
[1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,1,2,1,1,2] => [2,2,1,1,1,1] => 1
[1,1,2,1,2,1] => [2,2,1,1,1,1] => 1
[1,1,2,1,3] => [3,2,1,1,1] => 2
[1,1,2,2,1,1] => [2,2,1,1,1,1] => 1
[1,1,2,2,2] => [2,2,2,1,1] => 1
[1,1,2,3,1] => [3,2,1,1,1] => 2
[1,1,2,4] => [4,2,1,1] => 5
[1,1,3,1,1,1] => [3,1,1,1,1,1] => 1
[1,1,3,1,2] => [3,2,1,1,1] => 2
[1,1,3,2,1] => [3,2,1,1,1] => 2
[1,1,3,3] => [3,3,1,1] => 2
[1,1,4,1,1] => [4,1,1,1,1] => 2
[1,1,4,2] => [4,2,1,1] => 5
[1,1,5,1] => [5,1,1,1] => 4
[1,1,6] => [6,1,1] => 11
[1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[1,2,1,1,1,2] => [2,2,1,1,1,1] => 1
[1,2,1,1,2,1] => [2,2,1,1,1,1] => 1
[1,2,1,1,3] => [3,2,1,1,1] => 2
[1,2,1,2,1,1] => [2,2,1,1,1,1] => 1
[1,2,1,2,2] => [2,2,2,1,1] => 1
[1,2,1,3,1] => [3,2,1,1,1] => 2
[1,2,1,4] => [4,2,1,1] => 5
[1,2,2,1,1,1] => [2,2,1,1,1,1] => 1
[1,2,2,1,2] => [2,2,2,1,1] => 1
[1,2,2,2,1] => [2,2,2,1,1] => 1
[1,2,2,3] => [3,2,2,1] => 3
[1,2,3,1,1] => [3,2,1,1,1] => 2
[1,2,3,2] => [3,2,2,1] => 3
[1,2,4,1] => [4,2,1,1] => 5
[1,2,5] => [5,2,1] => 12
[1,3,1,1,1,1] => [3,1,1,1,1,1] => 1
[1,3,1,1,2] => [3,2,1,1,1] => 2
[1,3,1,2,1] => [3,2,1,1,1] => 2
[1,3,1,3] => [3,3,1,1] => 2
[1,3,2,1,1] => [3,2,1,1,1] => 2
[1,3,2,2] => [3,2,2,1] => 3
[1,3,3,1] => [3,3,1,1] => 2
[1,3,4] => [4,3,1] => 10
[1,4,1,1,1] => [4,1,1,1,1] => 2
[1,4,1,2] => [4,2,1,1] => 5
[1,4,2,1] => [4,2,1,1] => 5
[1,4,3] => [4,3,1] => 10
[1,5,1,1] => [5,1,1,1] => 4
[1,5,2] => [5,2,1] => 12
[1,6,1] => [6,1,1] => 11
[1,7] => [7,1] => 33
[2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 1
[2,1,1,1,1,2] => [2,2,1,1,1,1] => 1
[2,1,1,1,2,1] => [2,2,1,1,1,1] => 1
[2,1,1,1,3] => [3,2,1,1,1] => 2
[2,1,1,2,1,1] => [2,2,1,1,1,1] => 1
[2,1,1,2,2] => [2,2,2,1,1] => 1
[2,1,1,3,1] => [3,2,1,1,1] => 2
[2,1,1,4] => [4,2,1,1] => 5
[2,1,2,1,1,1] => [2,2,1,1,1,1] => 1
[2,1,2,1,2] => [2,2,2,1,1] => 1
[2,1,2,2,1] => [2,2,2,1,1] => 1
[2,1,2,3] => [3,2,2,1] => 3
[2,1,3,1,1] => [3,2,1,1,1] => 2
[2,1,3,2] => [3,2,2,1] => 3
[2,1,4,1] => [4,2,1,1] => 5
[2,1,5] => [5,2,1] => 12
[2,2,1,1,1,1] => [2,2,1,1,1,1] => 1
[2,2,1,1,2] => [2,2,2,1,1] => 1
[2,2,1,2,1] => [2,2,2,1,1] => 1
[2,2,1,3] => [3,2,2,1] => 3
[2,2,2,1,1] => [2,2,2,1,1] => 1
[2,2,2,2] => [2,2,2,2] => 1
[2,2,3,1] => [3,2,2,1] => 3
[2,2,4] => [4,2,2] => 9
[2,3,1,1,1] => [3,2,1,1,1] => 2
[2,3,1,2] => [3,2,2,1] => 3
[2,3,2,1] => [3,2,2,1] => 3
[2,3,3] => [3,3,2] => 5
[2,4,1,1] => [4,2,1,1] => 5
[2,4,2] => [4,2,2] => 9
[2,5,1] => [5,2,1] => 12
[2,6] => [6,2] => 37
[3,1,1,1,1,1] => [3,1,1,1,1,1] => 1
[3,1,1,1,2] => [3,2,1,1,1] => 2
[3,1,1,2,1] => [3,2,1,1,1] => 2
[3,1,1,3] => [3,3,1,1] => 2
[3,1,2,1,1] => [3,2,1,1,1] => 2
[3,1,2,2] => [3,2,2,1] => 3
[3,1,3,1] => [3,3,1,1] => 2
[3,1,4] => [4,3,1] => 10
[3,2,1,1,1] => [3,2,1,1,1] => 2
[3,2,1,2] => [3,2,2,1] => 3
[3,2,2,1] => [3,2,2,1] => 3
[3,2,3] => [3,3,2] => 5
[3,3,1,1] => [3,3,1,1] => 2
[3,3,2] => [3,3,2] => 5
[3,4,1] => [4,3,1] => 10
[3,5] => [5,3] => 27
[4,1,1,1,1] => [4,1,1,1,1] => 2
[4,1,1,2] => [4,2,1,1] => 5
[4,1,2,1] => [4,2,1,1] => 5
[4,1,3] => [4,3,1] => 10
[4,2,1,1] => [4,2,1,1] => 5
[4,2,2] => [4,2,2] => 9
[4,3,1] => [4,3,1] => 10
[4,4] => [4,4] => 19
[5,1,1,1] => [5,1,1,1] => 4
[5,1,2] => [5,2,1] => 12
[5,2,1] => [5,2,1] => 12
[5,3] => [5,3] => 27
[6,1,1] => [6,1,1] => 11
[6,2] => [6,2] => 37
[7,1] => [7,1] => 33
[8] => [8] => 116
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => 1
[1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => 1
[1,1,1,1,1,4] => [4,1,1,1,1,1] => 2
[1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => 1
[1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => 1
[1,1,1,1,2,3] => [3,2,1,1,1,1] => 2
[1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => 1
[1,1,1,1,3,2] => [3,2,1,1,1,1] => 2
[1,1,1,1,4,1] => [4,1,1,1,1,1] => 2
[1,1,1,1,5] => [5,1,1,1,1] => 4
[1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,2] => [2,2,1,1,1,1,1] => 1
[1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => 1
[1,1,1,2,1,3] => [3,2,1,1,1,1] => 2
[1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => 1
[1,1,1,2,2,2] => [2,2,2,1,1,1] => 1
[1,1,1,2,3,1] => [3,2,1,1,1,1] => 2
[1,1,1,2,4] => [4,2,1,1,1] => 5
[1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => 1
[1,1,1,3,1,2] => [3,2,1,1,1,1] => 2
[1,1,1,3,2,1] => [3,2,1,1,1,1] => 2
[1,1,1,3,3] => [3,3,1,1,1] => 2
[1,1,1,4,1,1] => [4,1,1,1,1,1] => 2
[1,1,1,4,2] => [4,2,1,1,1] => 5
[1,1,1,5,1] => [5,1,1,1,1] => 4
[1,1,1,6] => [6,1,1,1] => 11
[1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => 1
[1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => 1
[1,1,2,1,1,3] => [3,2,1,1,1,1] => 2
[1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => 1
[1,1,2,1,2,2] => [2,2,2,1,1,1] => 1
[1,1,2,1,3,1] => [3,2,1,1,1,1] => 2
[1,1,2,1,4] => [4,2,1,1,1] => 5
[1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => 1
[1,1,2,2,1,2] => [2,2,2,1,1,1] => 1
[1,1,2,2,2,1] => [2,2,2,1,1,1] => 1
[1,1,2,2,3] => [3,2,2,1,1] => 3
[1,1,2,3,1,1] => [3,2,1,1,1,1] => 2
[1,1,2,3,2] => [3,2,2,1,1] => 3
[1,1,2,4,1] => [4,2,1,1,1] => 5
[1,1,2,5] => [5,2,1,1] => 12
[1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => 1
[1,1,3,1,1,2] => [3,2,1,1,1,1] => 2
[1,1,3,1,2,1] => [3,2,1,1,1,1] => 2
[1,1,3,1,3] => [3,3,1,1,1] => 2
[1,1,3,2,1,1] => [3,2,1,1,1,1] => 2
[1,1,3,2,2] => [3,2,2,1,1] => 3
[1,1,3,3,1] => [3,3,1,1,1] => 2
[1,1,3,4] => [4,3,1,1] => 10
[1,1,4,1,1,1] => [4,1,1,1,1,1] => 2
[1,1,4,1,2] => [4,2,1,1,1] => 5
[1,1,4,2,1] => [4,2,1,1,1] => 5
[1,1,4,3] => [4,3,1,1] => 10
[1,1,5,1,1] => [5,1,1,1,1] => 4
[1,1,5,2] => [5,2,1,1] => 12
[1,1,6,1] => [6,1,1,1] => 11
[1,1,7] => [7,1,1] => 33
[1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => 1
[1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => 1
[1,2,1,1,1,3] => [3,2,1,1,1,1] => 2
[1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => 1
[1,2,1,1,2,2] => [2,2,2,1,1,1] => 1
[1,2,1,1,3,1] => [3,2,1,1,1,1] => 2
[1,2,1,1,4] => [4,2,1,1,1] => 5
[1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => 1
[1,2,1,2,1,2] => [2,2,2,1,1,1] => 1
[1,2,1,2,2,1] => [2,2,2,1,1,1] => 1
[1,2,1,2,3] => [3,2,2,1,1] => 3
[1,2,1,3,1,1] => [3,2,1,1,1,1] => 2
[1,2,1,3,2] => [3,2,2,1,1] => 3
[1,2,1,4,1] => [4,2,1,1,1] => 5
[1,2,1,5] => [5,2,1,1] => 12
[1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => 1
[1,2,2,1,1,2] => [2,2,2,1,1,1] => 1
[1,2,2,1,2,1] => [2,2,2,1,1,1] => 1
[1,2,2,1,3] => [3,2,2,1,1] => 3
[1,2,2,2,1,1] => [2,2,2,1,1,1] => 1
[1,2,2,2,2] => [2,2,2,2,1] => 1
[1,2,2,3,1] => [3,2,2,1,1] => 3
[1,2,2,4] => [4,2,2,1] => 9
[1,2,3,1,1,1] => [3,2,1,1,1,1] => 2
[1,2,3,1,2] => [3,2,2,1,1] => 3
[1,2,3,2,1] => [3,2,2,1,1] => 3
[1,2,3,3] => [3,3,2,1] => 5
[1,2,4,1,1] => [4,2,1,1,1] => 5
[1,2,4,2] => [4,2,2,1] => 9
[1,2,5,1] => [5,2,1,1] => 12
[1,2,6] => [6,2,1] => 37
[1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => 1
[1,3,1,1,1,2] => [3,2,1,1,1,1] => 2
[1,3,1,1,2,1] => [3,2,1,1,1,1] => 2
[1,3,1,1,3] => [3,3,1,1,1] => 2
[1,3,1,2,1,1] => [3,2,1,1,1,1] => 2
[1,3,1,2,2] => [3,2,2,1,1] => 3
[1,3,1,3,1] => [3,3,1,1,1] => 2
[1,3,1,4] => [4,3,1,1] => 10
[1,3,2,1,1,1] => [3,2,1,1,1,1] => 2
[1,3,2,1,2] => [3,2,2,1,1] => 3
[1,3,2,2,1] => [3,2,2,1,1] => 3
[1,3,2,3] => [3,3,2,1] => 5
[1,3,3,1,1] => [3,3,1,1,1] => 2
[1,3,3,2] => [3,3,2,1] => 5
[1,3,4,1] => [4,3,1,1] => 10
[1,3,5] => [5,3,1] => 27
[1,4,1,1,1,1] => [4,1,1,1,1,1] => 2
[1,4,1,1,2] => [4,2,1,1,1] => 5
[1,4,1,2,1] => [4,2,1,1,1] => 5
[1,4,1,3] => [4,3,1,1] => 10
[1,4,2,1,1] => [4,2,1,1,1] => 5
[1,4,2,2] => [4,2,2,1] => 9
[1,4,3,1] => [4,3,1,1] => 10
[1,4,4] => [4,4,1] => 19
[1,5,1,1,1] => [5,1,1,1,1] => 4
[1,5,1,2] => [5,2,1,1] => 12
[1,5,2,1] => [5,2,1,1] => 12
[1,5,3] => [5,3,1] => 27
[1,6,1,1] => [6,1,1,1] => 11
[1,6,2] => [6,2,1] => 37
[1,7,1] => [7,1,1] => 33
[1,8] => [8,1] => 116
[2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => 1
[2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => 1
[2,1,1,1,1,3] => [3,2,1,1,1,1] => 2
[2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => 1
[2,1,1,1,2,2] => [2,2,2,1,1,1] => 1
[2,1,1,1,3,1] => [3,2,1,1,1,1] => 2
[2,1,1,1,4] => [4,2,1,1,1] => 5
[2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => 1
[2,1,1,2,1,2] => [2,2,2,1,1,1] => 1
[2,1,1,2,2,1] => [2,2,2,1,1,1] => 1
[2,1,1,2,3] => [3,2,2,1,1] => 3
[2,1,1,3,1,1] => [3,2,1,1,1,1] => 2
[2,1,1,3,2] => [3,2,2,1,1] => 3
[2,1,1,4,1] => [4,2,1,1,1] => 5
[2,1,1,5] => [5,2,1,1] => 12
[2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => 1
[2,1,2,1,1,2] => [2,2,2,1,1,1] => 1
[2,1,2,1,2,1] => [2,2,2,1,1,1] => 1
[2,1,2,1,3] => [3,2,2,1,1] => 3
[2,1,2,2,1,1] => [2,2,2,1,1,1] => 1
[2,1,2,2,2] => [2,2,2,2,1] => 1
[2,1,2,3,1] => [3,2,2,1,1] => 3
[2,1,2,4] => [4,2,2,1] => 9
[2,1,3,1,1,1] => [3,2,1,1,1,1] => 2
[2,1,3,1,2] => [3,2,2,1,1] => 3
[2,1,3,2,1] => [3,2,2,1,1] => 3
[2,1,3,3] => [3,3,2,1] => 5
[2,1,4,1,1] => [4,2,1,1,1] => 5
[2,1,4,2] => [4,2,2,1] => 9
[2,1,5,1] => [5,2,1,1] => 12
[2,1,6] => [6,2,1] => 37
[2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 1
[2,2,1,1,1,2] => [2,2,2,1,1,1] => 1
[2,2,1,1,2,1] => [2,2,2,1,1,1] => 1
[2,2,1,1,3] => [3,2,2,1,1] => 3
[2,2,1,2,1,1] => [2,2,2,1,1,1] => 1
[2,2,1,2,2] => [2,2,2,2,1] => 1
[2,2,1,3,1] => [3,2,2,1,1] => 3
[2,2,1,4] => [4,2,2,1] => 9
[2,2,2,1,1,1] => [2,2,2,1,1,1] => 1
[2,2,2,1,2] => [2,2,2,2,1] => 1
[2,2,2,2,1] => [2,2,2,2,1] => 1
[2,2,2,3] => [3,2,2,2] => 4
[2,2,3,1,1] => [3,2,2,1,1] => 3
[2,2,3,2] => [3,2,2,2] => 4
[2,2,4,1] => [4,2,2,1] => 9
[2,2,5] => [5,2,2] => 25
[2,3,1,1,1,1] => [3,2,1,1,1,1] => 2
[2,3,1,1,2] => [3,2,2,1,1] => 3
[2,3,1,2,1] => [3,2,2,1,1] => 3
[2,3,1,3] => [3,3,2,1] => 5
[2,3,2,1,1] => [3,2,2,1,1] => 3
[2,3,2,2] => [3,2,2,2] => 4
[2,3,3,1] => [3,3,2,1] => 5
[2,3,4] => [4,3,2] => 28
[2,4,1,1,1] => [4,2,1,1,1] => 5
[2,4,1,2] => [4,2,2,1] => 9
[2,4,2,1] => [4,2,2,1] => 9
[2,4,3] => [4,3,2] => 28
[2,5,1,1] => [5,2,1,1] => 12
[2,5,2] => [5,2,2] => 25
[2,6,1] => [6,2,1] => 37
[2,7] => [7,2] => 123
[3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 1
[3,1,1,1,1,2] => [3,2,1,1,1,1] => 2
[3,1,1,1,2,1] => [3,2,1,1,1,1] => 2
[3,1,1,1,3] => [3,3,1,1,1] => 2
[3,1,1,2,1,1] => [3,2,1,1,1,1] => 2
[3,1,1,2,2] => [3,2,2,1,1] => 3
[3,1,1,3,1] => [3,3,1,1,1] => 2
[3,1,1,4] => [4,3,1,1] => 10
[3,1,2,1,1,1] => [3,2,1,1,1,1] => 2
[3,1,2,1,2] => [3,2,2,1,1] => 3
[3,1,2,2,1] => [3,2,2,1,1] => 3
[3,1,2,3] => [3,3,2,1] => 5
[3,1,3,1,1] => [3,3,1,1,1] => 2
[3,1,3,2] => [3,3,2,1] => 5
[3,1,4,1] => [4,3,1,1] => 10
[3,1,5] => [5,3,1] => 27
[3,2,1,1,1,1] => [3,2,1,1,1,1] => 2
[3,2,1,1,2] => [3,2,2,1,1] => 3
[3,2,1,2,1] => [3,2,2,1,1] => 3
[3,2,1,3] => [3,3,2,1] => 5
[3,2,2,1,1] => [3,2,2,1,1] => 3
[3,2,2,2] => [3,2,2,2] => 4
[3,2,3,1] => [3,3,2,1] => 5
[3,2,4] => [4,3,2] => 28
[3,3,1,1,1] => [3,3,1,1,1] => 2
[3,3,1,2] => [3,3,2,1] => 5
[3,3,2,1] => [3,3,2,1] => 5
[3,3,3] => [3,3,3] => 5
[3,4,1,1] => [4,3,1,1] => 10
[3,4,2] => [4,3,2] => 28
[3,5,1] => [5,3,1] => 27
[3,6] => [6,3] => 97
[4,1,1,1,1,1] => [4,1,1,1,1,1] => 2
[4,1,1,1,2] => [4,2,1,1,1] => 5
[4,1,1,2,1] => [4,2,1,1,1] => 5
[4,1,1,3] => [4,3,1,1] => 10
[4,1,2,1,1] => [4,2,1,1,1] => 5
[4,1,2,2] => [4,2,2,1] => 9
[4,1,3,1] => [4,3,1,1] => 10
[4,1,4] => [4,4,1] => 19
[4,2,1,1,1] => [4,2,1,1,1] => 5
[4,2,1,2] => [4,2,2,1] => 9
[4,2,2,1] => [4,2,2,1] => 9
[4,2,3] => [4,3,2] => 28
[4,3,1,1] => [4,3,1,1] => 10
[4,3,2] => [4,3,2] => 28
[4,4,1] => [4,4,1] => 19
[4,5] => [5,4] => 99
[5,1,1,1,1] => [5,1,1,1,1] => 4
[5,1,1,2] => [5,2,1,1] => 12
[5,1,2,1] => [5,2,1,1] => 12
[5,1,3] => [5,3,1] => 27
[5,2,1,1] => [5,2,1,1] => 12
[5,2,2] => [5,2,2] => 25
[5,3,1] => [5,3,1] => 27
[5,4] => [5,4] => 99
[6,1,1,1] => [6,1,1,1] => 11
[6,1,2] => [6,2,1] => 37
[6,2,1] => [6,2,1] => 37
[6,3] => [6,3] => 97
[7,1,1] => [7,1,1] => 33
[7,2] => [7,2] => 123
[8,1] => [8,1] => 116
[9] => [9] => 435
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => 2
[1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,1,2] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,3] => [3,2,1,1,1,1,1] => 2
[1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,3,2] => [3,2,1,1,1,1,1] => 2
[1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => 2
[1,1,1,1,1,5] => [5,1,1,1,1,1] => 4
[1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,1,2,1,3] => [3,2,1,1,1,1,1] => 2
[1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => 1
[1,1,1,1,2,3,1] => [3,2,1,1,1,1,1] => 2
[1,1,1,1,2,4] => [4,2,1,1,1,1] => 5
[1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1] => 1
[1,1,1,1,3,1,2] => [3,2,1,1,1,1,1] => 2
[1,1,1,1,3,2,1] => [3,2,1,1,1,1,1] => 2
[1,1,1,1,3,3] => [3,3,1,1,1,1] => 2
[1,1,1,1,4,1,1] => [4,1,1,1,1,1,1] => 2
[1,1,1,1,4,2] => [4,2,1,1,1,1] => 5
[1,1,1,1,5,1] => [5,1,1,1,1,1] => 4
[1,1,1,1,6] => [6,1,1,1,1] => 11
[1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,1,2] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,3] => [3,2,1,1,1,1,1] => 2
[1,1,1,2,1,2,1,1] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,2,1,2,2] => [2,2,2,1,1,1,1] => 1
[1,1,1,2,1,3,1] => [3,2,1,1,1,1,1] => 2
[1,1,1,2,1,4] => [4,2,1,1,1,1] => 5
[1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1] => 1
[1,1,1,2,2,1,2] => [2,2,2,1,1,1,1] => 1
[1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => 1
[1,1,1,2,2,3] => [3,2,2,1,1,1] => 3
[1,1,1,2,3,1,1] => [3,2,1,1,1,1,1] => 2
[1,1,1,2,3,2] => [3,2,2,1,1,1] => 3
[1,1,1,2,4,1] => [4,2,1,1,1,1] => 5
[1,1,1,2,5] => [5,2,1,1,1] => 12
[1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => 1
[1,1,1,3,1,1,2] => [3,2,1,1,1,1,1] => 2
[1,1,1,3,1,2,1] => [3,2,1,1,1,1,1] => 2
[1,1,1,3,1,3] => [3,3,1,1,1,1] => 2
[1,1,1,3,2,1,1] => [3,2,1,1,1,1,1] => 2
[1,1,1,3,2,2] => [3,2,2,1,1,1] => 3
[1,1,1,3,3,1] => [3,3,1,1,1,1] => 2
[1,1,1,3,4] => [4,3,1,1,1] => 10
[1,1,1,4,1,1,1] => [4,1,1,1,1,1,1] => 2
[1,1,1,4,1,2] => [4,2,1,1,1,1] => 5
[1,1,1,4,2,1] => [4,2,1,1,1,1] => 5
[1,1,1,4,3] => [4,3,1,1,1] => 10
[1,1,1,5,1,1] => [5,1,1,1,1,1] => 4
[1,1,1,5,2] => [5,2,1,1,1] => 12
[1,1,1,6,1] => [6,1,1,1,1] => 11
[1,1,1,7] => [7,1,1,1] => 33
[1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,3] => [3,2,1,1,1,1,1] => 2
[1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => 1
[1,1,2,1,1,2,2] => [2,2,2,1,1,1,1] => 1
[1,1,2,1,1,3,1] => [3,2,1,1,1,1,1] => 2
[1,1,2,1,1,4] => [4,2,1,1,1,1] => 5
[1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => 1
[1,1,2,1,2,1,2] => [2,2,2,1,1,1,1] => 1
[1,1,2,1,2,2,1] => [2,2,2,1,1,1,1] => 1
[1,1,2,1,2,3] => [3,2,2,1,1,1] => 3
[1,1,2,1,3,1,1] => [3,2,1,1,1,1,1] => 2
[1,1,2,1,3,2] => [3,2,2,1,1,1] => 3
[1,1,2,1,4,1] => [4,2,1,1,1,1] => 5
[1,1,2,1,5] => [5,2,1,1,1] => 12
[1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1
[1,1,2,2,1,1,2] => [2,2,2,1,1,1,1] => 1
[1,1,2,2,1,2,1] => [2,2,2,1,1,1,1] => 1
[1,1,2,2,1,3] => [3,2,2,1,1,1] => 3
[1,1,2,2,2,1,1] => [2,2,2,1,1,1,1] => 1
[1,1,2,2,2,2] => [2,2,2,2,1,1] => 1
[1,1,2,2,3,1] => [3,2,2,1,1,1] => 3
[1,1,2,2,4] => [4,2,2,1,1] => 9
[1,1,2,3,1,1,1] => [3,2,1,1,1,1,1] => 2
[1,1,2,3,1,2] => [3,2,2,1,1,1] => 3
[1,1,2,3,2,1] => [3,2,2,1,1,1] => 3
[1,1,2,3,3] => [3,3,2,1,1] => 5
[1,1,2,4,1,1] => [4,2,1,1,1,1] => 5
[1,1,2,4,2] => [4,2,2,1,1] => 9
[1,1,2,5,1] => [5,2,1,1,1] => 12
[1,1,2,6] => [6,2,1,1] => 37
[1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 1
[1,1,3,1,1,1,2] => [3,2,1,1,1,1,1] => 2
[1,1,3,1,1,2,1] => [3,2,1,1,1,1,1] => 2
[1,1,3,1,1,3] => [3,3,1,1,1,1] => 2
[1,1,3,1,2,1,1] => [3,2,1,1,1,1,1] => 2
[1,1,3,1,2,2] => [3,2,2,1,1,1] => 3
[1,1,3,1,3,1] => [3,3,1,1,1,1] => 2
[1,1,3,1,4] => [4,3,1,1,1] => 10
[1,1,3,2,1,1,1] => [3,2,1,1,1,1,1] => 2
[1,1,3,2,1,2] => [3,2,2,1,1,1] => 3
[1,1,3,2,2,1] => [3,2,2,1,1,1] => 3
[1,1,3,2,3] => [3,3,2,1,1] => 5
[1,1,3,3,1,1] => [3,3,1,1,1,1] => 2
[1,1,3,3,2] => [3,3,2,1,1] => 5
[1,1,3,4,1] => [4,3,1,1,1] => 10
[1,1,3,5] => [5,3,1,1] => 27
[1,1,4,1,1,1,1] => [4,1,1,1,1,1,1] => 2
[1,1,4,1,1,2] => [4,2,1,1,1,1] => 5
[1,1,4,1,2,1] => [4,2,1,1,1,1] => 5
[1,1,4,1,3] => [4,3,1,1,1] => 10
[1,1,4,2,1,1] => [4,2,1,1,1,1] => 5
[1,1,4,2,2] => [4,2,2,1,1] => 9
[1,1,4,3,1] => [4,3,1,1,1] => 10
[1,1,4,4] => [4,4,1,1] => 19
[1,1,5,1,1,1] => [5,1,1,1,1,1] => 4
[1,1,5,1,2] => [5,2,1,1,1] => 12
[1,1,5,2,1] => [5,2,1,1,1] => 12
[1,1,5,3] => [5,3,1,1] => 27
[1,1,6,1,1] => [6,1,1,1,1] => 11
[1,1,6,2] => [6,2,1,1] => 37
[1,1,7,1] => [7,1,1,1] => 33
[1,1,8] => [8,1,1] => 116
[1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => 2
[1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => 1
[1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => 1
[1,2,1,1,1,3,1] => [3,2,1,1,1,1,1] => 2
[1,2,1,1,1,4] => [4,2,1,1,1,1] => 5
[1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => 1
[1,2,1,1,2,1,2] => [2,2,2,1,1,1,1] => 1
[1,2,1,1,2,2,1] => [2,2,2,1,1,1,1] => 1
[1,2,1,1,2,3] => [3,2,2,1,1,1] => 3
[1,2,1,1,3,1,1] => [3,2,1,1,1,1,1] => 2
[1,2,1,1,3,2] => [3,2,2,1,1,1] => 3
[1,2,1,1,4,1] => [4,2,1,1,1,1] => 5
[1,2,1,1,5] => [5,2,1,1,1] => 12
[1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1
[1,2,1,2,1,1,2] => [2,2,2,1,1,1,1] => 1
[1,2,1,2,1,2,1] => [2,2,2,1,1,1,1] => 1
[1,2,1,2,1,3] => [3,2,2,1,1,1] => 3
[1,2,1,2,2,1,1] => [2,2,2,1,1,1,1] => 1
[1,2,1,2,2,2] => [2,2,2,2,1,1] => 1
[1,2,1,2,3,1] => [3,2,2,1,1,1] => 3
[1,2,1,2,4] => [4,2,2,1,1] => 9
[1,2,1,3,1,1,1] => [3,2,1,1,1,1,1] => 2
[1,2,1,3,1,2] => [3,2,2,1,1,1] => 3
[1,2,1,3,2,1] => [3,2,2,1,1,1] => 3
[1,2,1,3,3] => [3,3,2,1,1] => 5
[1,2,1,4,1,1] => [4,2,1,1,1,1] => 5
[1,2,1,4,2] => [4,2,2,1,1] => 9
[1,2,1,5,1] => [5,2,1,1,1] => 12
[1,2,1,6] => [6,2,1,1] => 37
[1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1
[1,2,2,1,1,1,2] => [2,2,2,1,1,1,1] => 1
[1,2,2,1,1,2,1] => [2,2,2,1,1,1,1] => 1
[1,2,2,1,1,3] => [3,2,2,1,1,1] => 3
[1,2,2,1,2,1,1] => [2,2,2,1,1,1,1] => 1
[1,2,2,1,2,2] => [2,2,2,2,1,1] => 1
[1,2,2,1,3,1] => [3,2,2,1,1,1] => 3
[1,2,2,1,4] => [4,2,2,1,1] => 9
[1,2,2,2,1,1,1] => [2,2,2,1,1,1,1] => 1
[1,2,2,2,1,2] => [2,2,2,2,1,1] => 1
[1,2,2,2,2,1] => [2,2,2,2,1,1] => 1
[1,2,2,2,3] => [3,2,2,2,1] => 4
[1,2,2,3,1,1] => [3,2,2,1,1,1] => 3
[1,2,2,3,2] => [3,2,2,2,1] => 4
[1,2,2,4,1] => [4,2,2,1,1] => 9
[1,2,2,5] => [5,2,2,1] => 25
[1,2,3,1,1,1,1] => [3,2,1,1,1,1,1] => 2
[1,2,3,1,1,2] => [3,2,2,1,1,1] => 3
[1,2,3,1,2,1] => [3,2,2,1,1,1] => 3
[1,2,3,1,3] => [3,3,2,1,1] => 5
[1,2,3,2,1,1] => [3,2,2,1,1,1] => 3
[1,2,3,2,2] => [3,2,2,2,1] => 4
[1,2,3,3,1] => [3,3,2,1,1] => 5
[1,2,3,4] => [4,3,2,1] => 28
[1,2,4,1,1,1] => [4,2,1,1,1,1] => 5
[1,2,4,1,2] => [4,2,2,1,1] => 9
[1,2,4,2,1] => [4,2,2,1,1] => 9
[1,2,4,3] => [4,3,2,1] => 28
[1,2,5,1,1] => [5,2,1,1,1] => 12
[1,2,5,2] => [5,2,2,1] => 25
[1,2,6,1] => [6,2,1,1] => 37
[1,2,7] => [7,2,1] => 123
[1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 1
[1,3,1,1,1,1,2] => [3,2,1,1,1,1,1] => 2
[1,3,1,1,1,2,1] => [3,2,1,1,1,1,1] => 2
[1,3,1,1,1,3] => [3,3,1,1,1,1] => 2
[1,3,1,1,2,1,1] => [3,2,1,1,1,1,1] => 2
[1,3,1,1,2,2] => [3,2,2,1,1,1] => 3
[1,3,1,1,3,1] => [3,3,1,1,1,1] => 2
[1,3,1,1,4] => [4,3,1,1,1] => 10
[1,3,1,2,1,1,1] => [3,2,1,1,1,1,1] => 2
[1,3,1,2,1,2] => [3,2,2,1,1,1] => 3
[1,3,1,2,2,1] => [3,2,2,1,1,1] => 3
[1,3,1,2,3] => [3,3,2,1,1] => 5
[1,3,1,3,1,1] => [3,3,1,1,1,1] => 2
[1,3,1,3,2] => [3,3,2,1,1] => 5
[1,3,1,4,1] => [4,3,1,1,1] => 10
[1,3,1,5] => [5,3,1,1] => 27
[1,3,2,1,1,1,1] => [3,2,1,1,1,1,1] => 2
[1,3,2,1,1,2] => [3,2,2,1,1,1] => 3
[1,3,2,1,2,1] => [3,2,2,1,1,1] => 3
[1,3,2,1,3] => [3,3,2,1,1] => 5
[1,3,2,2,1,1] => [3,2,2,1,1,1] => 3
[1,3,2,2,2] => [3,2,2,2,1] => 4
[1,3,2,3,1] => [3,3,2,1,1] => 5
[1,3,2,4] => [4,3,2,1] => 28
[1,3,3,1,1,1] => [3,3,1,1,1,1] => 2
[1,3,3,1,2] => [3,3,2,1,1] => 5
[1,3,3,2,1] => [3,3,2,1,1] => 5
[1,3,3,3] => [3,3,3,1] => 5
[1,3,4,1,1] => [4,3,1,1,1] => 10
[1,3,4,2] => [4,3,2,1] => 28
[1,3,5,1] => [5,3,1,1] => 27
[1,3,6] => [6,3,1] => 97
[1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => 2
[1,4,1,1,1,2] => [4,2,1,1,1,1] => 5
[1,4,1,1,2,1] => [4,2,1,1,1,1] => 5
[1,4,1,1,3] => [4,3,1,1,1] => 10
[1,4,1,2,1,1] => [4,2,1,1,1,1] => 5
[1,4,1,2,2] => [4,2,2,1,1] => 9
[1,4,1,3,1] => [4,3,1,1,1] => 10
[1,4,1,4] => [4,4,1,1] => 19
[1,4,2,1,1,1] => [4,2,1,1,1,1] => 5
[1,4,2,1,2] => [4,2,2,1,1] => 9
[1,4,2,2,1] => [4,2,2,1,1] => 9
[1,4,2,3] => [4,3,2,1] => 28
[1,4,3,1,1] => [4,3,1,1,1] => 10
[1,4,3,2] => [4,3,2,1] => 28
[1,4,4,1] => [4,4,1,1] => 19
[1,4,5] => [5,4,1] => 99
[1,5,1,1,1,1] => [5,1,1,1,1,1] => 4
[1,5,1,1,2] => [5,2,1,1,1] => 12
[1,5,1,2,1] => [5,2,1,1,1] => 12
[1,5,1,3] => [5,3,1,1] => 27
[1,5,2,1,1] => [5,2,1,1,1] => 12
[1,5,2,2] => [5,2,2,1] => 25
[1,5,3,1] => [5,3,1,1] => 27
[1,5,4] => [5,4,1] => 99
[1,6,1,1,1] => [6,1,1,1,1] => 11
[1,6,1,2] => [6,2,1,1] => 37
[1,6,2,1] => [6,2,1,1] => 37
[1,6,3] => [6,3,1] => 97
[1,7,1,1] => [7,1,1,1] => 33
[1,7,2] => [7,2,1] => 123
[1,8,1] => [8,1,1] => 116
[1,9] => [9,1] => 435
[2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,3] => [3,2,1,1,1,1,1] => 2
[2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => 1
[2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => 1
[2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => 2
[2,1,1,1,1,4] => [4,2,1,1,1,1] => 5
[2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => 1
[2,1,1,1,2,1,2] => [2,2,2,1,1,1,1] => 1
[2,1,1,1,2,2,1] => [2,2,2,1,1,1,1] => 1
[2,1,1,1,2,3] => [3,2,2,1,1,1] => 3
[2,1,1,1,3,1,1] => [3,2,1,1,1,1,1] => 2
[2,1,1,1,3,2] => [3,2,2,1,1,1] => 3
[2,1,1,1,4,1] => [4,2,1,1,1,1] => 5
[2,1,1,1,5] => [5,2,1,1,1] => 12
[2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1
[2,1,1,2,1,1,2] => [2,2,2,1,1,1,1] => 1
[2,1,1,2,1,2,1] => [2,2,2,1,1,1,1] => 1
[2,1,1,2,1,3] => [3,2,2,1,1,1] => 3
[2,1,1,2,2,1,1] => [2,2,2,1,1,1,1] => 1
[2,1,1,2,2,2] => [2,2,2,2,1,1] => 1
[2,1,1,2,3,1] => [3,2,2,1,1,1] => 3
[2,1,1,2,4] => [4,2,2,1,1] => 9
[2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => 2
[2,1,1,3,1,2] => [3,2,2,1,1,1] => 3
[2,1,1,3,2,1] => [3,2,2,1,1,1] => 3
[2,1,1,3,3] => [3,3,2,1,1] => 5
[2,1,1,4,1,1] => [4,2,1,1,1,1] => 5
[2,1,1,4,2] => [4,2,2,1,1] => 9
[2,1,1,5,1] => [5,2,1,1,1] => 12
[2,1,1,6] => [6,2,1,1] => 37
[2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1
[2,1,2,1,1,1,2] => [2,2,2,1,1,1,1] => 1
[2,1,2,1,1,2,1] => [2,2,2,1,1,1,1] => 1
[2,1,2,1,1,3] => [3,2,2,1,1,1] => 3
[2,1,2,1,2,1,1] => [2,2,2,1,1,1,1] => 1
[2,1,2,1,2,2] => [2,2,2,2,1,1] => 1
[2,1,2,1,3,1] => [3,2,2,1,1,1] => 3
[2,1,2,1,4] => [4,2,2,1,1] => 9
[2,1,2,2,1,1,1] => [2,2,2,1,1,1,1] => 1
[2,1,2,2,1,2] => [2,2,2,2,1,1] => 1
[2,1,2,2,2,1] => [2,2,2,2,1,1] => 1
[2,1,2,2,3] => [3,2,2,2,1] => 4
[2,1,2,3,1,1] => [3,2,2,1,1,1] => 3
[2,1,2,3,2] => [3,2,2,2,1] => 4
[2,1,2,4,1] => [4,2,2,1,1] => 9
[2,1,2,5] => [5,2,2,1] => 25
[2,1,3,1,1,1,1] => [3,2,1,1,1,1,1] => 2
[2,1,3,1,1,2] => [3,2,2,1,1,1] => 3
[2,1,3,1,2,1] => [3,2,2,1,1,1] => 3
[2,1,3,1,3] => [3,3,2,1,1] => 5
[2,1,3,2,1,1] => [3,2,2,1,1,1] => 3
[2,1,3,2,2] => [3,2,2,2,1] => 4
[2,1,3,3,1] => [3,3,2,1,1] => 5
[2,1,3,4] => [4,3,2,1] => 28
[2,1,4,1,1,1] => [4,2,1,1,1,1] => 5
[2,1,4,1,2] => [4,2,2,1,1] => 9
[2,1,4,2,1] => [4,2,2,1,1] => 9
[2,1,4,3] => [4,3,2,1] => 28
[2,1,5,1,1] => [5,2,1,1,1] => 12
[2,1,5,2] => [5,2,2,1] => 25
[2,1,6,1] => [6,2,1,1] => 37
[2,1,7] => [7,2,1] => 123
[2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 1
[2,2,1,1,1,1,2] => [2,2,2,1,1,1,1] => 1
[2,2,1,1,1,2,1] => [2,2,2,1,1,1,1] => 1
[2,2,1,1,1,3] => [3,2,2,1,1,1] => 3
[2,2,1,1,2,1,1] => [2,2,2,1,1,1,1] => 1
[2,2,1,1,2,2] => [2,2,2,2,1,1] => 1
[2,2,1,1,3,1] => [3,2,2,1,1,1] => 3
[2,2,1,1,4] => [4,2,2,1,1] => 9
[2,2,1,2,1,1,1] => [2,2,2,1,1,1,1] => 1
[2,2,1,2,1,2] => [2,2,2,2,1,1] => 1
[2,2,1,2,2,1] => [2,2,2,2,1,1] => 1
[2,2,1,2,3] => [3,2,2,2,1] => 4
[2,2,1,3,1,1] => [3,2,2,1,1,1] => 3
[2,2,1,3,2] => [3,2,2,2,1] => 4
[2,2,1,4,1] => [4,2,2,1,1] => 9
[2,2,1,5] => [5,2,2,1] => 25
[2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 1
[2,2,2,1,1,2] => [2,2,2,2,1,1] => 1
[2,2,2,1,2,1] => [2,2,2,2,1,1] => 1
[2,2,2,1,3] => [3,2,2,2,1] => 4
[2,2,2,2,1,1] => [2,2,2,2,1,1] => 1
[2,2,2,2,2] => [2,2,2,2,2] => 1
[2,2,2,3,1] => [3,2,2,2,1] => 4
[2,2,2,4] => [4,2,2,2] => 14
[2,2,3,1,1,1] => [3,2,2,1,1,1] => 3
[2,2,3,1,2] => [3,2,2,2,1] => 4
[2,2,3,2,1] => [3,2,2,2,1] => 4
[2,2,3,3] => [3,3,2,2] => 9
[2,2,4,1,1] => [4,2,2,1,1] => 9
[2,2,4,2] => [4,2,2,2] => 14
[2,2,5,1] => [5,2,2,1] => 25
[2,2,6] => [6,2,2] => 85
[2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => 2
[2,3,1,1,1,2] => [3,2,2,1,1,1] => 3
[2,3,1,1,2,1] => [3,2,2,1,1,1] => 3
[2,3,1,1,3] => [3,3,2,1,1] => 5
[2,3,1,2,1,1] => [3,2,2,1,1,1] => 3
[2,3,1,2,2] => [3,2,2,2,1] => 4
[2,3,1,3,1] => [3,3,2,1,1] => 5
[2,3,1,4] => [4,3,2,1] => 28
[2,3,2,1,1,1] => [3,2,2,1,1,1] => 3
[2,3,2,1,2] => [3,2,2,2,1] => 4
[2,3,2,2,1] => [3,2,2,2,1] => 4
[2,3,2,3] => [3,3,2,2] => 9
[2,3,3,1,1] => [3,3,2,1,1] => 5
[2,3,3,2] => [3,3,2,2] => 9
[2,3,4,1] => [4,3,2,1] => 28
[2,3,5] => [5,3,2] => 89
[2,4,1,1,1,1] => [4,2,1,1,1,1] => 5
[2,4,1,1,2] => [4,2,2,1,1] => 9
[2,4,1,2,1] => [4,2,2,1,1] => 9
[2,4,1,3] => [4,3,2,1] => 28
[2,4,2,1,1] => [4,2,2,1,1] => 9
[2,4,2,2] => [4,2,2,2] => 14
[2,4,3,1] => [4,3,2,1] => 28
[2,4,4] => [4,4,2] => 61
[2,5,1,1,1] => [5,2,1,1,1] => 12
[2,5,1,2] => [5,2,2,1] => 25
[2,5,2,1] => [5,2,2,1] => 25
[2,5,3] => [5,3,2] => 89
[2,6,1,1] => [6,2,1,1] => 37
[2,6,2] => [6,2,2] => 85
[2,7,1] => [7,2,1] => 123
[2,8] => [8,2] => 474
[3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 1
[3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => 2
[3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => 2
[3,1,1,1,1,3] => [3,3,1,1,1,1] => 2
[3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => 2
[3,1,1,1,2,2] => [3,2,2,1,1,1] => 3
[3,1,1,1,3,1] => [3,3,1,1,1,1] => 2
[3,1,1,1,4] => [4,3,1,1,1] => 10
[3,1,1,2,1,1,1] => [3,2,1,1,1,1,1] => 2
[3,1,1,2,1,2] => [3,2,2,1,1,1] => 3
[3,1,1,2,2,1] => [3,2,2,1,1,1] => 3
[3,1,1,2,3] => [3,3,2,1,1] => 5
[3,1,1,3,1,1] => [3,3,1,1,1,1] => 2
[3,1,1,3,2] => [3,3,2,1,1] => 5
[3,1,1,4,1] => [4,3,1,1,1] => 10
[3,1,1,5] => [5,3,1,1] => 27
[3,1,2,1,1,1,1] => [3,2,1,1,1,1,1] => 2
[3,1,2,1,1,2] => [3,2,2,1,1,1] => 3
[3,1,2,1,2,1] => [3,2,2,1,1,1] => 3
[3,1,2,1,3] => [3,3,2,1,1] => 5
[3,1,2,2,1,1] => [3,2,2,1,1,1] => 3
[3,1,2,2,2] => [3,2,2,2,1] => 4
[3,1,2,3,1] => [3,3,2,1,1] => 5
[3,1,2,4] => [4,3,2,1] => 28
[3,1,3,1,1,1] => [3,3,1,1,1,1] => 2
[3,1,3,1,2] => [3,3,2,1,1] => 5
[3,1,3,2,1] => [3,3,2,1,1] => 5
[3,1,3,3] => [3,3,3,1] => 5
[3,1,4,1,1] => [4,3,1,1,1] => 10
[3,1,4,2] => [4,3,2,1] => 28
[3,1,5,1] => [5,3,1,1] => 27
[3,1,6] => [6,3,1] => 97
[3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 2
[3,2,1,1,1,2] => [3,2,2,1,1,1] => 3
[3,2,1,1,2,1] => [3,2,2,1,1,1] => 3
[3,2,1,1,3] => [3,3,2,1,1] => 5
[3,2,1,2,1,1] => [3,2,2,1,1,1] => 3
[3,2,1,2,2] => [3,2,2,2,1] => 4
[3,2,1,3,1] => [3,3,2,1,1] => 5
[3,2,1,4] => [4,3,2,1] => 28
[3,2,2,1,1,1] => [3,2,2,1,1,1] => 3
[3,2,2,1,2] => [3,2,2,2,1] => 4
[3,2,2,2,1] => [3,2,2,2,1] => 4
[3,2,2,3] => [3,3,2,2] => 9
[3,2,3,1,1] => [3,3,2,1,1] => 5
[3,2,3,2] => [3,3,2,2] => 9
[3,2,4,1] => [4,3,2,1] => 28
[3,2,5] => [5,3,2] => 89
[3,3,1,1,1,1] => [3,3,1,1,1,1] => 2
[3,3,1,1,2] => [3,3,2,1,1] => 5
[3,3,1,2,1] => [3,3,2,1,1] => 5
[3,3,1,3] => [3,3,3,1] => 5
[3,3,2,1,1] => [3,3,2,1,1] => 5
[3,3,2,2] => [3,3,2,2] => 9
[3,3,3,1] => [3,3,3,1] => 5
[3,3,4] => [4,3,3] => 42
[3,4,1,1,1] => [4,3,1,1,1] => 10
[3,4,1,2] => [4,3,2,1] => 28
[3,4,2,1] => [4,3,2,1] => 28
[3,4,3] => [4,3,3] => 42
[3,5,1,1] => [5,3,1,1] => 27
[3,5,2] => [5,3,2] => 89
[3,6,1] => [6,3,1] => 97
[3,7] => [7,3] => 351
[4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 2
[4,1,1,1,1,2] => [4,2,1,1,1,1] => 5
[4,1,1,1,2,1] => [4,2,1,1,1,1] => 5
[4,1,1,1,3] => [4,3,1,1,1] => 10
[4,1,1,2,1,1] => [4,2,1,1,1,1] => 5
[4,1,1,2,2] => [4,2,2,1,1] => 9
[4,1,1,3,1] => [4,3,1,1,1] => 10
[4,1,1,4] => [4,4,1,1] => 19
[4,1,2,1,1,1] => [4,2,1,1,1,1] => 5
[4,1,2,1,2] => [4,2,2,1,1] => 9
[4,1,2,2,1] => [4,2,2,1,1] => 9
[4,1,2,3] => [4,3,2,1] => 28
[4,1,3,1,1] => [4,3,1,1,1] => 10
[4,1,3,2] => [4,3,2,1] => 28
[4,1,4,1] => [4,4,1,1] => 19
[4,1,5] => [5,4,1] => 99
[4,2,1,1,1,1] => [4,2,1,1,1,1] => 5
[4,2,1,1,2] => [4,2,2,1,1] => 9
[4,2,1,2,1] => [4,2,2,1,1] => 9
[4,2,1,3] => [4,3,2,1] => 28
[4,2,2,1,1] => [4,2,2,1,1] => 9
[4,2,2,2] => [4,2,2,2] => 14
[4,2,3,1] => [4,3,2,1] => 28
[4,2,4] => [4,4,2] => 61
[4,3,1,1,1] => [4,3,1,1,1] => 10
[4,3,1,2] => [4,3,2,1] => 28
[4,3,2,1] => [4,3,2,1] => 28
[4,3,3] => [4,3,3] => 42
[4,4,1,1] => [4,4,1,1] => 19
[4,4,2] => [4,4,2] => 61
[4,5,1] => [5,4,1] => 99
[4,6] => [6,4] => 384
[5,1,1,1,1,1] => [5,1,1,1,1,1] => 4
[5,1,1,1,2] => [5,2,1,1,1] => 12
[5,1,1,2,1] => [5,2,1,1,1] => 12
[5,1,1,3] => [5,3,1,1] => 27
[5,1,2,1,1] => [5,2,1,1,1] => 12
[5,1,2,2] => [5,2,2,1] => 25
[5,1,3,1] => [5,3,1,1] => 27
[5,1,4] => [5,4,1] => 99
[5,2,1,1,1] => [5,2,1,1,1] => 12
[5,2,1,2] => [5,2,2,1] => 25
[5,2,2,1] => [5,2,2,1] => 25
[5,2,3] => [5,3,2] => 89
[5,3,1,1] => [5,3,1,1] => 27
[5,3,2] => [5,3,2] => 89
[5,4,1] => [5,4,1] => 99
[5,5] => [5,5] => 188
[6,1,1,1,1] => [6,1,1,1,1] => 11
[6,1,1,2] => [6,2,1,1] => 37
[6,1,2,1] => [6,2,1,1] => 37
[6,1,3] => [6,3,1] => 97
[6,2,1,1] => [6,2,1,1] => 37
[6,2,2] => [6,2,2] => 85
[6,3,1] => [6,3,1] => 97
[6,4] => [6,4] => 384
[7,1,1,1] => [7,1,1,1] => 33
[7,1,2] => [7,2,1] => 123
[7,2,1] => [7,2,1] => 123
[7,3] => [7,3] => 351
[8,1,1] => [8,1,1] => 116
[8,2] => [8,2] => 474
[9,1] => [9,1] => 435
[10] => [10] => 1832
[1,10] => [10,1] => 1832
[1,8,1,1] => [8,1,1,1] => 116
[1,7,2,1] => [7,2,1,1] => 123
[1,6,3,1] => [6,3,1,1] => 97
[1,5,4,1] => [5,4,1,1] => 99
[1,4,5,1] => [5,4,1,1] => 99
[1,3,6,1] => [6,3,1,1] => 97
[1,2,7,1] => [7,2,1,1] => 123
[1,1,8,1] => [8,1,1,1] => 116
[10,1] => [10,1] => 1832
[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
[1,1,1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,3,3] => [3,3,1,1,1,1,1,1] => 2
[1,1,1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,2,2,2,2] => [2,2,2,2,1,1,1,1] => 1
[1,1,1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,2,1,2,3] => [3,2,2,1,1,1,1,1] => 3
[1,1,1,1,3,3,1,1] => [3,3,1,1,1,1,1,1] => 2
[1,1,1,1,3,2,1,2] => [3,2,2,1,1,1,1,1] => 3
[1,1,1,1,3,1,1,3] => [3,3,1,1,1,1,1,1] => 2
[1,1,1,1,4,4] => [4,4,1,1,1,1] => 19
[1,1,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,2,2,1,1,2,2] => [2,2,2,2,1,1,1,1] => 1
[1,1,2,2,2,2,1,1] => [2,2,2,2,1,1,1,1] => 1
[1,1,2,2,2,1,1,2] => [2,2,2,2,1,1,1,1] => 1
[1,1,2,2,3,3] => [3,3,2,2,1,1] => 9
[1,1,2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,2,1,1,2,2,2] => [2,2,2,2,1,1,1,1] => 1
[1,1,2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,2,3] => [3,2,2,1,1,1,1,1] => 3
[1,1,2,1,2,3,1,1] => [3,2,2,1,1,1,1,1] => 3
[1,1,2,1,2,2,1,2] => [2,2,2,2,1,1,1,1] => 1
[1,1,2,1,2,1,1,3] => [3,2,2,1,1,1,1,1] => 3
[1,1,2,1,3,4] => [4,3,2,1,1,1] => 28
[1,1,3,3,1,1,1,1] => [3,3,1,1,1,1,1,1] => 2
[1,1,3,3,2,2] => [3,3,2,2,1,1] => 9
[1,1,3,2,1,2,1,1] => [3,2,2,1,1,1,1,1] => 3
[1,1,3,2,1,1,1,2] => [3,2,2,1,1,1,1,1] => 3
[1,1,3,2,2,3] => [3,3,2,2,1,1] => 9
[1,1,3,1,1,3,1,1] => [3,3,1,1,1,1,1,1] => 2
[1,1,3,1,1,2,1,2] => [3,2,2,1,1,1,1,1] => 3
[1,1,3,1,1,1,1,3] => [3,3,1,1,1,1,1,1] => 2
[1,1,3,1,2,4] => [4,3,2,1,1,1] => 28
[1,1,4,4,1,1] => [4,4,1,1,1,1] => 19
[1,1,4,3,1,2] => [4,3,2,1,1,1] => 28
[1,1,4,2,1,3] => [4,3,2,1,1,1] => 28
[1,1,4,1,1,4] => [4,4,1,1,1,1] => 19
[1,1,5,5] => [5,5,1,1] => 188
[2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[2,2,1,1,1,1,2,2] => [2,2,2,2,1,1,1,1] => 1
[2,2,1,1,2,2,1,1] => [2,2,2,2,1,1,1,1] => 1
[2,2,1,1,2,1,1,2] => [2,2,2,2,1,1,1,1] => 1
[2,2,1,1,3,3] => [3,3,2,2,1,1] => 9
[2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 1
[2,2,2,2,2,2] => [2,2,2,2,2,2] => 1
[2,2,2,1,1,2,1,1] => [2,2,2,2,1,1,1,1] => 1
[2,2,2,1,1,1,1,2] => [2,2,2,2,1,1,1,1] => 1
[2,2,2,1,2,3] => [3,2,2,2,2,1] => 5
[2,2,3,3,1,1] => [3,3,2,2,1,1] => 9
[2,2,3,2,1,2] => [3,2,2,2,2,1] => 5
[2,2,3,1,1,3] => [3,3,2,2,1,1] => 9
[2,2,4,4] => [4,4,2,2] => 137
[2,1,1,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[2,1,1,2,1,1,2,2] => [2,2,2,2,1,1,1,1] => 1
[2,1,1,2,2,2,1,1] => [2,2,2,2,1,1,1,1] => 1
[2,1,1,2,2,1,1,2] => [2,2,2,2,1,1,1,1] => 1
[2,1,1,2,3,3] => [3,3,2,2,1,1] => 9
[2,1,1,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,2,2,2] => [2,2,2,2,1,1,1,1] => 1
[2,1,1,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,2,3] => [3,2,2,1,1,1,1,1] => 3
[2,1,1,1,2,3,1,1] => [3,2,2,1,1,1,1,1] => 3
[2,1,1,1,2,2,1,2] => [2,2,2,2,1,1,1,1] => 1
[2,1,1,1,2,1,1,3] => [3,2,2,1,1,1,1,1] => 3
[2,1,1,1,3,4] => [4,3,2,1,1,1] => 28
[2,1,2,3,1,1,1,1] => [3,2,2,1,1,1,1,1] => 3
[2,1,2,3,2,2] => [3,2,2,2,2,1] => 5
[2,1,2,2,1,2,1,1] => [2,2,2,2,1,1,1,1] => 1
[2,1,2,2,1,1,1,2] => [2,2,2,2,1,1,1,1] => 1
[2,1,2,2,2,3] => [3,2,2,2,2,1] => 5
[2,1,2,1,1,3,1,1] => [3,2,2,1,1,1,1,1] => 3
[2,1,2,1,1,2,1,2] => [2,2,2,2,1,1,1,1] => 1
[2,1,2,1,1,1,1,3] => [3,2,2,1,1,1,1,1] => 3
[2,1,2,1,2,4] => [4,2,2,2,1,1] => 14
[2,1,3,4,1,1] => [4,3,2,1,1,1] => 28
[2,1,3,3,1,2] => [3,3,2,2,1,1] => 9
[2,1,3,2,1,3] => [3,3,2,2,1,1] => 9
[2,1,3,1,1,4] => [4,3,2,1,1,1] => 28
[2,1,4,5] => [5,4,2,1] => 349
[3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => 2
[3,3,1,1,2,2] => [3,3,2,2,1,1] => 9
[3,3,2,2,1,1] => [3,3,2,2,1,1] => 9
[3,3,2,1,1,2] => [3,3,2,2,1,1] => 9
[3,3,3,3] => [3,3,3,3] => 14
[3,2,1,2,1,1,1,1] => [3,2,2,1,1,1,1,1] => 3
[3,2,1,2,2,2] => [3,2,2,2,2,1] => 5
[3,2,1,1,1,2,1,1] => [3,2,2,1,1,1,1,1] => 3
[3,2,1,1,1,1,1,2] => [3,2,2,1,1,1,1,1] => 3
[3,2,1,1,2,3] => [3,3,2,2,1,1] => 9
[3,2,2,3,1,1] => [3,3,2,2,1,1] => 9
[3,2,2,2,1,2] => [3,2,2,2,2,1] => 5
[3,2,2,1,1,3] => [3,3,2,2,1,1] => 9
[3,2,3,4] => [4,3,3,2] => 126
[3,1,1,3,1,1,1,1] => [3,3,1,1,1,1,1,1] => 2
[3,1,1,3,2,2] => [3,3,2,2,1,1] => 9
[3,1,1,2,1,2,1,1] => [3,2,2,1,1,1,1,1] => 3
[3,1,1,2,1,1,1,2] => [3,2,2,1,1,1,1,1] => 3
[3,1,1,2,2,3] => [3,3,2,2,1,1] => 9
[3,1,1,1,1,3,1,1] => [3,3,1,1,1,1,1,1] => 2
[3,1,1,1,1,2,1,2] => [3,2,2,1,1,1,1,1] => 3
[3,1,1,1,1,1,1,3] => [3,3,1,1,1,1,1,1] => 2
[3,1,1,1,2,4] => [4,3,2,1,1,1] => 28
[3,1,2,4,1,1] => [4,3,2,1,1,1] => 28
[3,1,2,3,1,2] => [3,3,2,2,1,1] => 9
[3,1,2,2,1,3] => [3,3,2,2,1,1] => 9
[3,1,2,1,1,4] => [4,3,2,1,1,1] => 28
[3,1,3,5] => [5,3,3,1] => 145
[4,4,1,1,1,1] => [4,4,1,1,1,1] => 19
[4,4,2,2] => [4,4,2,2] => 137
[4,3,1,2,1,1] => [4,3,2,1,1,1] => 28
[4,3,1,1,1,2] => [4,3,2,1,1,1] => 28
[4,3,2,3] => [4,3,3,2] => 126
[4,2,1,3,1,1] => [4,3,2,1,1,1] => 28
[4,2,1,2,1,2] => [4,2,2,2,1,1] => 14
[4,2,1,1,1,3] => [4,3,2,1,1,1] => 28
[4,2,2,4] => [4,4,2,2] => 137
[4,1,1,4,1,1] => [4,4,1,1,1,1] => 19
[4,1,1,3,1,2] => [4,3,2,1,1,1] => 28
[4,1,1,2,1,3] => [4,3,2,1,1,1] => 28
[4,1,1,1,1,4] => [4,4,1,1,1,1] => 19
[4,1,2,5] => [5,4,2,1] => 349
[5,5,1,1] => [5,5,1,1] => 188
[5,4,1,2] => [5,4,2,1] => 349
[5,3,1,3] => [5,3,3,1] => 145
[5,2,1,4] => [5,4,2,1] => 349
[5,1,1,5] => [5,5,1,1] => 188
[6,6] => [6,6] => 3533
[1,2,2,2,2,2,1] => [2,2,2,2,2,1,1] => 1
[1,2,2,2,3,2] => [3,2,2,2,2,1] => 5
[1,2,2,3,3,1] => [3,3,2,2,1,1] => 9
[1,2,2,3,2,2] => [3,2,2,2,2,1] => 5
[1,2,2,4,3] => [4,3,2,2,1] => 56
[1,2,3,3,2,1] => [3,3,2,2,1,1] => 9
[1,2,3,4,2] => [4,3,2,2,1] => 56
[1,2,3,2,3,1] => [3,3,2,2,1,1] => 9
[1,2,3,2,2,2] => [3,2,2,2,2,1] => 5
[1,2,3,3,3] => [3,3,3,2,1] => 14
[1,2,4,4,1] => [4,4,2,1,1] => 61
[1,2,4,3,2] => [4,3,2,2,1] => 56
[1,2,4,2,3] => [4,3,2,2,1] => 56
[1,2,5,4] => [5,4,2,1] => 349
[1,3,3,2,2,1] => [3,3,2,2,1,1] => 9
[1,3,3,3,2] => [3,3,3,2,1] => 14
[1,3,4,3,1] => [4,3,3,1,1] => 42
[1,3,4,2,2] => [4,3,2,2,1] => 56
[1,3,5,3] => [5,3,3,1] => 145
[1,3,2,3,2,1] => [3,3,2,2,1,1] => 9
[1,3,2,4,2] => [4,3,2,2,1] => 56
[1,3,2,2,3,1] => [3,3,2,2,1,1] => 9
[1,3,2,2,2,2] => [3,2,2,2,2,1] => 5
[1,3,2,3,3] => [3,3,3,2,1] => 14
[1,3,3,4,1] => [4,3,3,1,1] => 42
[1,3,3,2,3] => [3,3,3,2,1] => 14
[1,3,4,4] => [4,4,3,1] => 159
[1,4,4,2,1] => [4,4,2,1,1] => 61
[1,4,5,2] => [5,4,2,1] => 349
[1,4,3,3,1] => [4,3,3,1,1] => 42
[1,4,3,2,2] => [4,3,2,2,1] => 56
[1,4,4,3] => [4,4,3,1] => 159
[1,4,2,4,1] => [4,4,2,1,1] => 61
[1,4,2,3,2] => [4,3,2,2,1] => 56
[1,4,2,2,3] => [4,3,2,2,1] => 56
[1,4,3,4] => [4,4,3,1] => 159
[1,5,5,1] => [5,5,1,1] => 188
[1,5,4,2] => [5,4,2,1] => 349
[1,5,3,3] => [5,3,3,1] => 145
[1,5,2,4] => [5,4,2,1] => 349
[1,6,5] => [6,5,1] => 1407
[2,3,2,2,2,1] => [3,2,2,2,2,1] => 5
[2,3,2,3,2] => [3,3,2,2,2] => 14
[2,3,3,3,1] => [3,3,3,2,1] => 14
[2,3,3,2,2] => [3,3,2,2,2] => 14
[2,3,4,3] => [4,3,3,2] => 126
[2,4,3,2,1] => [4,3,2,2,1] => 56
[2,4,4,2] => [4,4,2,2] => 137
[2,4,2,3,1] => [4,3,2,2,1] => 56
[2,4,2,2,2] => [4,2,2,2,2] => 20
[2,4,3,3] => [4,3,3,2] => 126
[2,5,4,1] => [5,4,2,1] => 349
[2,5,3,2] => [5,3,2,2] => 203
[2,5,2,3] => [5,3,2,2] => 203
[2,6,4] => [6,4,2] => 1500
[2,2,3,2,2,1] => [3,2,2,2,2,1] => 5
[2,2,3,3,2] => [3,3,2,2,2] => 14
[2,2,4,3,1] => [4,3,2,2,1] => 56
[2,2,4,2,2] => [4,2,2,2,2] => 20
[2,2,5,3] => [5,3,2,2] => 203
[2,2,2,3,2,1] => [3,2,2,2,2,1] => 5
[2,2,2,4,2] => [4,2,2,2,2] => 20
[2,2,2,2,3,1] => [3,2,2,2,2,1] => 5
[2,2,2,3,3] => [3,3,2,2,2] => 14
[2,2,3,4,1] => [4,3,2,2,1] => 56
[2,2,3,2,3] => [3,3,2,2,2] => 14
[2,3,4,2,1] => [4,3,2,2,1] => 56
[2,3,5,2] => [5,3,2,2] => 203
[2,3,2,4,1] => [4,3,2,2,1] => 56
[2,3,2,2,3] => [3,3,2,2,2] => 14
[2,3,3,4] => [4,3,3,2] => 126
[2,4,5,1] => [5,4,2,1] => 349
[2,4,2,4] => [4,4,2,2] => 137
[2,5,5] => [5,5,2] => 740
[3,4,2,2,1] => [4,3,2,2,1] => 56
[3,4,3,2] => [4,3,3,2] => 126
[3,5,3,1] => [5,3,3,1] => 145
[3,5,2,2] => [5,3,2,2] => 203
[3,6,3] => [6,3,3] => 626
[3,3,3,2,1] => [3,3,3,2,1] => 14
[3,3,4,2] => [4,3,3,2] => 126
[3,3,2,3,1] => [3,3,3,2,1] => 14
[3,3,2,2,2] => [3,3,2,2,2] => 14
[3,4,4,1] => [4,4,3,1] => 159
[3,4,2,3] => [4,3,3,2] => 126
[3,5,4] => [5,4,3] => 982
[3,2,4,2,1] => [4,3,2,2,1] => 56
[3,2,5,2] => [5,3,2,2] => 203
[3,2,3,3,1] => [3,3,3,2,1] => 14
[3,2,3,2,2] => [3,3,2,2,2] => 14
[3,2,4,3] => [4,3,3,2] => 126
[3,2,2,4,1] => [4,3,2,2,1] => 56
[3,2,2,3,2] => [3,3,2,2,2] => 14
[3,2,2,2,3] => [3,3,2,2,2] => 14
[3,3,5,1] => [5,3,3,1] => 145
[3,3,2,4] => [4,3,3,2] => 126
[3,4,5] => [5,4,3] => 982
[4,5,2,1] => [5,4,2,1] => 349
[4,6,2] => [6,4,2] => 1500
[4,4,3,1] => [4,4,3,1] => 159
[4,5,3] => [5,4,3] => 982
[4,3,4,1] => [4,4,3,1] => 159
[4,3,3,2] => [4,3,3,2] => 126
[4,4,4] => [4,4,4] => 296
[4,2,5,1] => [5,4,2,1] => 349
[4,2,4,2] => [4,4,2,2] => 137
[4,2,3,3] => [4,3,3,2] => 126
[4,3,5] => [5,4,3] => 982
[5,6,1] => [6,5,1] => 1407
[5,5,2] => [5,5,2] => 740
[5,4,3] => [5,4,3] => 982
[5,3,4] => [5,4,3] => 982
[5,2,5] => [5,5,2] => 740
[1,8,2] => [8,2,1] => 474
[1,7,1,2] => [7,2,1,1] => 123
[1,6,1,1,2] => [6,2,1,1,1] => 37
[1,5,1,1,1,2] => [5,2,1,1,1,1] => 12
[1,4,1,1,1,1,2] => [4,2,1,1,1,1,1] => 5
[1,3,1,1,1,1,1,2] => [3,2,1,1,1,1,1,1] => 2
[1,2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1,1] => 1
[1,11] => [11,1] => 8167
[1,9,2] => [9,2,1] => 1907
[1,7,3] => [7,3,1] => 351
[1,8,1,2] => [8,2,1,1] => 474
[1,6,2,2] => [6,2,2,1] => 85
[1,7,1,1,2] => [7,2,1,1,1] => 123
[1,5,2,1,2] => [5,2,2,1,1] => 25
[1,6,1,1,1,2] => [6,2,1,1,1,1] => 37
[1,4,2,1,1,2] => [4,2,2,1,1,1] => 9
[1,5,1,1,1,1,2] => [5,2,1,1,1,1,1] => 12
[1,3,2,1,1,1,2] => [3,2,2,1,1,1,1] => 3
[1,4,1,1,1,1,1,2] => [4,2,1,1,1,1,1,1] => 5
[1,2,2,1,1,1,1,2] => [2,2,2,1,1,1,1,1] => 1
[1,3,1,1,1,1,1,1,2] => [3,2,1,1,1,1,1,1,1] => 2
[1,1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1,1,1] => 1
[1,2,2,2,2,2] => [2,2,2,2,2,1] => 1
[1,2,2,2,1,3] => [3,2,2,2,1,1] => 4
[1,2,2,1,3,2] => [3,2,2,2,1,1] => 4
[1,2,2,1,2,3] => [3,2,2,2,1,1] => 4
[1,2,2,1,1,4] => [4,2,2,1,1,1] => 9
[1,2,1,3,2,2] => [3,2,2,2,1,1] => 4
[1,2,1,3,1,3] => [3,3,2,1,1,1] => 5
[1,2,1,2,3,2] => [3,2,2,2,1,1] => 4
[1,2,1,2,2,3] => [3,2,2,2,1,1] => 4
[1,2,1,2,1,4] => [4,2,2,1,1,1] => 9
[1,2,1,1,4,2] => [4,2,2,1,1,1] => 9
[1,2,1,1,3,3] => [3,3,2,1,1,1] => 5
[1,2,1,1,2,4] => [4,2,2,1,1,1] => 9
[1,2,1,1,1,5] => [5,2,1,1,1,1] => 12
[1,1,3,2,2,2] => [3,2,2,2,1,1] => 4
[1,1,3,2,1,3] => [3,3,2,1,1,1] => 5
[1,1,3,1,3,2] => [3,3,2,1,1,1] => 5
[1,1,3,1,2,3] => [3,3,2,1,1,1] => 5
[1,1,3,1,1,4] => [4,3,1,1,1,1] => 10
[1,1,2,3,2,2] => [3,2,2,2,1,1] => 4
[1,1,2,3,1,3] => [3,3,2,1,1,1] => 5
[1,1,2,2,3,2] => [3,2,2,2,1,1] => 4
[1,1,2,2,2,3] => [3,2,2,2,1,1] => 4
[1,1,2,2,1,4] => [4,2,2,1,1,1] => 9
[1,1,2,1,4,2] => [4,2,2,1,1,1] => 9
[1,1,2,1,3,3] => [3,3,2,1,1,1] => 5
[1,1,2,1,2,4] => [4,2,2,1,1,1] => 9
[1,1,2,1,1,5] => [5,2,1,1,1,1] => 12
[1,1,1,4,2,2] => [4,2,2,1,1,1] => 9
[1,1,1,4,1,3] => [4,3,1,1,1,1] => 10
[1,1,1,3,3,2] => [3,3,2,1,1,1] => 5
[1,1,1,3,2,3] => [3,3,2,1,1,1] => 5
[1,1,1,3,1,4] => [4,3,1,1,1,1] => 10
[1,1,1,2,4,2] => [4,2,2,1,1,1] => 9
[1,1,1,2,3,3] => [3,3,2,1,1,1] => 5
[1,1,1,2,2,4] => [4,2,2,1,1,1] => 9
[1,1,1,2,1,5] => [5,2,1,1,1,1] => 12
[1,1,1,1,5,2] => [5,2,1,1,1,1] => 12
[1,1,1,1,4,3] => [4,3,1,1,1,1] => 10
[1,1,1,1,3,4] => [4,3,1,1,1,1] => 10
[1,1,1,1,2,5] => [5,2,1,1,1,1] => 12
[1,1,1,1,1,6] => [6,1,1,1,1,1] => 11
[12] => [12] => 39700
[1,2,9] => [9,2,1] => 1907
[3,2,7] => [7,3,2] => 1329
[1,4,7] => [7,4,1] => 1551
[1,1,2,1,7] => [7,2,1,1,1] => 123
[1,2,2,2,5] => [5,2,2,2,1] => 44
[1,1,2,3,5] => [5,3,2,1,1] => 89
[3,1,2,1,5] => [5,3,2,1,1] => 89
[1,3,2,1,5] => [5,3,2,1,1] => 89
[1,1,4,1,5] => [5,4,1,1,1] => 99
[1,1,1,2,1,1,5] => [5,2,1,1,1,1,1] => 12
[7,2,3] => [7,3,2] => 1329
[1,1,2,1,2,2,3] => [3,2,2,2,1,1,1] => 4
[1,8,3] => [8,3,1] => 1470
[1,1,2,5,3] => [5,3,2,1,1] => 89
[3,1,2,3,3] => [3,3,3,2,1] => 14
[1,1,4,3,3] => [4,3,3,1,1] => 42
[1,1,1,2,1,3,3] => [3,3,2,1,1,1,1] => 5
[5,1,2,1,3] => [5,3,2,1,1] => 89
[1,2,2,1,2,1,3] => [3,2,2,2,1,1,1] => 4
[3,3,2,1,3] => [3,3,3,2,1] => 14
[1,5,2,1,3] => [5,3,2,1,1] => 89
[1,1,2,2,2,1,3] => [3,2,2,2,1,1,1] => 4
[3,1,4,1,3] => [4,3,3,1,1] => 42
[1,3,4,1,3] => [4,3,3,1,1] => 42
[1,1,6,1,3] => [6,3,1,1,1] => 97
[1,1,1,2,3,1,3] => [3,3,2,1,1,1,1] => 5
[3,1,1,2,1,1,3] => [3,3,2,1,1,1,1] => 5
[1,3,1,2,1,1,3] => [3,3,2,1,1,1,1] => 5
[1,1,3,2,1,1,3] => [3,3,2,1,1,1,1] => 5
[1,1,1,4,1,1,3] => [4,3,1,1,1,1,1] => 10
[1,1,1,1,2,1,1,1,3] => [3,2,1,1,1,1,1,1,1] => 2
[9,2,1] => [9,2,1] => 1907
[1,2,6,2,1] => [6,2,2,1,1] => 85
[1,1,2,1,4,2,1] => [4,2,2,1,1,1,1] => 9
[5,2,2,2,1] => [5,2,2,2,1] => 44
[1,6,2,2,1] => [6,2,2,1,1] => 85
[1,1,2,3,2,2,1] => [3,2,2,2,1,1,1] => 4
[3,1,2,1,2,2,1] => [3,2,2,2,1,1,1] => 4
[1,3,2,1,2,2,1] => [3,2,2,2,1,1,1] => 4
[1,1,4,1,2,2,1] => [4,2,2,1,1,1,1] => 9
[1,1,1,2,1,1,2,2,1] => [2,2,2,1,1,1,1,1,1] => 1
[7,4,1] => [7,4,1] => 1551
[1,1,2,1,2,4,1] => [4,2,2,1,1,1,1] => 9
[1,2,2,6,1] => [6,2,2,1,1] => 85
[3,8,1] => [8,3,1] => 1470
[1,10,1] => [10,1,1] => 1832
[1,1,2,7,1] => [7,2,1,1,1] => 123
[3,1,2,5,1] => [5,3,2,1,1] => 89
[1,3,2,5,1] => [5,3,2,1,1] => 89
[1,1,4,5,1] => [5,4,1,1,1] => 99
[1,1,1,2,1,5,1] => [5,2,1,1,1,1,1] => 12
[5,1,2,3,1] => [5,3,2,1,1] => 89
[1,2,2,1,2,3,1] => [3,2,2,2,1,1,1] => 4
[1,5,2,3,1] => [5,3,2,1,1] => 89
[1,1,2,2,2,3,1] => [3,2,2,2,1,1,1] => 4
[3,1,4,3,1] => [4,3,3,1,1] => 42
[1,1,6,3,1] => [6,3,1,1,1] => 97
[1,1,1,2,3,3,1] => [3,3,2,1,1,1,1] => 5
[3,1,1,2,1,3,1] => [3,3,2,1,1,1,1] => 5
[1,3,1,2,1,3,1] => [3,3,2,1,1,1,1] => 5
[1,1,3,2,1,3,1] => [3,3,2,1,1,1,1] => 5
[1,1,1,4,1,3,1] => [4,3,1,1,1,1,1] => 10
[1,1,1,1,2,1,1,3,1] => [3,2,1,1,1,1,1,1,1] => 2
[7,1,2,1,1] => [7,2,1,1,1] => 123
[1,2,4,1,2,1,1] => [4,2,2,1,1,1,1] => 9
[3,2,2,1,2,1,1] => [3,2,2,2,1,1,1] => 4
[1,4,2,1,2,1,1] => [4,2,2,1,1,1,1] => 9
[1,1,2,1,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[5,3,2,1,1] => [5,3,2,1,1] => 89
[1,2,2,3,2,1,1] => [3,2,2,2,1,1,1] => 4
[3,5,2,1,1] => [5,3,2,1,1] => 89
[1,7,2,1,1] => [7,2,1,1,1] => 123
[1,1,2,4,2,1,1] => [4,2,2,1,1,1,1] => 9
[3,1,2,2,2,1,1] => [3,2,2,2,1,1,1] => 4
[1,3,2,2,2,1,1] => [3,2,2,2,1,1,1] => 4
[1,1,4,2,2,1,1] => [4,2,2,1,1,1,1] => 9
[1,1,1,2,1,2,2,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[5,1,4,1,1] => [5,4,1,1,1] => 99
[1,2,2,1,4,1,1] => [4,2,2,1,1,1,1] => 9
[3,3,4,1,1] => [4,3,3,1,1] => 42
[1,5,4,1,1] => [5,4,1,1,1] => 99
[1,1,2,2,4,1,1] => [4,2,2,1,1,1,1] => 9
[3,1,6,1,1] => [6,3,1,1,1] => 97
[1,3,6,1,1] => [6,3,1,1,1] => 97
[1,1,8,1,1] => [8,1,1,1,1] => 116
[1,1,1,2,5,1,1] => [5,2,1,1,1,1,1] => 12
[3,1,1,2,3,1,1] => [3,3,2,1,1,1,1] => 5
[1,3,1,2,3,1,1] => [3,3,2,1,1,1,1] => 5
[1,1,3,2,3,1,1] => [3,3,2,1,1,1,1] => 5
[1,1,1,4,3,1,1] => [4,3,1,1,1,1,1] => 10
[1,1,1,1,2,1,3,1,1] => [3,2,1,1,1,1,1,1,1] => 2
[5,1,1,2,1,1,1] => [5,2,1,1,1,1,1] => 12
[1,2,2,1,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[3,3,1,2,1,1,1] => [3,3,2,1,1,1,1] => 5
[1,5,1,2,1,1,1] => [5,2,1,1,1,1,1] => 12
[1,1,2,2,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[3,1,3,2,1,1,1] => [3,3,2,1,1,1,1] => 5
[1,3,3,2,1,1,1] => [3,3,2,1,1,1,1] => 5
[1,1,5,2,1,1,1] => [5,2,1,1,1,1,1] => 12
[1,1,1,2,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[3,1,1,4,1,1,1] => [4,3,1,1,1,1,1] => 10
[1,3,1,4,1,1,1] => [4,3,1,1,1,1,1] => 10
[1,1,3,4,1,1,1] => [4,3,1,1,1,1,1] => 10
[1,1,1,6,1,1,1] => [6,1,1,1,1,1,1] => 11
[1,1,1,1,2,3,1,1,1] => [3,2,1,1,1,1,1,1,1] => 2
[3,1,1,1,2,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => 2
[1,3,1,1,2,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => 2
[1,1,3,1,2,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => 2
[1,1,1,3,2,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => 2
[1,1,1,1,4,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => 2
[1,1,1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 1
[2,2,2,2,1,2,1] => [2,2,2,2,2,1,1] => 1
[2,2,2,1,2,1,2] => [2,2,2,2,2,1,1] => 1
[2,2,2,1,2,2,1] => [2,2,2,2,2,1,1] => 1
[2,2,2,1,1,2,2] => [2,2,2,2,2,1,1] => 1
[2,2,1,2,1,2,2] => [2,2,2,2,2,1,1] => 1
[2,2,1,2,1,1,2,1] => [2,2,2,2,1,1,1,1] => 1
[2,2,1,2,2,1,2] => [2,2,2,2,2,1,1] => 1
[2,2,1,2,2,2,1] => [2,2,2,2,2,1,1] => 1
[2,2,1,1,2,2,2] => [2,2,2,2,2,1,1] => 1
[2,2,1,1,2,1,2,1] => [2,2,2,2,1,1,1,1] => 1
[2,2,1,1,1,2,2,1] => [2,2,2,2,1,1,1,1] => 1
[2,1,2,1,2,2,2] => [2,2,2,2,2,1,1] => 1
[2,1,2,1,2,1,2,1] => [2,2,2,2,1,1,1,1] => 1
[2,1,2,1,1,2,2,1] => [2,2,2,2,1,1,1,1] => 1
[2,1,2,1,1,1,2,2] => [2,2,2,2,1,1,1,1] => 1
[2,1,2,2,1,2,2] => [2,2,2,2,2,1,1] => 1
[2,1,2,2,1,1,2,1] => [2,2,2,2,1,1,1,1] => 1
[2,1,2,2,2,1,2] => [2,2,2,2,2,1,1] => 1
[2,1,2,2,2,2,1] => [2,2,2,2,2,1,1] => 1
[2,1,1,2,2,2,2] => [2,2,2,2,2,1,1] => 1
[2,1,1,2,2,1,2,1] => [2,2,2,2,1,1,1,1] => 1
[2,1,1,2,1,2,1,2] => [2,2,2,2,1,1,1,1] => 1
[2,1,1,2,1,2,2,1] => [2,2,2,2,1,1,1,1] => 1
[2,1,1,1,2,2,2,1] => [2,2,2,2,1,1,1,1] => 1
[2,1,1,1,2,1,2,2] => [2,2,2,2,1,1,1,1] => 1
[1,2,1,2,2,2,2] => [2,2,2,2,2,1,1] => 1
[1,2,1,2,2,1,2,1] => [2,2,2,2,1,1,1,1] => 1
[1,2,1,2,1,2,1,2] => [2,2,2,2,1,1,1,1] => 1
[1,2,1,2,1,2,2,1] => [2,2,2,2,1,1,1,1] => 1
[1,2,1,2,1,1,2,2] => [2,2,2,2,1,1,1,1] => 1
[1,2,1,1,2,1,2,2] => [2,2,2,2,1,1,1,1] => 1
[1,2,1,1,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,2,1,1,2,2,1,2] => [2,2,2,2,1,1,1,1] => 1
[1,2,1,1,2,2,2,1] => [2,2,2,2,1,1,1,1] => 1
[1,2,1,1,1,2,2,2] => [2,2,2,2,1,1,1,1] => 1
[1,2,1,1,1,2,1,2,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,2,2,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,2,2,1,2,2,2] => [2,2,2,2,2,1,1] => 1
[1,2,2,1,2,1,2,1] => [2,2,2,2,1,1,1,1] => 1
[1,2,2,1,1,2,1,2] => [2,2,2,2,1,1,1,1] => 1
[1,2,2,1,1,2,2,1] => [2,2,2,2,1,1,1,1] => 1
[1,2,2,1,1,1,2,2] => [2,2,2,2,1,1,1,1] => 1
[1,2,2,2,1,2,2] => [2,2,2,2,2,1,1] => 1
[1,2,2,2,1,1,2,1] => [2,2,2,2,1,1,1,1] => 1
[1,2,2,2,2,1,2] => [2,2,2,2,2,1,1] => 1
[1,1,2,2,2,2,2] => [2,2,2,2,2,1,1] => 1
[1,1,2,2,2,1,2,1] => [2,2,2,2,1,1,1,1] => 1
[1,1,2,2,1,2,1,2] => [2,2,2,2,1,1,1,1] => 1
[1,1,2,2,1,2,2,1] => [2,2,2,2,1,1,1,1] => 1
[1,1,2,1,2,1,2,2] => [2,2,2,2,1,1,1,1] => 1
[1,1,2,1,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,2,1,2,2,2,1] => [2,2,2,2,1,1,1,1] => 1
[1,1,2,1,1,2,1,2,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,2,2,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,1,2,2,1,2,2] => [2,2,2,2,1,1,1,1] => 1
[1,1,1,2,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,1,2,2,2,1,2] => [2,2,2,2,1,1,1,1] => 1
[1,1,1,2,2,2,2,1] => [2,2,2,2,1,1,1,1] => 1
[1,1,1,2,1,2,2,2] => [2,2,2,2,1,1,1,1] => 1
[1,1,1,2,1,2,1,2,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,1,1,2,2,1,2,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,1,1,2,1,2,2,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,2,2,1] => [2,2,2,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 1
[3,2,2,2,2,1] => [3,2,2,2,2,1] => 5
[4,3,2,2,1] => [4,3,2,2,1] => 56
[4,2,3,2,1] => [4,3,2,2,1] => 56
[4,2,2,3,1] => [4,3,2,2,1] => 56
[4,2,2,2,2] => [4,2,2,2,2] => 20
[5,4,2,1] => [5,4,2,1] => 349
[5,3,3,1] => [5,3,3,1] => 145
[5,3,2,2] => [5,3,2,2] => 203
[5,2,4,1] => [5,4,2,1] => 349
[5,2,3,2] => [5,3,2,2] => 203
[5,2,2,3] => [5,3,2,2] => 203
[6,5,1] => [6,5,1] => 1407
[6,4,2] => [6,4,2] => 1500
[6,3,3] => [6,3,3] => 626
[6,2,4] => [6,4,2] => 1500
[7,5] => [7,5] => 6009
[2,8,1] => [8,2,1] => 474
[2,1,7,1] => [7,2,1,1] => 123
[2,1,1,6,1] => [6,2,1,1,1] => 37
[2,1,1,1,5,1] => [5,2,1,1,1,1] => 12
[2,1,1,1,1,4,1] => [4,2,1,1,1,1,1] => 5
[2,1,1,1,1,1,3,1] => [3,2,1,1,1,1,1,1] => 2
[2,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1] => 1
[11,1] => [11,1] => 8167
[2,9,1] => [9,2,1] => 1907
[3,7,1] => [7,3,1] => 351
[2,1,8,1] => [8,2,1,1] => 474
[2,2,6,1] => [6,2,2,1] => 85
[2,1,1,7,1] => [7,2,1,1,1] => 123
[2,1,2,5,1] => [5,2,2,1,1] => 25
[2,1,1,1,6,1] => [6,2,1,1,1,1] => 37
[2,1,1,2,4,1] => [4,2,2,1,1,1] => 9
[2,1,1,1,1,5,1] => [5,2,1,1,1,1,1] => 12
[2,1,1,1,2,3,1] => [3,2,2,1,1,1,1] => 3
[2,1,1,1,1,1,4,1] => [4,2,1,1,1,1,1,1] => 5
[2,1,1,1,1,2,2,1] => [2,2,2,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,3,1] => [3,2,1,1,1,1,1,1,1] => 2
[2,1,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 1
[2,2,2,2,2,1] => [2,2,2,2,2,1] => 1
[3,1,2,2,2,1] => [3,2,2,2,1,1] => 4
[2,3,1,2,2,1] => [3,2,2,2,1,1] => 4
[3,2,1,2,2,1] => [3,2,2,2,1,1] => 4
[4,1,1,2,2,1] => [4,2,2,1,1,1] => 9
[2,2,3,1,2,1] => [3,2,2,2,1,1] => 4
[3,1,3,1,2,1] => [3,3,2,1,1,1] => 5
[2,3,2,1,2,1] => [3,2,2,2,1,1] => 4
[3,2,2,1,2,1] => [3,2,2,2,1,1] => 4
[4,1,2,1,2,1] => [4,2,2,1,1,1] => 9
[2,4,1,1,2,1] => [4,2,2,1,1,1] => 9
[3,3,1,1,2,1] => [3,3,2,1,1,1] => 5
[4,2,1,1,2,1] => [4,2,2,1,1,1] => 9
[5,1,1,1,2,1] => [5,2,1,1,1,1] => 12
[2,2,2,3,1,1] => [3,2,2,2,1,1] => 4
[3,1,2,3,1,1] => [3,3,2,1,1,1] => 5
[2,3,1,3,1,1] => [3,3,2,1,1,1] => 5
[3,2,1,3,1,1] => [3,3,2,1,1,1] => 5
[4,1,1,3,1,1] => [4,3,1,1,1,1] => 10
[2,2,3,2,1,1] => [3,2,2,2,1,1] => 4
[3,1,3,2,1,1] => [3,3,2,1,1,1] => 5
[2,3,2,2,1,1] => [3,2,2,2,1,1] => 4
[3,2,2,2,1,1] => [3,2,2,2,1,1] => 4
[4,1,2,2,1,1] => [4,2,2,1,1,1] => 9
[2,4,1,2,1,1] => [4,2,2,1,1,1] => 9
[3,3,1,2,1,1] => [3,3,2,1,1,1] => 5
[4,2,1,2,1,1] => [4,2,2,1,1,1] => 9
[5,1,1,2,1,1] => [5,2,1,1,1,1] => 12
[2,2,4,1,1,1] => [4,2,2,1,1,1] => 9
[3,1,4,1,1,1] => [4,3,1,1,1,1] => 10
[2,3,3,1,1,1] => [3,3,2,1,1,1] => 5
[3,2,3,1,1,1] => [3,3,2,1,1,1] => 5
[4,1,3,1,1,1] => [4,3,1,1,1,1] => 10
[2,4,2,1,1,1] => [4,2,2,1,1,1] => 9
[3,3,2,1,1,1] => [3,3,2,1,1,1] => 5
[4,2,2,1,1,1] => [4,2,2,1,1,1] => 9
[5,1,2,1,1,1] => [5,2,1,1,1,1] => 12
[2,5,1,1,1,1] => [5,2,1,1,1,1] => 12
[3,4,1,1,1,1] => [4,3,1,1,1,1] => 10
[4,3,1,1,1,1] => [4,3,1,1,1,1] => 10
[5,2,1,1,1,1] => [5,2,1,1,1,1] => 12
[6,1,1,1,1,1] => [6,1,1,1,1,1] => 11
[2,2,1,2,1,2,1,1] => [2,2,2,2,1,1,1,1] => 1
[2,2,1,1,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[2,1,2,1,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[2,1,2,1,2,1,1,2] => [2,2,2,2,1,1,1,1] => 1
[2,1,2,1,2,2,1,1] => [2,2,2,2,1,1,1,1] => 1
[2,1,2,1,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[2,1,1,2,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 1
[2,1,1,2,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[2,1,1,2,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[2,1,1,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1] => 1
[2,1,1,1,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 1
[2,1,1,1,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[2,1,1,1,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,2,1,2,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,2,1,1,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,2,1,1,1,2,1,1,2] => [2,2,2,1,1,1,1,1,1] => 1
[1,2,1,1,1,2,2,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,2,2,1,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,2,2,2,1,2,1,1] => [2,2,2,2,1,1,1,1] => 1
[1,2,2,1,2,1,1,2] => [2,2,2,2,1,1,1,1] => 1
[1,2,2,1,2,2,1,1] => [2,2,2,2,1,1,1,1] => 1
[1,2,1,2,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,2,1,2,2,1,1,2] => [2,2,2,2,1,1,1,1] => 1
[1,2,1,2,2,2,1,1] => [2,2,2,2,1,1,1,1] => 1
[1,2,1,2,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,2,1,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1] => 1
[1,2,1,1,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,2,1,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,2,1,2] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,2,1,1,2,1,1,2] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,2,1,1,2,2,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,2,2,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,2,2,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,2,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,2,1,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,1,2,2] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,2,1,2] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,1,2,1,2,1,1,2] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,1,2,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,1,2,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,3] => [3,2,1,1,1,1,1,1] => 2
[2,1,1,1,1,1,2,2] => [2,2,2,1,1,1,1,1] => 1
[2,1,1,1,1,2,1,2] => [2,2,2,1,1,1,1,1] => 1
[2,1,1,1,2,1,1,2] => [2,2,2,1,1,1,1,1] => 1
[2,1,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1] => 1
[2,1,2,1,1,1,1,2] => [2,2,2,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,2] => [2,2,2,1,1,1,1,1] => 1
[3,1,1,1,1,1,1,2] => [3,2,1,1,1,1,1,1] => 2
[1,2,2,4,2,1] => [4,2,2,2,1,1] => 14
[1,2,4,2,2,1] => [4,2,2,2,1,1] => 14
[1,2,5,2,2] => [5,2,2,2,1] => 44
[1,3,5,2,1] => [5,3,2,1,1] => 89
[1,4,2,2,2,1] => [4,2,2,2,1,1] => 14
[1,5,2,2,2] => [5,2,2,2,1] => 44
[1,5,3,2,1] => [5,3,2,1,1] => 89
[2,5,2,2,1] => [5,2,2,2,1] => 44
[2,6,2,2] => [6,2,2,2] => 163
[2,2,5,2,1] => [5,2,2,2,1] => 44
[6,2,2,2] => [6,2,2,2] => 163
[2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 1
[1,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1,1] => 1
[1,2,2,1,2,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,2,1,2,2,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,2,1,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 1
[9,2] => [9,2] => 1907
[1,9,1] => [9,1,1] => 435
[10,2] => [10,2] => 8593
[1,1,1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,2,2,2,3,1,1] => [3,2,2,2,1,1,1] => 4
[1,2,2,3,1,2,1] => [3,2,2,2,1,1,1] => 4
[1,2,2,4,1,1,1] => [4,2,2,1,1,1,1] => 9
[1,2,3,1,2,2,1] => [3,2,2,2,1,1,1] => 4
[1,2,3,1,3,1,1] => [3,3,2,1,1,1,1] => 5
[1,2,3,2,1,2,1] => [3,2,2,2,1,1,1] => 4
[1,2,4,1,1,2,1] => [4,2,2,1,1,1,1] => 9
[1,2,3,2,2,1,1] => [3,2,2,2,1,1,1] => 4
[1,2,3,3,1,1,1] => [3,3,2,1,1,1,1] => 5
[1,2,4,2,1,1,1] => [4,2,2,1,1,1,1] => 9
[1,2,5,1,1,1,1] => [5,2,1,1,1,1,1] => 12
[1,3,1,2,2,2,1] => [3,2,2,2,1,1,1] => 4
[1,3,1,3,1,2,1] => [3,3,2,1,1,1,1] => 5
[1,3,1,3,2,1,1] => [3,3,2,1,1,1,1] => 5
[1,3,2,1,3,1,1] => [3,3,2,1,1,1,1] => 5
[1,4,1,1,2,2,1] => [4,2,2,1,1,1,1] => 9
[1,4,1,1,3,1,1] => [4,3,1,1,1,1,1] => 10
[1,3,2,2,1,2,1] => [3,2,2,2,1,1,1] => 4
[1,3,3,1,1,2,1] => [3,3,2,1,1,1,1] => 5
[1,4,1,2,1,2,1] => [4,2,2,1,1,1,1] => 9
[1,4,2,1,1,2,1] => [4,2,2,1,1,1,1] => 9
[1,5,1,1,1,2,1] => [5,2,1,1,1,1,1] => 12
[1,3,2,3,1,1,1] => [3,3,2,1,1,1,1] => 5
[1,3,3,1,2,1,1] => [3,3,2,1,1,1,1] => 5
[1,3,4,1,1,1,1] => [4,3,1,1,1,1,1] => 10
[1,4,1,2,2,1,1] => [4,2,2,1,1,1,1] => 9
[1,4,1,3,1,1,1] => [4,3,1,1,1,1,1] => 10
[1,5,1,1,2,1,1] => [5,2,1,1,1,1,1] => 12
[1,4,2,2,1,1,1] => [4,2,2,1,1,1,1] => 9
[1,4,3,1,1,1,1] => [4,3,1,1,1,1,1] => 10
[1,5,2,1,1,1,1] => [5,2,1,1,1,1,1] => 12
[1,6,1,1,1,1,1] => [6,1,1,1,1,1,1] => 11
[2,1,2,2,3,1,1] => [3,2,2,2,1,1,1] => 4
[2,1,2,3,1,2,1] => [3,2,2,2,1,1,1] => 4
[2,1,2,3,2,1,1] => [3,2,2,2,1,1,1] => 4
[2,1,2,4,1,1,1] => [4,2,2,1,1,1,1] => 9
[2,1,3,1,2,2,1] => [3,2,2,2,1,1,1] => 4
[2,1,3,1,3,1,1] => [3,3,2,1,1,1,1] => 5
[2,1,3,2,1,2,1] => [3,2,2,2,1,1,1] => 4
[2,1,4,1,1,2,1] => [4,2,2,1,1,1,1] => 9
[2,1,3,2,2,1,1] => [3,2,2,2,1,1,1] => 4
[2,1,3,3,1,1,1] => [3,3,2,1,1,1,1] => 5
[2,1,4,1,2,1,1] => [4,2,2,1,1,1,1] => 9
[2,1,4,2,1,1,1] => [4,2,2,1,1,1,1] => 9
[2,1,5,1,1,1,1] => [5,2,1,1,1,1,1] => 12
[2,2,1,2,3,1,1] => [3,2,2,2,1,1,1] => 4
[2,2,1,3,1,2,1] => [3,2,2,2,1,1,1] => 4
[2,2,1,3,2,1,1] => [3,2,2,2,1,1,1] => 4
[2,2,1,4,1,1,1] => [4,2,2,1,1,1,1] => 9
[3,1,1,2,2,2,1] => [3,2,2,2,1,1,1] => 4
[3,1,1,3,1,2,1] => [3,3,2,1,1,1,1] => 5
[3,1,1,3,2,1,1] => [3,3,2,1,1,1,1] => 5
[2,2,2,1,3,1,1] => [3,2,2,2,1,1,1] => 4
[2,3,1,1,2,2,1] => [3,2,2,2,1,1,1] => 4
[2,3,1,1,3,1,1] => [3,3,2,1,1,1,1] => 5
[3,1,2,1,3,1,1] => [3,3,2,1,1,1,1] => 5
[3,2,1,1,2,2,1] => [3,2,2,2,1,1,1] => 4
[3,2,1,1,3,1,1] => [3,3,2,1,1,1,1] => 5
[4,1,1,1,2,2,1] => [4,2,2,1,1,1,1] => 9
[4,1,1,1,3,1,1] => [4,3,1,1,1,1,1] => 10
[2,2,3,1,1,2,1] => [3,2,2,2,1,1,1] => 4
[2,3,1,2,1,2,1] => [3,2,2,2,1,1,1] => 4
[2,3,2,1,1,2,1] => [3,2,2,2,1,1,1] => 4
[2,4,1,1,1,2,1] => [4,2,2,1,1,1,1] => 9
[3,1,2,2,1,2,1] => [3,2,2,2,1,1,1] => 4
[3,1,3,1,1,2,1] => [3,3,2,1,1,1,1] => 5
[3,2,1,2,1,2,1] => [3,2,2,2,1,1,1] => 4
[4,1,1,2,1,2,1] => [4,2,2,1,1,1,1] => 9
[3,2,2,1,1,2,1] => [3,2,2,2,1,1,1] => 4
[3,3,1,1,1,2,1] => [3,3,2,1,1,1,1] => 5
[4,1,2,1,1,2,1] => [4,2,2,1,1,1,1] => 9
[4,2,1,1,1,2,1] => [4,2,2,1,1,1,1] => 9
[5,1,1,1,1,2,1] => [5,2,1,1,1,1,1] => 12
[2,2,2,3,1,1,1] => [3,2,2,2,1,1,1] => 4
[2,2,3,1,2,1,1] => [3,2,2,2,1,1,1] => 4
[2,2,3,2,1,1,1] => [3,2,2,2,1,1,1] => 4
[2,2,4,1,1,1,1] => [4,2,2,1,1,1,1] => 9
[2,3,1,2,2,1,1] => [3,2,2,2,1,1,1] => 4
[2,3,1,3,1,1,1] => [3,3,2,1,1,1,1] => 5
[2,3,2,1,2,1,1] => [3,2,2,2,1,1,1] => 4
[2,4,1,1,2,1,1] => [4,2,2,1,1,1,1] => 9
[2,3,2,2,1,1,1] => [3,2,2,2,1,1,1] => 4
[2,3,3,1,1,1,1] => [3,3,2,1,1,1,1] => 5
[2,4,1,2,1,1,1] => [4,2,2,1,1,1,1] => 9
[2,4,2,1,1,1,1] => [4,2,2,1,1,1,1] => 9
[2,5,1,1,1,1,1] => [5,2,1,1,1,1,1] => 12
[3,1,2,3,1,1,1] => [3,3,2,1,1,1,1] => 5
[3,1,3,1,2,1,1] => [3,3,2,1,1,1,1] => 5
[3,1,4,1,1,1,1] => [4,3,1,1,1,1,1] => 10
[3,2,1,2,2,1,1] => [3,2,2,2,1,1,1] => 4
[3,2,1,3,1,1,1] => [3,3,2,1,1,1,1] => 5
[4,1,1,2,2,1,1] => [4,2,2,1,1,1,1] => 9
[4,1,1,3,1,1,1] => [4,3,1,1,1,1,1] => 10
[3,3,1,1,2,1,1] => [3,3,2,1,1,1,1] => 5
[4,1,2,1,2,1,1] => [4,2,2,1,1,1,1] => 9
[4,2,1,1,2,1,1] => [4,2,2,1,1,1,1] => 9
[5,1,1,1,2,1,1] => [5,2,1,1,1,1,1] => 12
[3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => 4
[3,2,3,1,1,1,1] => [3,3,2,1,1,1,1] => 5
[3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => 5
[3,4,1,1,1,1,1] => [4,3,1,1,1,1,1] => 10
[4,1,2,2,1,1,1] => [4,2,2,1,1,1,1] => 9
[4,1,3,1,1,1,1] => [4,3,1,1,1,1,1] => 10
[4,2,1,2,1,1,1] => [4,2,2,1,1,1,1] => 9
[4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => 9
[4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => 10
[5,1,2,1,1,1,1] => [5,2,1,1,1,1,1] => 12
[5,2,1,1,1,1,1] => [5,2,1,1,1,1,1] => 12
[6,1,1,1,1,1,1] => [6,1,1,1,1,1,1] => 11
[11] => [11] => 8167
[2,9] => [9,2] => 1907
[1,1,2,2,4,1] => [4,2,2,1,1,1] => 9
[1,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 1
[1,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,2,2,1,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,2,3,2,3] => [3,3,2,2,1,1] => 9
[1,2,2,2,2,3] => [3,2,2,2,2,1] => 5
[5,1,1,1,1,2] => [5,2,1,1,1,1] => 12
[1,1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,5,1] => [5,1,1,1,1,1,1] => 4
[1,1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1,1] => 1
[1,1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => 1
[1,1,1,3,1,3,1] => [3,3,1,1,1,1,1] => 2
[1,1,1,5,1,1,1] => [5,1,1,1,1,1,1] => 4
[1,1,1,7,1] => [7,1,1,1,1] => 33
[1,1,1,4,1,2,1] => [4,2,1,1,1,1,1] => 5
[1,1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1] => 1
[1,1,1,2,1,4,1] => [4,2,1,1,1,1,1] => 5
[1,1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1] => 1
[1,1,1,2,3,2,1] => [3,2,2,1,1,1,1] => 3
[1,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => 1
[1,3,1,1,1,3,1] => [3,3,1,1,1,1,1] => 2
[1,3,1,3,1,1,1] => [3,3,1,1,1,1,1] => 2
[1,3,1,5,1] => [5,3,1,1,1] => 27
[1,3,1,2,1,2,1] => [3,2,2,1,1,1,1] => 3
[1,5,1,1,1,1,1] => [5,1,1,1,1,1,1] => 4
[1,5,1,3,1] => [5,3,1,1,1] => 27
[1,7,1,1,1] => [7,1,1,1,1] => 33
[1,6,1,2,1] => [6,2,1,1,1] => 37
[1,4,1,2,1,1,1] => [4,2,1,1,1,1,1] => 5
[1,4,1,4,1] => [4,4,1,1,1] => 19
[1,4,1,1,1,2,1] => [4,2,1,1,1,1,1] => 5
[1,4,3,2,1] => [4,3,2,1,1] => 28
[1,2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 1
[1,2,1,2,1,3,1] => [3,2,2,1,1,1,1] => 3
[1,2,1,4,1,1,1] => [4,2,1,1,1,1,1] => 5
[1,2,1,6,1] => [6,2,1,1,1] => 37
[1,2,1,3,1,2,1] => [3,2,2,1,1,1,1] => 3
[1,2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1] => 1
[1,2,1,1,1,4,1] => [4,2,1,1,1,1,1] => 5
[1,2,1,1,3,2,1] => [3,2,2,1,1,1,1] => 3
[1,2,3,2,1,1,1] => [3,2,2,1,1,1,1] => 3
[1,2,3,4,1] => [4,3,2,1,1] => 28
[1,2,3,1,1,2,1] => [3,2,2,1,1,1,1] => 3
[1,2,5,2,1] => [5,2,2,1,1] => 25
[1,2,2,1,2,2,1] => [2,2,2,2,1,1,1] => 1
[1,4,3,4,1] => [4,4,3,1,1] => 159
[1,4,5,2,1] => [5,4,2,1,1] => 349
[1,2,5,4,1] => [5,4,2,1,1] => 349
[1,1,9] => [9,1,1] => 435
[1,1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,2,2,1,2,3] => [3,2,2,2,1,1,1] => 4
[1,1,1,1,2,2,2,1,1] => [2,2,2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,2,2,2,3] => [3,2,2,2,1,1,1] => 4
[1,6,4] => [6,4,1] => 384
[1,5,5] => [5,5,1] => 188
[1,4,6] => [6,4,1] => 384
[1,3,7] => [7,3,1] => 351
[1,2,8] => [8,2,1] => 474
[1,2,1,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,2,1,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,2,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 1
[1,1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1] => 1
[1,1,2,2,2,2,1] => [2,2,2,2,1,1,1] => 1
[1,1,2,2,2,1,1,1] => [2,2,2,1,1,1,1,1] => 1
[1,1,2,2,3,1,1] => [3,2,2,1,1,1,1] => 3
[1,1,2,2,1,2,1,1] => [2,2,2,1,1,1,1,1] => 1
[1,1,2,3,2,1,1] => [3,2,2,1,1,1,1] => 3
[1,1,2,1,2,2,1,1] => [2,2,2,1,1,1,1,1] => 1
[1,1,3,2,2,1,1] => [3,2,2,1,1,1,1] => 3
[1,1,1,2,2,2,1,1] => [2,2,2,1,1,1,1,1] => 1
[1,2,2,2,2,1,1] => [2,2,2,2,1,1,1] => 1
[1,1,2,2,2,4] => [4,2,2,2,1,1] => 14
[1,1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 1
[1,1,2,5,1,1] => [5,2,1,1,1,1] => 12
[1,1,5,2,1,1] => [5,2,1,1,1,1] => 12
[1,1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1,1] => 1
[1,4,2,2,1,1] => [4,2,2,1,1,1] => 9
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
7,1 11,4,0,1 17,10,0,2,2,0,0,0,0,0,1 26,19,3,3,6,0,0,0,0,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 4\ q$
$F_{4} = 7\ q + q^{2}$
$F_{5} = 11\ q + 4\ q^{2} + q^{4}$
$F_{6} = 17\ q + 10\ q^{2} + 2\ q^{4} + 2\ q^{5} + q^{11}$
$F_{7} = 26\ q + 19\ q^{2} + 3\ q^{3} + 3\ q^{4} + 6\ q^{5} + 2\ q^{10} + 2\ q^{11} + 2\ q^{12} + q^{33}$
$F_{8} = 40\ q + 31\ q^{2} + 12\ q^{3} + 4\ q^{4} + 15\ q^{5} + 3\ q^{9} + 6\ q^{10} + 3\ q^{11} + 6\ q^{12} + q^{19} + 2\ q^{27} + 2\ q^{33} + 2\ q^{37} + q^{116}$
$F_{9} = 62\ q + 46\ q^{2} + 30\ q^{3} + 9\ q^{4} + 33\ q^{5} + 12\ q^{9} + 12\ q^{10} + 4\ q^{11} + 12\ q^{12} + 3\ q^{19} + 3\ q^{25} + 6\ q^{27} + 6\ q^{28} + 3\ q^{33} + 6\ q^{37} + 2\ q^{97} + 2\ q^{99} + 2\ q^{116} + 2\ q^{123} + q^{435}$
$F_{10} = 97\ q + 64\ q^{2} + 60\ q^{3} + 26\ q^{4} + 64\ q^{5} + 36\ q^{9} + 20\ q^{10} + 5\ q^{11} + 20\ q^{12} + 4\ q^{14} + 6\ q^{19} + 12\ q^{25} + 12\ q^{27} + 24\ q^{28} + 4\ q^{33} + 12\ q^{37} + 3\ q^{42} + 3\ q^{61} + 3\ q^{85} + 6\ q^{89} + 6\ q^{97} + 6\ q^{99} + 3\ q^{116} + 6\ q^{123} + q^{188} + 2\ q^{351} + 2\ q^{384} + 2\ q^{435} + 2\ q^{474} + q^{1832}$
Description
The number of ways to refine the partition into singletons.
For example there is only one way to refine $[2,2]$: $[2,2] > [2,1,1] > [1,1,1,1]$. However, there are two ways to refine $[3,2]$: $[3,2] > [2,2,1] > [2,1,1,1] > [1,1,1,1,1$ and $[3,2] > [3,1,1] > [2,1,1,1] > [1,1,1,1,1]$.
In other words, this is the number of saturated chains in the refinement order from the bottom element to the given partition.
The sequence of values on the partitions with only one part is A002846.
For example there is only one way to refine $[2,2]$: $[2,2] > [2,1,1] > [1,1,1,1]$. However, there are two ways to refine $[3,2]$: $[3,2] > [2,2,1] > [2,1,1,1] > [1,1,1,1,1$ and $[3,2] > [3,1,1] > [2,1,1,1] > [1,1,1,1,1]$.
In other words, this is the number of saturated chains in the refinement order from the bottom element to the given partition.
The sequence of values on the partitions with only one part is A002846.
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
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