Identifier
-
Mp00040:
Integer compositions
—to partition⟶
Integer partitions
St000003: 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] => 2
[2,1] => [2,1] => 2
[3] => [3] => 1
[1,1,1,1] => [1,1,1,1] => 1
[1,1,2] => [2,1,1] => 3
[1,2,1] => [2,1,1] => 3
[1,3] => [3,1] => 3
[2,1,1] => [2,1,1] => 3
[2,2] => [2,2] => 2
[3,1] => [3,1] => 3
[4] => [4] => 1
[1,1,1,1,1] => [1,1,1,1,1] => 1
[1,1,1,2] => [2,1,1,1] => 4
[1,1,2,1] => [2,1,1,1] => 4
[1,1,3] => [3,1,1] => 6
[1,2,1,1] => [2,1,1,1] => 4
[1,2,2] => [2,2,1] => 5
[1,3,1] => [3,1,1] => 6
[1,4] => [4,1] => 4
[2,1,1,1] => [2,1,1,1] => 4
[2,1,2] => [2,2,1] => 5
[2,2,1] => [2,2,1] => 5
[2,3] => [3,2] => 5
[3,1,1] => [3,1,1] => 6
[3,2] => [3,2] => 5
[4,1] => [4,1] => 4
[5] => [5] => 1
[1,1,1,1,1,1] => [1,1,1,1,1,1] => 1
[1,1,1,1,2] => [2,1,1,1,1] => 5
[1,1,1,2,1] => [2,1,1,1,1] => 5
[1,1,1,3] => [3,1,1,1] => 10
[1,1,2,1,1] => [2,1,1,1,1] => 5
[1,1,2,2] => [2,2,1,1] => 9
[1,1,3,1] => [3,1,1,1] => 10
[1,1,4] => [4,1,1] => 10
[1,2,1,1,1] => [2,1,1,1,1] => 5
[1,2,1,2] => [2,2,1,1] => 9
[1,2,2,1] => [2,2,1,1] => 9
[1,2,3] => [3,2,1] => 16
[1,3,1,1] => [3,1,1,1] => 10
[1,3,2] => [3,2,1] => 16
[1,4,1] => [4,1,1] => 10
[1,5] => [5,1] => 5
[2,1,1,1,1] => [2,1,1,1,1] => 5
[2,1,1,2] => [2,2,1,1] => 9
[2,1,2,1] => [2,2,1,1] => 9
[2,1,3] => [3,2,1] => 16
[2,2,1,1] => [2,2,1,1] => 9
[2,2,2] => [2,2,2] => 5
[2,3,1] => [3,2,1] => 16
[2,4] => [4,2] => 9
[3,1,1,1] => [3,1,1,1] => 10
[3,1,2] => [3,2,1] => 16
[3,2,1] => [3,2,1] => 16
[3,3] => [3,3] => 5
[4,1,1] => [4,1,1] => 10
[4,2] => [4,2] => 9
[5,1] => [5,1] => 5
[6] => [6] => 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] => 6
[1,1,1,1,2,1] => [2,1,1,1,1,1] => 6
[1,1,1,1,3] => [3,1,1,1,1] => 15
[1,1,1,2,1,1] => [2,1,1,1,1,1] => 6
[1,1,1,2,2] => [2,2,1,1,1] => 14
[1,1,1,3,1] => [3,1,1,1,1] => 15
[1,1,1,4] => [4,1,1,1] => 20
[1,1,2,1,1,1] => [2,1,1,1,1,1] => 6
[1,1,2,1,2] => [2,2,1,1,1] => 14
[1,1,2,2,1] => [2,2,1,1,1] => 14
[1,1,2,3] => [3,2,1,1] => 35
[1,1,3,1,1] => [3,1,1,1,1] => 15
[1,1,3,2] => [3,2,1,1] => 35
[1,1,4,1] => [4,1,1,1] => 20
[1,1,5] => [5,1,1] => 15
[1,2,1,1,1,1] => [2,1,1,1,1,1] => 6
[1,2,1,1,2] => [2,2,1,1,1] => 14
[1,2,1,2,1] => [2,2,1,1,1] => 14
[1,2,1,3] => [3,2,1,1] => 35
[1,2,2,1,1] => [2,2,1,1,1] => 14
[1,2,2,2] => [2,2,2,1] => 14
[1,2,3,1] => [3,2,1,1] => 35
[1,2,4] => [4,2,1] => 35
[1,3,1,1,1] => [3,1,1,1,1] => 15
[1,3,1,2] => [3,2,1,1] => 35
[1,3,2,1] => [3,2,1,1] => 35
[1,3,3] => [3,3,1] => 21
[1,4,1,1] => [4,1,1,1] => 20
[1,4,2] => [4,2,1] => 35
[1,5,1] => [5,1,1] => 15
[1,6] => [6,1] => 6
[2,1,1,1,1,1] => [2,1,1,1,1,1] => 6
[2,1,1,1,2] => [2,2,1,1,1] => 14
[2,1,1,2,1] => [2,2,1,1,1] => 14
[2,1,1,3] => [3,2,1,1] => 35
[2,1,2,1,1] => [2,2,1,1,1] => 14
[2,1,2,2] => [2,2,2,1] => 14
>>> Load all 1889 entries. <<<[2,1,3,1] => [3,2,1,1] => 35
[2,1,4] => [4,2,1] => 35
[2,2,1,1,1] => [2,2,1,1,1] => 14
[2,2,1,2] => [2,2,2,1] => 14
[2,2,2,1] => [2,2,2,1] => 14
[2,2,3] => [3,2,2] => 21
[2,3,1,1] => [3,2,1,1] => 35
[2,3,2] => [3,2,2] => 21
[2,4,1] => [4,2,1] => 35
[2,5] => [5,2] => 14
[3,1,1,1,1] => [3,1,1,1,1] => 15
[3,1,1,2] => [3,2,1,1] => 35
[3,1,2,1] => [3,2,1,1] => 35
[3,1,3] => [3,3,1] => 21
[3,2,1,1] => [3,2,1,1] => 35
[3,2,2] => [3,2,2] => 21
[3,3,1] => [3,3,1] => 21
[3,4] => [4,3] => 14
[4,1,1,1] => [4,1,1,1] => 20
[4,1,2] => [4,2,1] => 35
[4,2,1] => [4,2,1] => 35
[4,3] => [4,3] => 14
[5,1,1] => [5,1,1] => 15
[5,2] => [5,2] => 14
[6,1] => [6,1] => 6
[7] => [7] => 1
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => 7
[1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => 7
[1,1,1,1,1,3] => [3,1,1,1,1,1] => 21
[1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => 7
[1,1,1,1,2,2] => [2,2,1,1,1,1] => 20
[1,1,1,1,3,1] => [3,1,1,1,1,1] => 21
[1,1,1,1,4] => [4,1,1,1,1] => 35
[1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => 7
[1,1,1,2,1,2] => [2,2,1,1,1,1] => 20
[1,1,1,2,2,1] => [2,2,1,1,1,1] => 20
[1,1,1,2,3] => [3,2,1,1,1] => 64
[1,1,1,3,1,1] => [3,1,1,1,1,1] => 21
[1,1,1,3,2] => [3,2,1,1,1] => 64
[1,1,1,4,1] => [4,1,1,1,1] => 35
[1,1,1,5] => [5,1,1,1] => 35
[1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => 7
[1,1,2,1,1,2] => [2,2,1,1,1,1] => 20
[1,1,2,1,2,1] => [2,2,1,1,1,1] => 20
[1,1,2,1,3] => [3,2,1,1,1] => 64
[1,1,2,2,1,1] => [2,2,1,1,1,1] => 20
[1,1,2,2,2] => [2,2,2,1,1] => 28
[1,1,2,3,1] => [3,2,1,1,1] => 64
[1,1,2,4] => [4,2,1,1] => 90
[1,1,3,1,1,1] => [3,1,1,1,1,1] => 21
[1,1,3,1,2] => [3,2,1,1,1] => 64
[1,1,3,2,1] => [3,2,1,1,1] => 64
[1,1,3,3] => [3,3,1,1] => 56
[1,1,4,1,1] => [4,1,1,1,1] => 35
[1,1,4,2] => [4,2,1,1] => 90
[1,1,5,1] => [5,1,1,1] => 35
[1,1,6] => [6,1,1] => 21
[1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => 7
[1,2,1,1,1,2] => [2,2,1,1,1,1] => 20
[1,2,1,1,2,1] => [2,2,1,1,1,1] => 20
[1,2,1,1,3] => [3,2,1,1,1] => 64
[1,2,1,2,1,1] => [2,2,1,1,1,1] => 20
[1,2,1,2,2] => [2,2,2,1,1] => 28
[1,2,1,3,1] => [3,2,1,1,1] => 64
[1,2,1,4] => [4,2,1,1] => 90
[1,2,2,1,1,1] => [2,2,1,1,1,1] => 20
[1,2,2,1,2] => [2,2,2,1,1] => 28
[1,2,2,2,1] => [2,2,2,1,1] => 28
[1,2,2,3] => [3,2,2,1] => 70
[1,2,3,1,1] => [3,2,1,1,1] => 64
[1,2,3,2] => [3,2,2,1] => 70
[1,2,4,1] => [4,2,1,1] => 90
[1,2,5] => [5,2,1] => 64
[1,3,1,1,1,1] => [3,1,1,1,1,1] => 21
[1,3,1,1,2] => [3,2,1,1,1] => 64
[1,3,1,2,1] => [3,2,1,1,1] => 64
[1,3,1,3] => [3,3,1,1] => 56
[1,3,2,1,1] => [3,2,1,1,1] => 64
[1,3,2,2] => [3,2,2,1] => 70
[1,3,3,1] => [3,3,1,1] => 56
[1,3,4] => [4,3,1] => 70
[1,4,1,1,1] => [4,1,1,1,1] => 35
[1,4,1,2] => [4,2,1,1] => 90
[1,4,2,1] => [4,2,1,1] => 90
[1,4,3] => [4,3,1] => 70
[1,5,1,1] => [5,1,1,1] => 35
[1,5,2] => [5,2,1] => 64
[1,6,1] => [6,1,1] => 21
[1,7] => [7,1] => 7
[2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 7
[2,1,1,1,1,2] => [2,2,1,1,1,1] => 20
[2,1,1,1,2,1] => [2,2,1,1,1,1] => 20
[2,1,1,1,3] => [3,2,1,1,1] => 64
[2,1,1,2,1,1] => [2,2,1,1,1,1] => 20
[2,1,1,2,2] => [2,2,2,1,1] => 28
[2,1,1,3,1] => [3,2,1,1,1] => 64
[2,1,1,4] => [4,2,1,1] => 90
[2,1,2,1,1,1] => [2,2,1,1,1,1] => 20
[2,1,2,1,2] => [2,2,2,1,1] => 28
[2,1,2,2,1] => [2,2,2,1,1] => 28
[2,1,2,3] => [3,2,2,1] => 70
[2,1,3,1,1] => [3,2,1,1,1] => 64
[2,1,3,2] => [3,2,2,1] => 70
[2,1,4,1] => [4,2,1,1] => 90
[2,1,5] => [5,2,1] => 64
[2,2,1,1,1,1] => [2,2,1,1,1,1] => 20
[2,2,1,1,2] => [2,2,2,1,1] => 28
[2,2,1,2,1] => [2,2,2,1,1] => 28
[2,2,1,3] => [3,2,2,1] => 70
[2,2,2,1,1] => [2,2,2,1,1] => 28
[2,2,2,2] => [2,2,2,2] => 14
[2,2,3,1] => [3,2,2,1] => 70
[2,2,4] => [4,2,2] => 56
[2,3,1,1,1] => [3,2,1,1,1] => 64
[2,3,1,2] => [3,2,2,1] => 70
[2,3,2,1] => [3,2,2,1] => 70
[2,3,3] => [3,3,2] => 42
[2,4,1,1] => [4,2,1,1] => 90
[2,4,2] => [4,2,2] => 56
[2,5,1] => [5,2,1] => 64
[2,6] => [6,2] => 20
[3,1,1,1,1,1] => [3,1,1,1,1,1] => 21
[3,1,1,1,2] => [3,2,1,1,1] => 64
[3,1,1,2,1] => [3,2,1,1,1] => 64
[3,1,1,3] => [3,3,1,1] => 56
[3,1,2,1,1] => [3,2,1,1,1] => 64
[3,1,2,2] => [3,2,2,1] => 70
[3,1,3,1] => [3,3,1,1] => 56
[3,1,4] => [4,3,1] => 70
[3,2,1,1,1] => [3,2,1,1,1] => 64
[3,2,1,2] => [3,2,2,1] => 70
[3,2,2,1] => [3,2,2,1] => 70
[3,2,3] => [3,3,2] => 42
[3,3,1,1] => [3,3,1,1] => 56
[3,3,2] => [3,3,2] => 42
[3,4,1] => [4,3,1] => 70
[3,5] => [5,3] => 28
[4,1,1,1,1] => [4,1,1,1,1] => 35
[4,1,1,2] => [4,2,1,1] => 90
[4,1,2,1] => [4,2,1,1] => 90
[4,1,3] => [4,3,1] => 70
[4,2,1,1] => [4,2,1,1] => 90
[4,2,2] => [4,2,2] => 56
[4,3,1] => [4,3,1] => 70
[4,4] => [4,4] => 14
[5,1,1,1] => [5,1,1,1] => 35
[5,1,2] => [5,2,1] => 64
[5,2,1] => [5,2,1] => 64
[5,3] => [5,3] => 28
[6,1,1] => [6,1,1] => 21
[6,2] => [6,2] => 20
[7,1] => [7,1] => 7
[8] => [8] => 1
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => 28
[1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => 27
[1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => 28
[1,1,1,1,1,4] => [4,1,1,1,1,1] => 56
[1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1] => 8
[1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => 27
[1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => 27
[1,1,1,1,2,3] => [3,2,1,1,1,1] => 105
[1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => 28
[1,1,1,1,3,2] => [3,2,1,1,1,1] => 105
[1,1,1,1,4,1] => [4,1,1,1,1,1] => 56
[1,1,1,1,5] => [5,1,1,1,1] => 70
[1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => 8
[1,1,1,2,1,1,2] => [2,2,1,1,1,1,1] => 27
[1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => 27
[1,1,1,2,1,3] => [3,2,1,1,1,1] => 105
[1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => 27
[1,1,1,2,2,2] => [2,2,2,1,1,1] => 48
[1,1,1,2,3,1] => [3,2,1,1,1,1] => 105
[1,1,1,2,4] => [4,2,1,1,1] => 189
[1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => 28
[1,1,1,3,1,2] => [3,2,1,1,1,1] => 105
[1,1,1,3,2,1] => [3,2,1,1,1,1] => 105
[1,1,1,3,3] => [3,3,1,1,1] => 120
[1,1,1,4,1,1] => [4,1,1,1,1,1] => 56
[1,1,1,4,2] => [4,2,1,1,1] => 189
[1,1,1,5,1] => [5,1,1,1,1] => 70
[1,1,1,6] => [6,1,1,1] => 56
[1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 8
[1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => 27
[1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => 27
[1,1,2,1,1,3] => [3,2,1,1,1,1] => 105
[1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => 27
[1,1,2,1,2,2] => [2,2,2,1,1,1] => 48
[1,1,2,1,3,1] => [3,2,1,1,1,1] => 105
[1,1,2,1,4] => [4,2,1,1,1] => 189
[1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => 27
[1,1,2,2,1,2] => [2,2,2,1,1,1] => 48
[1,1,2,2,2,1] => [2,2,2,1,1,1] => 48
[1,1,2,2,3] => [3,2,2,1,1] => 162
[1,1,2,3,1,1] => [3,2,1,1,1,1] => 105
[1,1,2,3,2] => [3,2,2,1,1] => 162
[1,1,2,4,1] => [4,2,1,1,1] => 189
[1,1,2,5] => [5,2,1,1] => 189
[1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => 28
[1,1,3,1,1,2] => [3,2,1,1,1,1] => 105
[1,1,3,1,2,1] => [3,2,1,1,1,1] => 105
[1,1,3,1,3] => [3,3,1,1,1] => 120
[1,1,3,2,1,1] => [3,2,1,1,1,1] => 105
[1,1,3,2,2] => [3,2,2,1,1] => 162
[1,1,3,3,1] => [3,3,1,1,1] => 120
[1,1,3,4] => [4,3,1,1] => 216
[1,1,4,1,1,1] => [4,1,1,1,1,1] => 56
[1,1,4,1,2] => [4,2,1,1,1] => 189
[1,1,4,2,1] => [4,2,1,1,1] => 189
[1,1,4,3] => [4,3,1,1] => 216
[1,1,5,1,1] => [5,1,1,1,1] => 70
[1,1,5,2] => [5,2,1,1] => 189
[1,1,6,1] => [6,1,1,1] => 56
[1,1,7] => [7,1,1] => 28
[1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 8
[1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => 27
[1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => 27
[1,2,1,1,1,3] => [3,2,1,1,1,1] => 105
[1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => 27
[1,2,1,1,2,2] => [2,2,2,1,1,1] => 48
[1,2,1,1,3,1] => [3,2,1,1,1,1] => 105
[1,2,1,1,4] => [4,2,1,1,1] => 189
[1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => 27
[1,2,1,2,1,2] => [2,2,2,1,1,1] => 48
[1,2,1,2,2,1] => [2,2,2,1,1,1] => 48
[1,2,1,2,3] => [3,2,2,1,1] => 162
[1,2,1,3,1,1] => [3,2,1,1,1,1] => 105
[1,2,1,3,2] => [3,2,2,1,1] => 162
[1,2,1,4,1] => [4,2,1,1,1] => 189
[1,2,1,5] => [5,2,1,1] => 189
[1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => 27
[1,2,2,1,1,2] => [2,2,2,1,1,1] => 48
[1,2,2,1,2,1] => [2,2,2,1,1,1] => 48
[1,2,2,1,3] => [3,2,2,1,1] => 162
[1,2,2,2,1,1] => [2,2,2,1,1,1] => 48
[1,2,2,2,2] => [2,2,2,2,1] => 42
[1,2,2,3,1] => [3,2,2,1,1] => 162
[1,2,2,4] => [4,2,2,1] => 216
[1,2,3,1,1,1] => [3,2,1,1,1,1] => 105
[1,2,3,1,2] => [3,2,2,1,1] => 162
[1,2,3,2,1] => [3,2,2,1,1] => 162
[1,2,3,3] => [3,3,2,1] => 168
[1,2,4,1,1] => [4,2,1,1,1] => 189
[1,2,4,2] => [4,2,2,1] => 216
[1,2,5,1] => [5,2,1,1] => 189
[1,2,6] => [6,2,1] => 105
[1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => 28
[1,3,1,1,1,2] => [3,2,1,1,1,1] => 105
[1,3,1,1,2,1] => [3,2,1,1,1,1] => 105
[1,3,1,1,3] => [3,3,1,1,1] => 120
[1,3,1,2,1,1] => [3,2,1,1,1,1] => 105
[1,3,1,2,2] => [3,2,2,1,1] => 162
[1,3,1,3,1] => [3,3,1,1,1] => 120
[1,3,1,4] => [4,3,1,1] => 216
[1,3,2,1,1,1] => [3,2,1,1,1,1] => 105
[1,3,2,1,2] => [3,2,2,1,1] => 162
[1,3,2,2,1] => [3,2,2,1,1] => 162
[1,3,2,3] => [3,3,2,1] => 168
[1,3,3,1,1] => [3,3,1,1,1] => 120
[1,3,3,2] => [3,3,2,1] => 168
[1,3,4,1] => [4,3,1,1] => 216
[1,3,5] => [5,3,1] => 162
[1,4,1,1,1,1] => [4,1,1,1,1,1] => 56
[1,4,1,1,2] => [4,2,1,1,1] => 189
[1,4,1,2,1] => [4,2,1,1,1] => 189
[1,4,1,3] => [4,3,1,1] => 216
[1,4,2,1,1] => [4,2,1,1,1] => 189
[1,4,2,2] => [4,2,2,1] => 216
[1,4,3,1] => [4,3,1,1] => 216
[1,4,4] => [4,4,1] => 84
[1,5,1,1,1] => [5,1,1,1,1] => 70
[1,5,1,2] => [5,2,1,1] => 189
[1,5,2,1] => [5,2,1,1] => 189
[1,5,3] => [5,3,1] => 162
[1,6,1,1] => [6,1,1,1] => 56
[1,6,2] => [6,2,1] => 105
[1,7,1] => [7,1,1] => 28
[1,8] => [8,1] => 8
[2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 8
[2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => 27
[2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => 27
[2,1,1,1,1,3] => [3,2,1,1,1,1] => 105
[2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => 27
[2,1,1,1,2,2] => [2,2,2,1,1,1] => 48
[2,1,1,1,3,1] => [3,2,1,1,1,1] => 105
[2,1,1,1,4] => [4,2,1,1,1] => 189
[2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => 27
[2,1,1,2,1,2] => [2,2,2,1,1,1] => 48
[2,1,1,2,2,1] => [2,2,2,1,1,1] => 48
[2,1,1,2,3] => [3,2,2,1,1] => 162
[2,1,1,3,1,1] => [3,2,1,1,1,1] => 105
[2,1,1,3,2] => [3,2,2,1,1] => 162
[2,1,1,4,1] => [4,2,1,1,1] => 189
[2,1,1,5] => [5,2,1,1] => 189
[2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => 27
[2,1,2,1,1,2] => [2,2,2,1,1,1] => 48
[2,1,2,1,2,1] => [2,2,2,1,1,1] => 48
[2,1,2,1,3] => [3,2,2,1,1] => 162
[2,1,2,2,1,1] => [2,2,2,1,1,1] => 48
[2,1,2,2,2] => [2,2,2,2,1] => 42
[2,1,2,3,1] => [3,2,2,1,1] => 162
[2,1,2,4] => [4,2,2,1] => 216
[2,1,3,1,1,1] => [3,2,1,1,1,1] => 105
[2,1,3,1,2] => [3,2,2,1,1] => 162
[2,1,3,2,1] => [3,2,2,1,1] => 162
[2,1,3,3] => [3,3,2,1] => 168
[2,1,4,1,1] => [4,2,1,1,1] => 189
[2,1,4,2] => [4,2,2,1] => 216
[2,1,5,1] => [5,2,1,1] => 189
[2,1,6] => [6,2,1] => 105
[2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 27
[2,2,1,1,1,2] => [2,2,2,1,1,1] => 48
[2,2,1,1,2,1] => [2,2,2,1,1,1] => 48
[2,2,1,1,3] => [3,2,2,1,1] => 162
[2,2,1,2,1,1] => [2,2,2,1,1,1] => 48
[2,2,1,2,2] => [2,2,2,2,1] => 42
[2,2,1,3,1] => [3,2,2,1,1] => 162
[2,2,1,4] => [4,2,2,1] => 216
[2,2,2,1,1,1] => [2,2,2,1,1,1] => 48
[2,2,2,1,2] => [2,2,2,2,1] => 42
[2,2,2,2,1] => [2,2,2,2,1] => 42
[2,2,2,3] => [3,2,2,2] => 84
[2,2,3,1,1] => [3,2,2,1,1] => 162
[2,2,3,2] => [3,2,2,2] => 84
[2,2,4,1] => [4,2,2,1] => 216
[2,2,5] => [5,2,2] => 120
[2,3,1,1,1,1] => [3,2,1,1,1,1] => 105
[2,3,1,1,2] => [3,2,2,1,1] => 162
[2,3,1,2,1] => [3,2,2,1,1] => 162
[2,3,1,3] => [3,3,2,1] => 168
[2,3,2,1,1] => [3,2,2,1,1] => 162
[2,3,2,2] => [3,2,2,2] => 84
[2,3,3,1] => [3,3,2,1] => 168
[2,3,4] => [4,3,2] => 168
[2,4,1,1,1] => [4,2,1,1,1] => 189
[2,4,1,2] => [4,2,2,1] => 216
[2,4,2,1] => [4,2,2,1] => 216
[2,4,3] => [4,3,2] => 168
[2,5,1,1] => [5,2,1,1] => 189
[2,5,2] => [5,2,2] => 120
[2,6,1] => [6,2,1] => 105
[2,7] => [7,2] => 27
[3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 28
[3,1,1,1,1,2] => [3,2,1,1,1,1] => 105
[3,1,1,1,2,1] => [3,2,1,1,1,1] => 105
[3,1,1,1,3] => [3,3,1,1,1] => 120
[3,1,1,2,1,1] => [3,2,1,1,1,1] => 105
[3,1,1,2,2] => [3,2,2,1,1] => 162
[3,1,1,3,1] => [3,3,1,1,1] => 120
[3,1,1,4] => [4,3,1,1] => 216
[3,1,2,1,1,1] => [3,2,1,1,1,1] => 105
[3,1,2,1,2] => [3,2,2,1,1] => 162
[3,1,2,2,1] => [3,2,2,1,1] => 162
[3,1,2,3] => [3,3,2,1] => 168
[3,1,3,1,1] => [3,3,1,1,1] => 120
[3,1,3,2] => [3,3,2,1] => 168
[3,1,4,1] => [4,3,1,1] => 216
[3,1,5] => [5,3,1] => 162
[3,2,1,1,1,1] => [3,2,1,1,1,1] => 105
[3,2,1,1,2] => [3,2,2,1,1] => 162
[3,2,1,2,1] => [3,2,2,1,1] => 162
[3,2,1,3] => [3,3,2,1] => 168
[3,2,2,1,1] => [3,2,2,1,1] => 162
[3,2,2,2] => [3,2,2,2] => 84
[3,2,3,1] => [3,3,2,1] => 168
[3,2,4] => [4,3,2] => 168
[3,3,1,1,1] => [3,3,1,1,1] => 120
[3,3,1,2] => [3,3,2,1] => 168
[3,3,2,1] => [3,3,2,1] => 168
[3,3,3] => [3,3,3] => 42
[3,4,1,1] => [4,3,1,1] => 216
[3,4,2] => [4,3,2] => 168
[3,5,1] => [5,3,1] => 162
[3,6] => [6,3] => 48
[4,1,1,1,1,1] => [4,1,1,1,1,1] => 56
[4,1,1,1,2] => [4,2,1,1,1] => 189
[4,1,1,2,1] => [4,2,1,1,1] => 189
[4,1,1,3] => [4,3,1,1] => 216
[4,1,2,1,1] => [4,2,1,1,1] => 189
[4,1,2,2] => [4,2,2,1] => 216
[4,1,3,1] => [4,3,1,1] => 216
[4,1,4] => [4,4,1] => 84
[4,2,1,1,1] => [4,2,1,1,1] => 189
[4,2,1,2] => [4,2,2,1] => 216
[4,2,2,1] => [4,2,2,1] => 216
[4,2,3] => [4,3,2] => 168
[4,3,1,1] => [4,3,1,1] => 216
[4,3,2] => [4,3,2] => 168
[4,4,1] => [4,4,1] => 84
[4,5] => [5,4] => 42
[5,1,1,1,1] => [5,1,1,1,1] => 70
[5,1,1,2] => [5,2,1,1] => 189
[5,1,2,1] => [5,2,1,1] => 189
[5,1,3] => [5,3,1] => 162
[5,2,1,1] => [5,2,1,1] => 189
[5,2,2] => [5,2,2] => 120
[5,3,1] => [5,3,1] => 162
[5,4] => [5,4] => 42
[6,1,1,1] => [6,1,1,1] => 56
[6,1,2] => [6,2,1] => 105
[6,2,1] => [6,2,1] => 105
[6,3] => [6,3] => 48
[7,1,1] => [7,1,1] => 28
[7,2] => [7,2] => 27
[8,1] => [8,1] => 8
[9] => [9] => 1
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1] => 9
[1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => 9
[1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => 36
[1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1] => 9
[1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1] => 35
[1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => 36
[1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => 84
[1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => 9
[1,1,1,1,1,2,1,2] => [2,2,1,1,1,1,1,1] => 35
[1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1] => 35
[1,1,1,1,1,2,3] => [3,2,1,1,1,1,1] => 160
[1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => 36
[1,1,1,1,1,3,2] => [3,2,1,1,1,1,1] => 160
[1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => 84
[1,1,1,1,1,5] => [5,1,1,1,1,1] => 126
[1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 9
[1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1] => 35
[1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1] => 35
[1,1,1,1,2,1,3] => [3,2,1,1,1,1,1] => 160
[1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1] => 35
[1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => 75
[1,1,1,1,2,3,1] => [3,2,1,1,1,1,1] => 160
[1,1,1,1,2,4] => [4,2,1,1,1,1] => 350
[1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1] => 36
[1,1,1,1,3,1,2] => [3,2,1,1,1,1,1] => 160
[1,1,1,1,3,2,1] => [3,2,1,1,1,1,1] => 160
[1,1,1,1,3,3] => [3,3,1,1,1,1] => 225
[1,1,1,1,4,1,1] => [4,1,1,1,1,1,1] => 84
[1,1,1,1,4,2] => [4,2,1,1,1,1] => 350
[1,1,1,1,5,1] => [5,1,1,1,1,1] => 126
[1,1,1,1,6] => [6,1,1,1,1] => 126
[1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 9
[1,1,1,2,1,1,1,2] => [2,2,1,1,1,1,1,1] => 35
[1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1] => 35
[1,1,1,2,1,1,3] => [3,2,1,1,1,1,1] => 160
[1,1,1,2,1,2,1,1] => [2,2,1,1,1,1,1,1] => 35
[1,1,1,2,1,2,2] => [2,2,2,1,1,1,1] => 75
[1,1,1,2,1,3,1] => [3,2,1,1,1,1,1] => 160
[1,1,1,2,1,4] => [4,2,1,1,1,1] => 350
[1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1] => 35
[1,1,1,2,2,1,2] => [2,2,2,1,1,1,1] => 75
[1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => 75
[1,1,1,2,2,3] => [3,2,2,1,1,1] => 315
[1,1,1,2,3,1,1] => [3,2,1,1,1,1,1] => 160
[1,1,1,2,3,2] => [3,2,2,1,1,1] => 315
[1,1,1,2,4,1] => [4,2,1,1,1,1] => 350
[1,1,1,2,5] => [5,2,1,1,1] => 448
[1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => 36
[1,1,1,3,1,1,2] => [3,2,1,1,1,1,1] => 160
[1,1,1,3,1,2,1] => [3,2,1,1,1,1,1] => 160
[1,1,1,3,1,3] => [3,3,1,1,1,1] => 225
[1,1,1,3,2,1,1] => [3,2,1,1,1,1,1] => 160
[1,1,1,3,2,2] => [3,2,2,1,1,1] => 315
[1,1,1,3,3,1] => [3,3,1,1,1,1] => 225
[1,1,1,3,4] => [4,3,1,1,1] => 525
[1,1,1,4,1,1,1] => [4,1,1,1,1,1,1] => 84
[1,1,1,4,1,2] => [4,2,1,1,1,1] => 350
[1,1,1,4,2,1] => [4,2,1,1,1,1] => 350
[1,1,1,4,3] => [4,3,1,1,1] => 525
[1,1,1,5,1,1] => [5,1,1,1,1,1] => 126
[1,1,1,5,2] => [5,2,1,1,1] => 448
[1,1,1,6,1] => [6,1,1,1,1] => 126
[1,1,1,7] => [7,1,1,1] => 84
[1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 9
[1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 35
[1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 35
[1,1,2,1,1,1,3] => [3,2,1,1,1,1,1] => 160
[1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => 35
[1,1,2,1,1,2,2] => [2,2,2,1,1,1,1] => 75
[1,1,2,1,1,3,1] => [3,2,1,1,1,1,1] => 160
[1,1,2,1,1,4] => [4,2,1,1,1,1] => 350
[1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => 35
[1,1,2,1,2,1,2] => [2,2,2,1,1,1,1] => 75
[1,1,2,1,2,2,1] => [2,2,2,1,1,1,1] => 75
[1,1,2,1,2,3] => [3,2,2,1,1,1] => 315
[1,1,2,1,3,1,1] => [3,2,1,1,1,1,1] => 160
[1,1,2,1,3,2] => [3,2,2,1,1,1] => 315
[1,1,2,1,4,1] => [4,2,1,1,1,1] => 350
[1,1,2,1,5] => [5,2,1,1,1] => 448
[1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => 35
[1,1,2,2,1,1,2] => [2,2,2,1,1,1,1] => 75
[1,1,2,2,1,2,1] => [2,2,2,1,1,1,1] => 75
[1,1,2,2,1,3] => [3,2,2,1,1,1] => 315
[1,1,2,2,2,1,1] => [2,2,2,1,1,1,1] => 75
[1,1,2,2,2,2] => [2,2,2,2,1,1] => 90
[1,1,2,2,3,1] => [3,2,2,1,1,1] => 315
[1,1,2,2,4] => [4,2,2,1,1] => 567
[1,1,2,3,1,1,1] => [3,2,1,1,1,1,1] => 160
[1,1,2,3,1,2] => [3,2,2,1,1,1] => 315
[1,1,2,3,2,1] => [3,2,2,1,1,1] => 315
[1,1,2,3,3] => [3,3,2,1,1] => 450
[1,1,2,4,1,1] => [4,2,1,1,1,1] => 350
[1,1,2,4,2] => [4,2,2,1,1] => 567
[1,1,2,5,1] => [5,2,1,1,1] => 448
[1,1,2,6] => [6,2,1,1] => 350
[1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 36
[1,1,3,1,1,1,2] => [3,2,1,1,1,1,1] => 160
[1,1,3,1,1,2,1] => [3,2,1,1,1,1,1] => 160
[1,1,3,1,1,3] => [3,3,1,1,1,1] => 225
[1,1,3,1,2,1,1] => [3,2,1,1,1,1,1] => 160
[1,1,3,1,2,2] => [3,2,2,1,1,1] => 315
[1,1,3,1,3,1] => [3,3,1,1,1,1] => 225
[1,1,3,1,4] => [4,3,1,1,1] => 525
[1,1,3,2,1,1,1] => [3,2,1,1,1,1,1] => 160
[1,1,3,2,1,2] => [3,2,2,1,1,1] => 315
[1,1,3,2,2,1] => [3,2,2,1,1,1] => 315
[1,1,3,2,3] => [3,3,2,1,1] => 450
[1,1,3,3,1,1] => [3,3,1,1,1,1] => 225
[1,1,3,3,2] => [3,3,2,1,1] => 450
[1,1,3,4,1] => [4,3,1,1,1] => 525
[1,1,3,5] => [5,3,1,1] => 567
[1,1,4,1,1,1,1] => [4,1,1,1,1,1,1] => 84
[1,1,4,1,1,2] => [4,2,1,1,1,1] => 350
[1,1,4,1,2,1] => [4,2,1,1,1,1] => 350
[1,1,4,1,3] => [4,3,1,1,1] => 525
[1,1,4,2,1,1] => [4,2,1,1,1,1] => 350
[1,1,4,2,2] => [4,2,2,1,1] => 567
[1,1,4,3,1] => [4,3,1,1,1] => 525
[1,1,4,4] => [4,4,1,1] => 300
[1,1,5,1,1,1] => [5,1,1,1,1,1] => 126
[1,1,5,1,2] => [5,2,1,1,1] => 448
[1,1,5,2,1] => [5,2,1,1,1] => 448
[1,1,5,3] => [5,3,1,1] => 567
[1,1,6,1,1] => [6,1,1,1,1] => 126
[1,1,6,2] => [6,2,1,1] => 350
[1,1,7,1] => [7,1,1,1] => 84
[1,1,8] => [8,1,1] => 36
[1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 9
[1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 35
[1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 35
[1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => 160
[1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => 35
[1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => 75
[1,2,1,1,1,3,1] => [3,2,1,1,1,1,1] => 160
[1,2,1,1,1,4] => [4,2,1,1,1,1] => 350
[1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => 35
[1,2,1,1,2,1,2] => [2,2,2,1,1,1,1] => 75
[1,2,1,1,2,2,1] => [2,2,2,1,1,1,1] => 75
[1,2,1,1,2,3] => [3,2,2,1,1,1] => 315
[1,2,1,1,3,1,1] => [3,2,1,1,1,1,1] => 160
[1,2,1,1,3,2] => [3,2,2,1,1,1] => 315
[1,2,1,1,4,1] => [4,2,1,1,1,1] => 350
[1,2,1,1,5] => [5,2,1,1,1] => 448
[1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => 35
[1,2,1,2,1,1,2] => [2,2,2,1,1,1,1] => 75
[1,2,1,2,1,2,1] => [2,2,2,1,1,1,1] => 75
[1,2,1,2,1,3] => [3,2,2,1,1,1] => 315
[1,2,1,2,2,1,1] => [2,2,2,1,1,1,1] => 75
[1,2,1,2,2,2] => [2,2,2,2,1,1] => 90
[1,2,1,2,3,1] => [3,2,2,1,1,1] => 315
[1,2,1,2,4] => [4,2,2,1,1] => 567
[1,2,1,3,1,1,1] => [3,2,1,1,1,1,1] => 160
[1,2,1,3,1,2] => [3,2,2,1,1,1] => 315
[1,2,1,3,2,1] => [3,2,2,1,1,1] => 315
[1,2,1,3,3] => [3,3,2,1,1] => 450
[1,2,1,4,1,1] => [4,2,1,1,1,1] => 350
[1,2,1,4,2] => [4,2,2,1,1] => 567
[1,2,1,5,1] => [5,2,1,1,1] => 448
[1,2,1,6] => [6,2,1,1] => 350
[1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 35
[1,2,2,1,1,1,2] => [2,2,2,1,1,1,1] => 75
[1,2,2,1,1,2,1] => [2,2,2,1,1,1,1] => 75
[1,2,2,1,1,3] => [3,2,2,1,1,1] => 315
[1,2,2,1,2,1,1] => [2,2,2,1,1,1,1] => 75
[1,2,2,1,2,2] => [2,2,2,2,1,1] => 90
[1,2,2,1,3,1] => [3,2,2,1,1,1] => 315
[1,2,2,1,4] => [4,2,2,1,1] => 567
[1,2,2,2,1,1,1] => [2,2,2,1,1,1,1] => 75
[1,2,2,2,1,2] => [2,2,2,2,1,1] => 90
[1,2,2,2,2,1] => [2,2,2,2,1,1] => 90
[1,2,2,2,3] => [3,2,2,2,1] => 288
[1,2,2,3,1,1] => [3,2,2,1,1,1] => 315
[1,2,2,3,2] => [3,2,2,2,1] => 288
[1,2,2,4,1] => [4,2,2,1,1] => 567
[1,2,2,5] => [5,2,2,1] => 525
[1,2,3,1,1,1,1] => [3,2,1,1,1,1,1] => 160
[1,2,3,1,1,2] => [3,2,2,1,1,1] => 315
[1,2,3,1,2,1] => [3,2,2,1,1,1] => 315
[1,2,3,1,3] => [3,3,2,1,1] => 450
[1,2,3,2,1,1] => [3,2,2,1,1,1] => 315
[1,2,3,2,2] => [3,2,2,2,1] => 288
[1,2,3,3,1] => [3,3,2,1,1] => 450
[1,2,3,4] => [4,3,2,1] => 768
[1,2,4,1,1,1] => [4,2,1,1,1,1] => 350
[1,2,4,1,2] => [4,2,2,1,1] => 567
[1,2,4,2,1] => [4,2,2,1,1] => 567
[1,2,4,3] => [4,3,2,1] => 768
[1,2,5,1,1] => [5,2,1,1,1] => 448
[1,2,5,2] => [5,2,2,1] => 525
[1,2,6,1] => [6,2,1,1] => 350
[1,2,7] => [7,2,1] => 160
[1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 36
[1,3,1,1,1,1,2] => [3,2,1,1,1,1,1] => 160
[1,3,1,1,1,2,1] => [3,2,1,1,1,1,1] => 160
[1,3,1,1,1,3] => [3,3,1,1,1,1] => 225
[1,3,1,1,2,1,1] => [3,2,1,1,1,1,1] => 160
[1,3,1,1,2,2] => [3,2,2,1,1,1] => 315
[1,3,1,1,3,1] => [3,3,1,1,1,1] => 225
[1,3,1,1,4] => [4,3,1,1,1] => 525
[1,3,1,2,1,1,1] => [3,2,1,1,1,1,1] => 160
[1,3,1,2,1,2] => [3,2,2,1,1,1] => 315
[1,3,1,2,2,1] => [3,2,2,1,1,1] => 315
[1,3,1,2,3] => [3,3,2,1,1] => 450
[1,3,1,3,1,1] => [3,3,1,1,1,1] => 225
[1,3,1,3,2] => [3,3,2,1,1] => 450
[1,3,1,4,1] => [4,3,1,1,1] => 525
[1,3,1,5] => [5,3,1,1] => 567
[1,3,2,1,1,1,1] => [3,2,1,1,1,1,1] => 160
[1,3,2,1,1,2] => [3,2,2,1,1,1] => 315
[1,3,2,1,2,1] => [3,2,2,1,1,1] => 315
[1,3,2,1,3] => [3,3,2,1,1] => 450
[1,3,2,2,1,1] => [3,2,2,1,1,1] => 315
[1,3,2,2,2] => [3,2,2,2,1] => 288
[1,3,2,3,1] => [3,3,2,1,1] => 450
[1,3,2,4] => [4,3,2,1] => 768
[1,3,3,1,1,1] => [3,3,1,1,1,1] => 225
[1,3,3,1,2] => [3,3,2,1,1] => 450
[1,3,3,2,1] => [3,3,2,1,1] => 450
[1,3,3,3] => [3,3,3,1] => 210
[1,3,4,1,1] => [4,3,1,1,1] => 525
[1,3,4,2] => [4,3,2,1] => 768
[1,3,5,1] => [5,3,1,1] => 567
[1,3,6] => [6,3,1] => 315
[1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => 84
[1,4,1,1,1,2] => [4,2,1,1,1,1] => 350
[1,4,1,1,2,1] => [4,2,1,1,1,1] => 350
[1,4,1,1,3] => [4,3,1,1,1] => 525
[1,4,1,2,1,1] => [4,2,1,1,1,1] => 350
[1,4,1,2,2] => [4,2,2,1,1] => 567
[1,4,1,3,1] => [4,3,1,1,1] => 525
[1,4,1,4] => [4,4,1,1] => 300
[1,4,2,1,1,1] => [4,2,1,1,1,1] => 350
[1,4,2,1,2] => [4,2,2,1,1] => 567
[1,4,2,2,1] => [4,2,2,1,1] => 567
[1,4,2,3] => [4,3,2,1] => 768
[1,4,3,1,1] => [4,3,1,1,1] => 525
[1,4,3,2] => [4,3,2,1] => 768
[1,4,4,1] => [4,4,1,1] => 300
[1,4,5] => [5,4,1] => 288
[1,5,1,1,1,1] => [5,1,1,1,1,1] => 126
[1,5,1,1,2] => [5,2,1,1,1] => 448
[1,5,1,2,1] => [5,2,1,1,1] => 448
[1,5,1,3] => [5,3,1,1] => 567
[1,5,2,1,1] => [5,2,1,1,1] => 448
[1,5,2,2] => [5,2,2,1] => 525
[1,5,3,1] => [5,3,1,1] => 567
[1,5,4] => [5,4,1] => 288
[1,6,1,1,1] => [6,1,1,1,1] => 126
[1,6,1,2] => [6,2,1,1] => 350
[1,6,2,1] => [6,2,1,1] => 350
[1,6,3] => [6,3,1] => 315
[1,7,1,1] => [7,1,1,1] => 84
[1,7,2] => [7,2,1] => 160
[1,8,1] => [8,1,1] => 36
[1,9] => [9,1] => 9
[2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 9
[2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 35
[2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 35
[2,1,1,1,1,1,3] => [3,2,1,1,1,1,1] => 160
[2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => 35
[2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => 75
[2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => 160
[2,1,1,1,1,4] => [4,2,1,1,1,1] => 350
[2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => 35
[2,1,1,1,2,1,2] => [2,2,2,1,1,1,1] => 75
[2,1,1,1,2,2,1] => [2,2,2,1,1,1,1] => 75
[2,1,1,1,2,3] => [3,2,2,1,1,1] => 315
[2,1,1,1,3,1,1] => [3,2,1,1,1,1,1] => 160
[2,1,1,1,3,2] => [3,2,2,1,1,1] => 315
[2,1,1,1,4,1] => [4,2,1,1,1,1] => 350
[2,1,1,1,5] => [5,2,1,1,1] => 448
[2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => 35
[2,1,1,2,1,1,2] => [2,2,2,1,1,1,1] => 75
[2,1,1,2,1,2,1] => [2,2,2,1,1,1,1] => 75
[2,1,1,2,1,3] => [3,2,2,1,1,1] => 315
[2,1,1,2,2,1,1] => [2,2,2,1,1,1,1] => 75
[2,1,1,2,2,2] => [2,2,2,2,1,1] => 90
[2,1,1,2,3,1] => [3,2,2,1,1,1] => 315
[2,1,1,2,4] => [4,2,2,1,1] => 567
[2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => 160
[2,1,1,3,1,2] => [3,2,2,1,1,1] => 315
[2,1,1,3,2,1] => [3,2,2,1,1,1] => 315
[2,1,1,3,3] => [3,3,2,1,1] => 450
[2,1,1,4,1,1] => [4,2,1,1,1,1] => 350
[2,1,1,4,2] => [4,2,2,1,1] => 567
[2,1,1,5,1] => [5,2,1,1,1] => 448
[2,1,1,6] => [6,2,1,1] => 350
[2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 35
[2,1,2,1,1,1,2] => [2,2,2,1,1,1,1] => 75
[2,1,2,1,1,2,1] => [2,2,2,1,1,1,1] => 75
[2,1,2,1,1,3] => [3,2,2,1,1,1] => 315
[2,1,2,1,2,1,1] => [2,2,2,1,1,1,1] => 75
[2,1,2,1,2,2] => [2,2,2,2,1,1] => 90
[2,1,2,1,3,1] => [3,2,2,1,1,1] => 315
[2,1,2,1,4] => [4,2,2,1,1] => 567
[2,1,2,2,1,1,1] => [2,2,2,1,1,1,1] => 75
[2,1,2,2,1,2] => [2,2,2,2,1,1] => 90
[2,1,2,2,2,1] => [2,2,2,2,1,1] => 90
[2,1,2,2,3] => [3,2,2,2,1] => 288
[2,1,2,3,1,1] => [3,2,2,1,1,1] => 315
[2,1,2,3,2] => [3,2,2,2,1] => 288
[2,1,2,4,1] => [4,2,2,1,1] => 567
[2,1,2,5] => [5,2,2,1] => 525
[2,1,3,1,1,1,1] => [3,2,1,1,1,1,1] => 160
[2,1,3,1,1,2] => [3,2,2,1,1,1] => 315
[2,1,3,1,2,1] => [3,2,2,1,1,1] => 315
[2,1,3,1,3] => [3,3,2,1,1] => 450
[2,1,3,2,1,1] => [3,2,2,1,1,1] => 315
[2,1,3,2,2] => [3,2,2,2,1] => 288
[2,1,3,3,1] => [3,3,2,1,1] => 450
[2,1,3,4] => [4,3,2,1] => 768
[2,1,4,1,1,1] => [4,2,1,1,1,1] => 350
[2,1,4,1,2] => [4,2,2,1,1] => 567
[2,1,4,2,1] => [4,2,2,1,1] => 567
[2,1,4,3] => [4,3,2,1] => 768
[2,1,5,1,1] => [5,2,1,1,1] => 448
[2,1,5,2] => [5,2,2,1] => 525
[2,1,6,1] => [6,2,1,1] => 350
[2,1,7] => [7,2,1] => 160
[2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 35
[2,2,1,1,1,1,2] => [2,2,2,1,1,1,1] => 75
[2,2,1,1,1,2,1] => [2,2,2,1,1,1,1] => 75
[2,2,1,1,1,3] => [3,2,2,1,1,1] => 315
[2,2,1,1,2,1,1] => [2,2,2,1,1,1,1] => 75
[2,2,1,1,2,2] => [2,2,2,2,1,1] => 90
[2,2,1,1,3,1] => [3,2,2,1,1,1] => 315
[2,2,1,1,4] => [4,2,2,1,1] => 567
[2,2,1,2,1,1,1] => [2,2,2,1,1,1,1] => 75
[2,2,1,2,1,2] => [2,2,2,2,1,1] => 90
[2,2,1,2,2,1] => [2,2,2,2,1,1] => 90
[2,2,1,2,3] => [3,2,2,2,1] => 288
[2,2,1,3,1,1] => [3,2,2,1,1,1] => 315
[2,2,1,3,2] => [3,2,2,2,1] => 288
[2,2,1,4,1] => [4,2,2,1,1] => 567
[2,2,1,5] => [5,2,2,1] => 525
[2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 75
[2,2,2,1,1,2] => [2,2,2,2,1,1] => 90
[2,2,2,1,2,1] => [2,2,2,2,1,1] => 90
[2,2,2,1,3] => [3,2,2,2,1] => 288
[2,2,2,2,1,1] => [2,2,2,2,1,1] => 90
[2,2,2,2,2] => [2,2,2,2,2] => 42
[2,2,2,3,1] => [3,2,2,2,1] => 288
[2,2,2,4] => [4,2,2,2] => 300
[2,2,3,1,1,1] => [3,2,2,1,1,1] => 315
[2,2,3,1,2] => [3,2,2,2,1] => 288
[2,2,3,2,1] => [3,2,2,2,1] => 288
[2,2,3,3] => [3,3,2,2] => 252
[2,2,4,1,1] => [4,2,2,1,1] => 567
[2,2,4,2] => [4,2,2,2] => 300
[2,2,5,1] => [5,2,2,1] => 525
[2,2,6] => [6,2,2] => 225
[2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => 160
[2,3,1,1,1,2] => [3,2,2,1,1,1] => 315
[2,3,1,1,2,1] => [3,2,2,1,1,1] => 315
[2,3,1,1,3] => [3,3,2,1,1] => 450
[2,3,1,2,1,1] => [3,2,2,1,1,1] => 315
[2,3,1,2,2] => [3,2,2,2,1] => 288
[2,3,1,3,1] => [3,3,2,1,1] => 450
[2,3,1,4] => [4,3,2,1] => 768
[2,3,2,1,1,1] => [3,2,2,1,1,1] => 315
[2,3,2,1,2] => [3,2,2,2,1] => 288
[2,3,2,2,1] => [3,2,2,2,1] => 288
[2,3,2,3] => [3,3,2,2] => 252
[2,3,3,1,1] => [3,3,2,1,1] => 450
[2,3,3,2] => [3,3,2,2] => 252
[2,3,4,1] => [4,3,2,1] => 768
[2,3,5] => [5,3,2] => 450
[2,4,1,1,1,1] => [4,2,1,1,1,1] => 350
[2,4,1,1,2] => [4,2,2,1,1] => 567
[2,4,1,2,1] => [4,2,2,1,1] => 567
[2,4,1,3] => [4,3,2,1] => 768
[2,4,2,1,1] => [4,2,2,1,1] => 567
[2,4,2,2] => [4,2,2,2] => 300
[2,4,3,1] => [4,3,2,1] => 768
[2,4,4] => [4,4,2] => 252
[2,5,1,1,1] => [5,2,1,1,1] => 448
[2,5,1,2] => [5,2,2,1] => 525
[2,5,2,1] => [5,2,2,1] => 525
[2,5,3] => [5,3,2] => 450
[2,6,1,1] => [6,2,1,1] => 350
[2,6,2] => [6,2,2] => 225
[2,7,1] => [7,2,1] => 160
[2,8] => [8,2] => 35
[3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 36
[3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => 160
[3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => 160
[3,1,1,1,1,3] => [3,3,1,1,1,1] => 225
[3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => 160
[3,1,1,1,2,2] => [3,2,2,1,1,1] => 315
[3,1,1,1,3,1] => [3,3,1,1,1,1] => 225
[3,1,1,1,4] => [4,3,1,1,1] => 525
[3,1,1,2,1,1,1] => [3,2,1,1,1,1,1] => 160
[3,1,1,2,1,2] => [3,2,2,1,1,1] => 315
[3,1,1,2,2,1] => [3,2,2,1,1,1] => 315
[3,1,1,2,3] => [3,3,2,1,1] => 450
[3,1,1,3,1,1] => [3,3,1,1,1,1] => 225
[3,1,1,3,2] => [3,3,2,1,1] => 450
[3,1,1,4,1] => [4,3,1,1,1] => 525
[3,1,1,5] => [5,3,1,1] => 567
[3,1,2,1,1,1,1] => [3,2,1,1,1,1,1] => 160
[3,1,2,1,1,2] => [3,2,2,1,1,1] => 315
[3,1,2,1,2,1] => [3,2,2,1,1,1] => 315
[3,1,2,1,3] => [3,3,2,1,1] => 450
[3,1,2,2,1,1] => [3,2,2,1,1,1] => 315
[3,1,2,2,2] => [3,2,2,2,1] => 288
[3,1,2,3,1] => [3,3,2,1,1] => 450
[3,1,2,4] => [4,3,2,1] => 768
[3,1,3,1,1,1] => [3,3,1,1,1,1] => 225
[3,1,3,1,2] => [3,3,2,1,1] => 450
[3,1,3,2,1] => [3,3,2,1,1] => 450
[3,1,3,3] => [3,3,3,1] => 210
[3,1,4,1,1] => [4,3,1,1,1] => 525
[3,1,4,2] => [4,3,2,1] => 768
[3,1,5,1] => [5,3,1,1] => 567
[3,1,6] => [6,3,1] => 315
[3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 160
[3,2,1,1,1,2] => [3,2,2,1,1,1] => 315
[3,2,1,1,2,1] => [3,2,2,1,1,1] => 315
[3,2,1,1,3] => [3,3,2,1,1] => 450
[3,2,1,2,1,1] => [3,2,2,1,1,1] => 315
[3,2,1,2,2] => [3,2,2,2,1] => 288
[3,2,1,3,1] => [3,3,2,1,1] => 450
[3,2,1,4] => [4,3,2,1] => 768
[3,2,2,1,1,1] => [3,2,2,1,1,1] => 315
[3,2,2,1,2] => [3,2,2,2,1] => 288
[3,2,2,2,1] => [3,2,2,2,1] => 288
[3,2,2,3] => [3,3,2,2] => 252
[3,2,3,1,1] => [3,3,2,1,1] => 450
[3,2,3,2] => [3,3,2,2] => 252
[3,2,4,1] => [4,3,2,1] => 768
[3,2,5] => [5,3,2] => 450
[3,3,1,1,1,1] => [3,3,1,1,1,1] => 225
[3,3,1,1,2] => [3,3,2,1,1] => 450
[3,3,1,2,1] => [3,3,2,1,1] => 450
[3,3,1,3] => [3,3,3,1] => 210
[3,3,2,1,1] => [3,3,2,1,1] => 450
[3,3,2,2] => [3,3,2,2] => 252
[3,3,3,1] => [3,3,3,1] => 210
[3,3,4] => [4,3,3] => 210
[3,4,1,1,1] => [4,3,1,1,1] => 525
[3,4,1,2] => [4,3,2,1] => 768
[3,4,2,1] => [4,3,2,1] => 768
[3,4,3] => [4,3,3] => 210
[3,5,1,1] => [5,3,1,1] => 567
[3,5,2] => [5,3,2] => 450
[3,6,1] => [6,3,1] => 315
[3,7] => [7,3] => 75
[4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 84
[4,1,1,1,1,2] => [4,2,1,1,1,1] => 350
[4,1,1,1,2,1] => [4,2,1,1,1,1] => 350
[4,1,1,1,3] => [4,3,1,1,1] => 525
[4,1,1,2,1,1] => [4,2,1,1,1,1] => 350
[4,1,1,2,2] => [4,2,2,1,1] => 567
[4,1,1,3,1] => [4,3,1,1,1] => 525
[4,1,1,4] => [4,4,1,1] => 300
[4,1,2,1,1,1] => [4,2,1,1,1,1] => 350
[4,1,2,1,2] => [4,2,2,1,1] => 567
[4,1,2,2,1] => [4,2,2,1,1] => 567
[4,1,2,3] => [4,3,2,1] => 768
[4,1,3,1,1] => [4,3,1,1,1] => 525
[4,1,3,2] => [4,3,2,1] => 768
[4,1,4,1] => [4,4,1,1] => 300
[4,1,5] => [5,4,1] => 288
[4,2,1,1,1,1] => [4,2,1,1,1,1] => 350
[4,2,1,1,2] => [4,2,2,1,1] => 567
[4,2,1,2,1] => [4,2,2,1,1] => 567
[4,2,1,3] => [4,3,2,1] => 768
[4,2,2,1,1] => [4,2,2,1,1] => 567
[4,2,2,2] => [4,2,2,2] => 300
[4,2,3,1] => [4,3,2,1] => 768
[4,2,4] => [4,4,2] => 252
[4,3,1,1,1] => [4,3,1,1,1] => 525
[4,3,1,2] => [4,3,2,1] => 768
[4,3,2,1] => [4,3,2,1] => 768
[4,3,3] => [4,3,3] => 210
[4,4,1,1] => [4,4,1,1] => 300
[4,4,2] => [4,4,2] => 252
[4,5,1] => [5,4,1] => 288
[4,6] => [6,4] => 90
[5,1,1,1,1,1] => [5,1,1,1,1,1] => 126
[5,1,1,1,2] => [5,2,1,1,1] => 448
[5,1,1,2,1] => [5,2,1,1,1] => 448
[5,1,1,3] => [5,3,1,1] => 567
[5,1,2,1,1] => [5,2,1,1,1] => 448
[5,1,2,2] => [5,2,2,1] => 525
[5,1,3,1] => [5,3,1,1] => 567
[5,1,4] => [5,4,1] => 288
[5,2,1,1,1] => [5,2,1,1,1] => 448
[5,2,1,2] => [5,2,2,1] => 525
[5,2,2,1] => [5,2,2,1] => 525
[5,2,3] => [5,3,2] => 450
[5,3,1,1] => [5,3,1,1] => 567
[5,3,2] => [5,3,2] => 450
[5,4,1] => [5,4,1] => 288
[5,5] => [5,5] => 42
[6,1,1,1,1] => [6,1,1,1,1] => 126
[6,1,1,2] => [6,2,1,1] => 350
[6,1,2,1] => [6,2,1,1] => 350
[6,1,3] => [6,3,1] => 315
[6,2,1,1] => [6,2,1,1] => 350
[6,2,2] => [6,2,2] => 225
[6,3,1] => [6,3,1] => 315
[6,4] => [6,4] => 90
[7,1,1,1] => [7,1,1,1] => 84
[7,1,2] => [7,2,1] => 160
[7,2,1] => [7,2,1] => 160
[7,3] => [7,3] => 75
[8,1,1] => [8,1,1] => 36
[8,2] => [8,2] => 35
[9,1] => [9,1] => 9
[10] => [10] => 1
[1,10] => [10,1] => 10
[1,8,1,1] => [8,1,1,1] => 120
[1,7,2,1] => [7,2,1,1] => 594
[1,6,3,1] => [6,3,1,1] => 1232
[1,5,4,1] => [5,4,1,1] => 1155
[1,4,5,1] => [5,4,1,1] => 1155
[1,3,6,1] => [6,3,1,1] => 1232
[1,2,7,1] => [7,2,1,1] => 594
[1,1,8,1] => [8,1,1,1] => 120
[10,1] => [10,1] => 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
[1,1,1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,1,1,1,1,3,3] => [3,3,1,1,1,1,1,1] => 616
[1,1,1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,1,1,2,2,2,2] => [2,2,2,2,1,1,1,1] => 275
[1,1,1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,1,1,2,1,2,3] => [3,2,2,1,1,1,1,1] => 891
[1,1,1,1,3,3,1,1] => [3,3,1,1,1,1,1,1] => 616
[1,1,1,1,3,2,1,2] => [3,2,2,1,1,1,1,1] => 891
[1,1,1,1,3,1,1,3] => [3,3,1,1,1,1,1,1] => 616
[1,1,1,1,4,4] => [4,4,1,1,1,1] => 1925
[1,1,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,2,2,1,1,2,2] => [2,2,2,2,1,1,1,1] => 275
[1,1,2,2,2,2,1,1] => [2,2,2,2,1,1,1,1] => 275
[1,1,2,2,2,1,1,2] => [2,2,2,2,1,1,1,1] => 275
[1,1,2,2,3,3] => [3,3,2,2,1,1] => 2673
[1,1,2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,2,1,1,2,2,2] => [2,2,2,2,1,1,1,1] => 275
[1,1,2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,2,1,1,1,2,3] => [3,2,2,1,1,1,1,1] => 891
[1,1,2,1,2,3,1,1] => [3,2,2,1,1,1,1,1] => 891
[1,1,2,1,2,2,1,2] => [2,2,2,2,1,1,1,1] => 275
[1,1,2,1,2,1,1,3] => [3,2,2,1,1,1,1,1] => 891
[1,1,2,1,3,4] => [4,3,2,1,1,1] => 5632
[1,1,3,3,1,1,1,1] => [3,3,1,1,1,1,1,1] => 616
[1,1,3,3,2,2] => [3,3,2,2,1,1] => 2673
[1,1,3,2,1,2,1,1] => [3,2,2,1,1,1,1,1] => 891
[1,1,3,2,1,1,1,2] => [3,2,2,1,1,1,1,1] => 891
[1,1,3,2,2,3] => [3,3,2,2,1,1] => 2673
[1,1,3,1,1,3,1,1] => [3,3,1,1,1,1,1,1] => 616
[1,1,3,1,1,2,1,2] => [3,2,2,1,1,1,1,1] => 891
[1,1,3,1,1,1,1,3] => [3,3,1,1,1,1,1,1] => 616
[1,1,3,1,2,4] => [4,3,2,1,1,1] => 5632
[1,1,4,4,1,1] => [4,4,1,1,1,1] => 1925
[1,1,4,3,1,2] => [4,3,2,1,1,1] => 5632
[1,1,4,2,1,3] => [4,3,2,1,1,1] => 5632
[1,1,4,1,1,4] => [4,4,1,1,1,1] => 1925
[1,1,5,5] => [5,5,1,1] => 1485
[2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[2,2,1,1,1,1,2,2] => [2,2,2,2,1,1,1,1] => 275
[2,2,1,1,2,2,1,1] => [2,2,2,2,1,1,1,1] => 275
[2,2,1,1,2,1,1,2] => [2,2,2,2,1,1,1,1] => 275
[2,2,1,1,3,3] => [3,3,2,2,1,1] => 2673
[2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 275
[2,2,2,2,2,2] => [2,2,2,2,2,2] => 132
[2,2,2,1,1,2,1,1] => [2,2,2,2,1,1,1,1] => 275
[2,2,2,1,1,1,1,2] => [2,2,2,2,1,1,1,1] => 275
[2,2,2,1,2,3] => [3,2,2,2,2,1] => 1155
[2,2,3,3,1,1] => [3,3,2,2,1,1] => 2673
[2,2,3,2,1,2] => [3,2,2,2,2,1] => 1155
[2,2,3,1,1,3] => [3,3,2,2,1,1] => 2673
[2,2,4,4] => [4,4,2,2] => 2640
[2,1,1,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[2,1,1,2,1,1,2,2] => [2,2,2,2,1,1,1,1] => 275
[2,1,1,2,2,2,1,1] => [2,2,2,2,1,1,1,1] => 275
[2,1,1,2,2,1,1,2] => [2,2,2,2,1,1,1,1] => 275
[2,1,1,2,3,3] => [3,3,2,2,1,1] => 2673
[2,1,1,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[2,1,1,1,1,2,2,2] => [2,2,2,2,1,1,1,1] => 275
[2,1,1,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[2,1,1,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 54
[2,1,1,1,1,1,2,3] => [3,2,2,1,1,1,1,1] => 891
[2,1,1,1,2,3,1,1] => [3,2,2,1,1,1,1,1] => 891
[2,1,1,1,2,2,1,2] => [2,2,2,2,1,1,1,1] => 275
[2,1,1,1,2,1,1,3] => [3,2,2,1,1,1,1,1] => 891
[2,1,1,1,3,4] => [4,3,2,1,1,1] => 5632
[2,1,2,3,1,1,1,1] => [3,2,2,1,1,1,1,1] => 891
[2,1,2,3,2,2] => [3,2,2,2,2,1] => 1155
[2,1,2,2,1,2,1,1] => [2,2,2,2,1,1,1,1] => 275
[2,1,2,2,1,1,1,2] => [2,2,2,2,1,1,1,1] => 275
[2,1,2,2,2,3] => [3,2,2,2,2,1] => 1155
[2,1,2,1,1,3,1,1] => [3,2,2,1,1,1,1,1] => 891
[2,1,2,1,1,2,1,2] => [2,2,2,2,1,1,1,1] => 275
[2,1,2,1,1,1,1,3] => [3,2,2,1,1,1,1,1] => 891
[2,1,2,1,2,4] => [4,2,2,2,1,1] => 3080
[2,1,3,4,1,1] => [4,3,2,1,1,1] => 5632
[2,1,3,3,1,2] => [3,3,2,2,1,1] => 2673
[2,1,3,2,1,3] => [3,3,2,2,1,1] => 2673
[2,1,3,1,1,4] => [4,3,2,1,1,1] => 5632
[2,1,4,5] => [5,4,2,1] => 5775
[3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => 616
[3,3,1,1,2,2] => [3,3,2,2,1,1] => 2673
[3,3,2,2,1,1] => [3,3,2,2,1,1] => 2673
[3,3,2,1,1,2] => [3,3,2,2,1,1] => 2673
[3,3,3,3] => [3,3,3,3] => 462
[3,2,1,2,1,1,1,1] => [3,2,2,1,1,1,1,1] => 891
[3,2,1,2,2,2] => [3,2,2,2,2,1] => 1155
[3,2,1,1,1,2,1,1] => [3,2,2,1,1,1,1,1] => 891
[3,2,1,1,1,1,1,2] => [3,2,2,1,1,1,1,1] => 891
[3,2,1,1,2,3] => [3,3,2,2,1,1] => 2673
[3,2,2,3,1,1] => [3,3,2,2,1,1] => 2673
[3,2,2,2,1,2] => [3,2,2,2,2,1] => 1155
[3,2,2,1,1,3] => [3,3,2,2,1,1] => 2673
[3,2,3,4] => [4,3,3,2] => 2970
[3,1,1,3,1,1,1,1] => [3,3,1,1,1,1,1,1] => 616
[3,1,1,3,2,2] => [3,3,2,2,1,1] => 2673
[3,1,1,2,1,2,1,1] => [3,2,2,1,1,1,1,1] => 891
[3,1,1,2,1,1,1,2] => [3,2,2,1,1,1,1,1] => 891
[3,1,1,2,2,3] => [3,3,2,2,1,1] => 2673
[3,1,1,1,1,3,1,1] => [3,3,1,1,1,1,1,1] => 616
[3,1,1,1,1,2,1,2] => [3,2,2,1,1,1,1,1] => 891
[3,1,1,1,1,1,1,3] => [3,3,1,1,1,1,1,1] => 616
[3,1,1,1,2,4] => [4,3,2,1,1,1] => 5632
[3,1,2,4,1,1] => [4,3,2,1,1,1] => 5632
[3,1,2,3,1,2] => [3,3,2,2,1,1] => 2673
[3,1,2,2,1,3] => [3,3,2,2,1,1] => 2673
[3,1,2,1,1,4] => [4,3,2,1,1,1] => 5632
[3,1,3,5] => [5,3,3,1] => 4158
[4,4,1,1,1,1] => [4,4,1,1,1,1] => 1925
[4,4,2,2] => [4,4,2,2] => 2640
[4,3,1,2,1,1] => [4,3,2,1,1,1] => 5632
[4,3,1,1,1,2] => [4,3,2,1,1,1] => 5632
[4,3,2,3] => [4,3,3,2] => 2970
[4,2,1,3,1,1] => [4,3,2,1,1,1] => 5632
[4,2,1,2,1,2] => [4,2,2,2,1,1] => 3080
[4,2,1,1,1,3] => [4,3,2,1,1,1] => 5632
[4,2,2,4] => [4,4,2,2] => 2640
[4,1,1,4,1,1] => [4,4,1,1,1,1] => 1925
[4,1,1,3,1,2] => [4,3,2,1,1,1] => 5632
[4,1,1,2,1,3] => [4,3,2,1,1,1] => 5632
[4,1,1,1,1,4] => [4,4,1,1,1,1] => 1925
[4,1,2,5] => [5,4,2,1] => 5775
[5,5,1,1] => [5,5,1,1] => 1485
[5,4,1,2] => [5,4,2,1] => 5775
[5,3,1,3] => [5,3,3,1] => 4158
[5,2,1,4] => [5,4,2,1] => 5775
[5,1,1,5] => [5,5,1,1] => 1485
[6,6] => [6,6] => 132
[1,2,2,2,2,2,1] => [2,2,2,2,2,1,1] => 297
[1,2,2,2,3,2] => [3,2,2,2,2,1] => 1155
[1,2,2,3,3,1] => [3,3,2,2,1,1] => 2673
[1,2,2,3,2,2] => [3,2,2,2,2,1] => 1155
[1,2,2,4,3] => [4,3,2,2,1] => 5775
[1,2,3,3,2,1] => [3,3,2,2,1,1] => 2673
[1,2,3,4,2] => [4,3,2,2,1] => 5775
[1,2,3,2,3,1] => [3,3,2,2,1,1] => 2673
[1,2,3,2,2,2] => [3,2,2,2,2,1] => 1155
[1,2,3,3,3] => [3,3,3,2,1] => 2112
[1,2,4,4,1] => [4,4,2,1,1] => 4455
[1,2,4,3,2] => [4,3,2,2,1] => 5775
[1,2,4,2,3] => [4,3,2,2,1] => 5775
[1,2,5,4] => [5,4,2,1] => 5775
[1,3,3,2,2,1] => [3,3,2,2,1,1] => 2673
[1,3,3,3,2] => [3,3,3,2,1] => 2112
[1,3,4,3,1] => [4,3,3,1,1] => 4158
[1,3,4,2,2] => [4,3,2,2,1] => 5775
[1,3,5,3] => [5,3,3,1] => 4158
[1,3,2,3,2,1] => [3,3,2,2,1,1] => 2673
[1,3,2,4,2] => [4,3,2,2,1] => 5775
[1,3,2,2,3,1] => [3,3,2,2,1,1] => 2673
[1,3,2,2,2,2] => [3,2,2,2,2,1] => 1155
[1,3,2,3,3] => [3,3,3,2,1] => 2112
[1,3,3,4,1] => [4,3,3,1,1] => 4158
[1,3,3,2,3] => [3,3,3,2,1] => 2112
[1,3,4,4] => [4,4,3,1] => 2970
[1,4,4,2,1] => [4,4,2,1,1] => 4455
[1,4,5,2] => [5,4,2,1] => 5775
[1,4,3,3,1] => [4,3,3,1,1] => 4158
[1,4,3,2,2] => [4,3,2,2,1] => 5775
[1,4,4,3] => [4,4,3,1] => 2970
[1,4,2,4,1] => [4,4,2,1,1] => 4455
[1,4,2,3,2] => [4,3,2,2,1] => 5775
[1,4,2,2,3] => [4,3,2,2,1] => 5775
[1,4,3,4] => [4,4,3,1] => 2970
[1,5,5,1] => [5,5,1,1] => 1485
[1,5,4,2] => [5,4,2,1] => 5775
[1,5,3,3] => [5,3,3,1] => 4158
[1,5,2,4] => [5,4,2,1] => 5775
[1,6,5] => [6,5,1] => 1155
[2,3,2,2,2,1] => [3,2,2,2,2,1] => 1155
[2,3,2,3,2] => [3,3,2,2,2] => 1320
[2,3,3,3,1] => [3,3,3,2,1] => 2112
[2,3,3,2,2] => [3,3,2,2,2] => 1320
[2,3,4,3] => [4,3,3,2] => 2970
[2,4,3,2,1] => [4,3,2,2,1] => 5775
[2,4,4,2] => [4,4,2,2] => 2640
[2,4,2,3,1] => [4,3,2,2,1] => 5775
[2,4,2,2,2] => [4,2,2,2,2] => 1485
[2,4,3,3] => [4,3,3,2] => 2970
[2,5,4,1] => [5,4,2,1] => 5775
[2,5,3,2] => [5,3,2,2] => 4455
[2,5,2,3] => [5,3,2,2] => 4455
[2,6,4] => [6,4,2] => 2673
[2,2,3,2,2,1] => [3,2,2,2,2,1] => 1155
[2,2,3,3,2] => [3,3,2,2,2] => 1320
[2,2,4,3,1] => [4,3,2,2,1] => 5775
[2,2,4,2,2] => [4,2,2,2,2] => 1485
[2,2,5,3] => [5,3,2,2] => 4455
[2,2,2,3,2,1] => [3,2,2,2,2,1] => 1155
[2,2,2,4,2] => [4,2,2,2,2] => 1485
[2,2,2,2,3,1] => [3,2,2,2,2,1] => 1155
[2,2,2,3,3] => [3,3,2,2,2] => 1320
[2,2,3,4,1] => [4,3,2,2,1] => 5775
[2,2,3,2,3] => [3,3,2,2,2] => 1320
[2,3,4,2,1] => [4,3,2,2,1] => 5775
[2,3,5,2] => [5,3,2,2] => 4455
[2,3,2,4,1] => [4,3,2,2,1] => 5775
[2,3,2,2,3] => [3,3,2,2,2] => 1320
[2,3,3,4] => [4,3,3,2] => 2970
[2,4,5,1] => [5,4,2,1] => 5775
[2,4,2,4] => [4,4,2,2] => 2640
[2,5,5] => [5,5,2] => 1320
[3,4,2,2,1] => [4,3,2,2,1] => 5775
[3,4,3,2] => [4,3,3,2] => 2970
[3,5,3,1] => [5,3,3,1] => 4158
[3,5,2,2] => [5,3,2,2] => 4455
[3,6,3] => [6,3,3] => 1650
[3,3,3,2,1] => [3,3,3,2,1] => 2112
[3,3,4,2] => [4,3,3,2] => 2970
[3,3,2,3,1] => [3,3,3,2,1] => 2112
[3,3,2,2,2] => [3,3,2,2,2] => 1320
[3,4,4,1] => [4,4,3,1] => 2970
[3,4,2,3] => [4,3,3,2] => 2970
[3,5,4] => [5,4,3] => 2112
[3,2,4,2,1] => [4,3,2,2,1] => 5775
[3,2,5,2] => [5,3,2,2] => 4455
[3,2,3,3,1] => [3,3,3,2,1] => 2112
[3,2,3,2,2] => [3,3,2,2,2] => 1320
[3,2,4,3] => [4,3,3,2] => 2970
[3,2,2,4,1] => [4,3,2,2,1] => 5775
[3,2,2,3,2] => [3,3,2,2,2] => 1320
[3,2,2,2,3] => [3,3,2,2,2] => 1320
[3,3,5,1] => [5,3,3,1] => 4158
[3,3,2,4] => [4,3,3,2] => 2970
[3,4,5] => [5,4,3] => 2112
[4,5,2,1] => [5,4,2,1] => 5775
[4,6,2] => [6,4,2] => 2673
[4,4,3,1] => [4,4,3,1] => 2970
[4,5,3] => [5,4,3] => 2112
[4,3,4,1] => [4,4,3,1] => 2970
[4,3,3,2] => [4,3,3,2] => 2970
[4,4,4] => [4,4,4] => 462
[4,2,5,1] => [5,4,2,1] => 5775
[4,2,4,2] => [4,4,2,2] => 2640
[4,2,3,3] => [4,3,3,2] => 2970
[4,3,5] => [5,4,3] => 2112
[5,6,1] => [6,5,1] => 1155
[5,5,2] => [5,5,2] => 1320
[5,4,3] => [5,4,3] => 2112
[5,3,4] => [5,4,3] => 2112
[5,2,5] => [5,5,2] => 1320
[1,8,2] => [8,2,1] => 231
[1,7,1,2] => [7,2,1,1] => 594
[1,6,1,1,2] => [6,2,1,1,1] => 924
[1,5,1,1,1,2] => [5,2,1,1,1,1] => 924
[1,4,1,1,1,1,2] => [4,2,1,1,1,1,1] => 594
[1,3,1,1,1,1,1,2] => [3,2,1,1,1,1,1,1] => 231
[1,2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1] => 44
[1,1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1,1] => 10
[1,11] => [11,1] => 11
[1,9,2] => [9,2,1] => 320
[1,7,3] => [7,3,1] => 550
[1,8,1,2] => [8,2,1,1] => 945
[1,6,2,2] => [6,2,2,1] => 1100
[1,7,1,1,2] => [7,2,1,1,1] => 1728
[1,5,2,1,2] => [5,2,2,1,1] => 1540
[1,6,1,1,1,2] => [6,2,1,1,1,1] => 2100
[1,4,2,1,1,2] => [4,2,2,1,1,1] => 1232
[1,5,1,1,1,1,2] => [5,2,1,1,1,1,1] => 1728
[1,3,2,1,1,1,2] => [3,2,2,1,1,1,1] => 550
[1,4,1,1,1,1,1,2] => [4,2,1,1,1,1,1,1] => 945
[1,2,2,1,1,1,1,2] => [2,2,2,1,1,1,1,1] => 110
[1,3,1,1,1,1,1,1,2] => [3,2,1,1,1,1,1,1,1] => 320
[1,1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1] => 44
[1,2,1,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1,1,1] => 11
[1,2,2,2,2,2] => [2,2,2,2,2,1] => 132
[1,2,2,2,1,3] => [3,2,2,2,1,1] => 693
[1,2,2,1,3,2] => [3,2,2,2,1,1] => 693
[1,2,2,1,2,3] => [3,2,2,2,1,1] => 693
[1,2,2,1,1,4] => [4,2,2,1,1,1] => 1232
[1,2,1,3,2,2] => [3,2,2,2,1,1] => 693
[1,2,1,3,1,3] => [3,3,2,1,1,1] => 990
[1,2,1,2,3,2] => [3,2,2,2,1,1] => 693
[1,2,1,2,2,3] => [3,2,2,2,1,1] => 693
[1,2,1,2,1,4] => [4,2,2,1,1,1] => 1232
[1,2,1,1,4,2] => [4,2,2,1,1,1] => 1232
[1,2,1,1,3,3] => [3,3,2,1,1,1] => 990
[1,2,1,1,2,4] => [4,2,2,1,1,1] => 1232
[1,2,1,1,1,5] => [5,2,1,1,1,1] => 924
[1,1,3,2,2,2] => [3,2,2,2,1,1] => 693
[1,1,3,2,1,3] => [3,3,2,1,1,1] => 990
[1,1,3,1,3,2] => [3,3,2,1,1,1] => 990
[1,1,3,1,2,3] => [3,3,2,1,1,1] => 990
[1,1,3,1,1,4] => [4,3,1,1,1,1] => 1100
[1,1,2,3,2,2] => [3,2,2,2,1,1] => 693
[1,1,2,3,1,3] => [3,3,2,1,1,1] => 990
[1,1,2,2,3,2] => [3,2,2,2,1,1] => 693
[1,1,2,2,2,3] => [3,2,2,2,1,1] => 693
[1,1,2,2,1,4] => [4,2,2,1,1,1] => 1232
[1,1,2,1,4,2] => [4,2,2,1,1,1] => 1232
[1,1,2,1,3,3] => [3,3,2,1,1,1] => 990
[1,1,2,1,2,4] => [4,2,2,1,1,1] => 1232
[1,1,2,1,1,5] => [5,2,1,1,1,1] => 924
[1,1,1,4,2,2] => [4,2,2,1,1,1] => 1232
[1,1,1,4,1,3] => [4,3,1,1,1,1] => 1100
[1,1,1,3,3,2] => [3,3,2,1,1,1] => 990
[1,1,1,3,2,3] => [3,3,2,1,1,1] => 990
[1,1,1,3,1,4] => [4,3,1,1,1,1] => 1100
[1,1,1,2,4,2] => [4,2,2,1,1,1] => 1232
[1,1,1,2,3,3] => [3,3,2,1,1,1] => 990
[1,1,1,2,2,4] => [4,2,2,1,1,1] => 1232
[1,1,1,2,1,5] => [5,2,1,1,1,1] => 924
[1,1,1,1,5,2] => [5,2,1,1,1,1] => 924
[1,1,1,1,4,3] => [4,3,1,1,1,1] => 1100
[1,1,1,1,3,4] => [4,3,1,1,1,1] => 1100
[1,1,1,1,2,5] => [5,2,1,1,1,1] => 924
[1,1,1,1,1,6] => [6,1,1,1,1,1] => 252
[1,2,2,2,2,2,2] => [2,2,2,2,2,2,1] => 429
[12] => [12] => 1
[1,2,9] => [9,2,1] => 320
[3,2,7] => [7,3,2] => 1925
[1,4,7] => [7,4,1] => 1408
[1,1,2,1,7] => [7,2,1,1,1] => 1728
[1,2,2,2,5] => [5,2,2,2,1] => 3520
[1,1,2,3,5] => [5,3,2,1,1] => 7700
[3,1,2,1,5] => [5,3,2,1,1] => 7700
[1,3,2,1,5] => [5,3,2,1,1] => 7700
[1,1,4,1,5] => [5,4,1,1,1] => 3520
[1,1,1,2,1,1,5] => [5,2,1,1,1,1,1] => 1728
[7,2,3] => [7,3,2] => 1925
[1,1,2,1,2,2,3] => [3,2,2,2,1,1,1] => 1408
[1,8,3] => [8,3,1] => 891
[1,1,2,5,3] => [5,3,2,1,1] => 7700
[3,1,2,3,3] => [3,3,3,2,1] => 2112
[1,1,4,3,3] => [4,3,3,1,1] => 4158
[1,1,1,2,1,3,3] => [3,3,2,1,1,1,1] => 1925
[5,1,2,1,3] => [5,3,2,1,1] => 7700
[1,2,2,1,2,1,3] => [3,2,2,2,1,1,1] => 1408
[3,3,2,1,3] => [3,3,3,2,1] => 2112
[1,5,2,1,3] => [5,3,2,1,1] => 7700
[1,1,2,2,2,1,3] => [3,2,2,2,1,1,1] => 1408
[3,1,4,1,3] => [4,3,3,1,1] => 4158
[1,3,4,1,3] => [4,3,3,1,1] => 4158
[1,1,6,1,3] => [6,3,1,1,1] => 3696
[1,1,1,2,3,1,3] => [3,3,2,1,1,1,1] => 1925
[3,1,1,2,1,1,3] => [3,3,2,1,1,1,1] => 1925
[1,3,1,2,1,1,3] => [3,3,2,1,1,1,1] => 1925
[1,1,3,2,1,1,3] => [3,3,2,1,1,1,1] => 1925
[1,1,1,4,1,1,3] => [4,3,1,1,1,1,1] => 2079
[1,1,1,1,2,1,1,1,3] => [3,2,1,1,1,1,1,1,1] => 320
[9,2,1] => [9,2,1] => 320
[1,2,6,2,1] => [6,2,2,1,1] => 3564
[1,1,2,1,4,2,1] => [4,2,2,1,1,1,1] => 2376
[5,2,2,2,1] => [5,2,2,2,1] => 3520
[1,6,2,2,1] => [6,2,2,1,1] => 3564
[1,1,2,3,2,2,1] => [3,2,2,2,1,1,1] => 1408
[3,1,2,1,2,2,1] => [3,2,2,2,1,1,1] => 1408
[1,3,2,1,2,2,1] => [3,2,2,2,1,1,1] => 1408
[1,1,4,1,2,2,1] => [4,2,2,1,1,1,1] => 2376
[1,1,1,2,1,1,2,2,1] => [2,2,2,1,1,1,1,1,1] => 154
[7,4,1] => [7,4,1] => 1408
[1,1,2,1,2,4,1] => [4,2,2,1,1,1,1] => 2376
[1,2,2,6,1] => [6,2,2,1,1] => 3564
[3,8,1] => [8,3,1] => 891
[1,10,1] => [10,1,1] => 55
[1,1,2,7,1] => [7,2,1,1,1] => 1728
[3,1,2,5,1] => [5,3,2,1,1] => 7700
[1,3,2,5,1] => [5,3,2,1,1] => 7700
[1,1,4,5,1] => [5,4,1,1,1] => 3520
[1,1,1,2,1,5,1] => [5,2,1,1,1,1,1] => 1728
[5,1,2,3,1] => [5,3,2,1,1] => 7700
[1,2,2,1,2,3,1] => [3,2,2,2,1,1,1] => 1408
[1,5,2,3,1] => [5,3,2,1,1] => 7700
[1,1,2,2,2,3,1] => [3,2,2,2,1,1,1] => 1408
[3,1,4,3,1] => [4,3,3,1,1] => 4158
[1,1,6,3,1] => [6,3,1,1,1] => 3696
[1,1,1,2,3,3,1] => [3,3,2,1,1,1,1] => 1925
[3,1,1,2,1,3,1] => [3,3,2,1,1,1,1] => 1925
[1,3,1,2,1,3,1] => [3,3,2,1,1,1,1] => 1925
[1,1,3,2,1,3,1] => [3,3,2,1,1,1,1] => 1925
[1,1,1,4,1,3,1] => [4,3,1,1,1,1,1] => 2079
[1,1,1,1,2,1,1,3,1] => [3,2,1,1,1,1,1,1,1] => 320
[7,1,2,1,1] => [7,2,1,1,1] => 1728
[1,2,4,1,2,1,1] => [4,2,2,1,1,1,1] => 2376
[3,2,2,1,2,1,1] => [3,2,2,2,1,1,1] => 1408
[1,4,2,1,2,1,1] => [4,2,2,1,1,1,1] => 2376
[1,1,2,1,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[5,3,2,1,1] => [5,3,2,1,1] => 7700
[1,2,2,3,2,1,1] => [3,2,2,2,1,1,1] => 1408
[3,5,2,1,1] => [5,3,2,1,1] => 7700
[1,7,2,1,1] => [7,2,1,1,1] => 1728
[1,1,2,4,2,1,1] => [4,2,2,1,1,1,1] => 2376
[3,1,2,2,2,1,1] => [3,2,2,2,1,1,1] => 1408
[1,3,2,2,2,1,1] => [3,2,2,2,1,1,1] => 1408
[1,1,4,2,2,1,1] => [4,2,2,1,1,1,1] => 2376
[1,1,1,2,1,2,2,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[5,1,4,1,1] => [5,4,1,1,1] => 3520
[1,2,2,1,4,1,1] => [4,2,2,1,1,1,1] => 2376
[3,3,4,1,1] => [4,3,3,1,1] => 4158
[1,5,4,1,1] => [5,4,1,1,1] => 3520
[1,1,2,2,4,1,1] => [4,2,2,1,1,1,1] => 2376
[3,1,6,1,1] => [6,3,1,1,1] => 3696
[1,3,6,1,1] => [6,3,1,1,1] => 3696
[1,1,8,1,1] => [8,1,1,1,1] => 330
[1,1,1,2,5,1,1] => [5,2,1,1,1,1,1] => 1728
[3,1,1,2,3,1,1] => [3,3,2,1,1,1,1] => 1925
[1,3,1,2,3,1,1] => [3,3,2,1,1,1,1] => 1925
[1,1,3,2,3,1,1] => [3,3,2,1,1,1,1] => 1925
[1,1,1,4,3,1,1] => [4,3,1,1,1,1,1] => 2079
[1,1,1,1,2,1,3,1,1] => [3,2,1,1,1,1,1,1,1] => 320
[5,1,1,2,1,1,1] => [5,2,1,1,1,1,1] => 1728
[1,2,2,1,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[3,3,1,2,1,1,1] => [3,3,2,1,1,1,1] => 1925
[1,5,1,2,1,1,1] => [5,2,1,1,1,1,1] => 1728
[1,1,2,2,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[3,1,3,2,1,1,1] => [3,3,2,1,1,1,1] => 1925
[1,3,3,2,1,1,1] => [3,3,2,1,1,1,1] => 1925
[1,1,5,2,1,1,1] => [5,2,1,1,1,1,1] => 1728
[1,1,1,2,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[3,1,1,4,1,1,1] => [4,3,1,1,1,1,1] => 2079
[1,3,1,4,1,1,1] => [4,3,1,1,1,1,1] => 2079
[1,1,3,4,1,1,1] => [4,3,1,1,1,1,1] => 2079
[1,1,1,6,1,1,1] => [6,1,1,1,1,1,1] => 462
[1,1,1,1,2,3,1,1,1] => [3,2,1,1,1,1,1,1,1] => 320
[3,1,1,1,2,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => 320
[1,3,1,1,2,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => 320
[1,1,3,1,2,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => 320
[1,1,1,3,2,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => 320
[1,1,1,1,4,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => 165
[1,1,1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 11
[2,2,2,2,1,2,1] => [2,2,2,2,2,1,1] => 297
[2,2,2,1,2,1,2] => [2,2,2,2,2,1,1] => 297
[2,2,2,1,2,2,1] => [2,2,2,2,2,1,1] => 297
[2,2,2,1,1,2,2] => [2,2,2,2,2,1,1] => 297
[2,2,1,2,1,2,2] => [2,2,2,2,2,1,1] => 297
[2,2,1,2,1,1,2,1] => [2,2,2,2,1,1,1,1] => 275
[2,2,1,2,2,1,2] => [2,2,2,2,2,1,1] => 297
[2,2,1,2,2,2,1] => [2,2,2,2,2,1,1] => 297
[2,2,1,1,2,2,2] => [2,2,2,2,2,1,1] => 297
[2,2,1,1,2,1,2,1] => [2,2,2,2,1,1,1,1] => 275
[2,2,1,1,1,2,2,1] => [2,2,2,2,1,1,1,1] => 275
[2,1,2,1,2,2,2] => [2,2,2,2,2,1,1] => 297
[2,1,2,1,2,1,2,1] => [2,2,2,2,1,1,1,1] => 275
[2,1,2,1,1,2,2,1] => [2,2,2,2,1,1,1,1] => 275
[2,1,2,1,1,1,2,2] => [2,2,2,2,1,1,1,1] => 275
[2,1,2,2,1,2,2] => [2,2,2,2,2,1,1] => 297
[2,1,2,2,1,1,2,1] => [2,2,2,2,1,1,1,1] => 275
[2,1,2,2,2,1,2] => [2,2,2,2,2,1,1] => 297
[2,1,2,2,2,2,1] => [2,2,2,2,2,1,1] => 297
[2,1,1,2,2,2,2] => [2,2,2,2,2,1,1] => 297
[2,1,1,2,2,1,2,1] => [2,2,2,2,1,1,1,1] => 275
[2,1,1,2,1,2,1,2] => [2,2,2,2,1,1,1,1] => 275
[2,1,1,2,1,2,2,1] => [2,2,2,2,1,1,1,1] => 275
[2,1,1,1,2,2,2,1] => [2,2,2,2,1,1,1,1] => 275
[2,1,1,1,2,1,2,2] => [2,2,2,2,1,1,1,1] => 275
[1,2,1,2,2,2,2] => [2,2,2,2,2,1,1] => 297
[1,2,1,2,2,1,2,1] => [2,2,2,2,1,1,1,1] => 275
[1,2,1,2,1,2,1,2] => [2,2,2,2,1,1,1,1] => 275
[1,2,1,2,1,2,2,1] => [2,2,2,2,1,1,1,1] => 275
[1,2,1,2,1,1,2,2] => [2,2,2,2,1,1,1,1] => 275
[1,2,1,1,2,1,2,2] => [2,2,2,2,1,1,1,1] => 275
[1,2,1,1,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,2,1,1,2,2,1,2] => [2,2,2,2,1,1,1,1] => 275
[1,2,1,1,2,2,2,1] => [2,2,2,2,1,1,1,1] => 275
[1,2,1,1,1,2,2,2] => [2,2,2,2,1,1,1,1] => 275
[1,2,1,1,1,2,1,2,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,2,1,1,1,1,2,2,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,2,2,1,2,2,2] => [2,2,2,2,2,1,1] => 297
[1,2,2,1,2,1,2,1] => [2,2,2,2,1,1,1,1] => 275
[1,2,2,1,1,2,1,2] => [2,2,2,2,1,1,1,1] => 275
[1,2,2,1,1,2,2,1] => [2,2,2,2,1,1,1,1] => 275
[1,2,2,1,1,1,2,2] => [2,2,2,2,1,1,1,1] => 275
[1,2,2,2,1,2,2] => [2,2,2,2,2,1,1] => 297
[1,2,2,2,1,1,2,1] => [2,2,2,2,1,1,1,1] => 275
[1,2,2,2,2,1,2] => [2,2,2,2,2,1,1] => 297
[1,1,2,2,2,2,2] => [2,2,2,2,2,1,1] => 297
[1,1,2,2,2,1,2,1] => [2,2,2,2,1,1,1,1] => 275
[1,1,2,2,1,2,1,2] => [2,2,2,2,1,1,1,1] => 275
[1,1,2,2,1,2,2,1] => [2,2,2,2,1,1,1,1] => 275
[1,1,2,1,2,1,2,2] => [2,2,2,2,1,1,1,1] => 275
[1,1,2,1,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,2,1,2,2,2,1] => [2,2,2,2,1,1,1,1] => 275
[1,1,2,1,1,2,1,2,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,2,1,1,1,2,2,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,1,2,2,1,2,2] => [2,2,2,2,1,1,1,1] => 275
[1,1,1,2,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,1,2,2,2,1,2] => [2,2,2,2,1,1,1,1] => 275
[1,1,1,2,2,2,2,1] => [2,2,2,2,1,1,1,1] => 275
[1,1,1,2,1,2,2,2] => [2,2,2,2,1,1,1,1] => 275
[1,1,1,2,1,2,1,2,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,1,1,2,2,1,2,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,1,1,2,1,2,2,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,1,1,1,2,2,2,1] => [2,2,2,1,1,1,1,1,1] => 154
[2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 10
[3,2,2,2,2,1] => [3,2,2,2,2,1] => 1155
[4,3,2,2,1] => [4,3,2,2,1] => 5775
[4,2,3,2,1] => [4,3,2,2,1] => 5775
[4,2,2,3,1] => [4,3,2,2,1] => 5775
[4,2,2,2,2] => [4,2,2,2,2] => 1485
[5,4,2,1] => [5,4,2,1] => 5775
[5,3,3,1] => [5,3,3,1] => 4158
[5,3,2,2] => [5,3,2,2] => 4455
[5,2,4,1] => [5,4,2,1] => 5775
[5,2,3,2] => [5,3,2,2] => 4455
[5,2,2,3] => [5,3,2,2] => 4455
[6,5,1] => [6,5,1] => 1155
[6,4,2] => [6,4,2] => 2673
[6,3,3] => [6,3,3] => 1650
[6,2,4] => [6,4,2] => 2673
[7,5] => [7,5] => 297
[2,8,1] => [8,2,1] => 231
[2,1,7,1] => [7,2,1,1] => 594
[2,1,1,6,1] => [6,2,1,1,1] => 924
[2,1,1,1,5,1] => [5,2,1,1,1,1] => 924
[2,1,1,1,1,4,1] => [4,2,1,1,1,1,1] => 594
[2,1,1,1,1,1,3,1] => [3,2,1,1,1,1,1,1] => 231
[2,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1] => 44
[11,1] => [11,1] => 11
[2,9,1] => [9,2,1] => 320
[3,7,1] => [7,3,1] => 550
[2,1,8,1] => [8,2,1,1] => 945
[2,2,6,1] => [6,2,2,1] => 1100
[2,1,1,7,1] => [7,2,1,1,1] => 1728
[2,1,2,5,1] => [5,2,2,1,1] => 1540
[2,1,1,1,6,1] => [6,2,1,1,1,1] => 2100
[2,1,1,2,4,1] => [4,2,2,1,1,1] => 1232
[2,1,1,1,1,5,1] => [5,2,1,1,1,1,1] => 1728
[2,1,1,1,2,3,1] => [3,2,2,1,1,1,1] => 550
[2,1,1,1,1,1,4,1] => [4,2,1,1,1,1,1,1] => 945
[2,1,1,1,1,2,2,1] => [2,2,2,1,1,1,1,1] => 110
[2,1,1,1,1,1,1,3,1] => [3,2,1,1,1,1,1,1,1] => 320
[2,1,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1] => 44
[2,1,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 11
[2,2,2,2,2,1] => [2,2,2,2,2,1] => 132
[3,1,2,2,2,1] => [3,2,2,2,1,1] => 693
[2,3,1,2,2,1] => [3,2,2,2,1,1] => 693
[3,2,1,2,2,1] => [3,2,2,2,1,1] => 693
[4,1,1,2,2,1] => [4,2,2,1,1,1] => 1232
[2,2,3,1,2,1] => [3,2,2,2,1,1] => 693
[3,1,3,1,2,1] => [3,3,2,1,1,1] => 990
[2,3,2,1,2,1] => [3,2,2,2,1,1] => 693
[3,2,2,1,2,1] => [3,2,2,2,1,1] => 693
[4,1,2,1,2,1] => [4,2,2,1,1,1] => 1232
[2,4,1,1,2,1] => [4,2,2,1,1,1] => 1232
[3,3,1,1,2,1] => [3,3,2,1,1,1] => 990
[4,2,1,1,2,1] => [4,2,2,1,1,1] => 1232
[5,1,1,1,2,1] => [5,2,1,1,1,1] => 924
[2,2,2,3,1,1] => [3,2,2,2,1,1] => 693
[3,1,2,3,1,1] => [3,3,2,1,1,1] => 990
[2,3,1,3,1,1] => [3,3,2,1,1,1] => 990
[3,2,1,3,1,1] => [3,3,2,1,1,1] => 990
[4,1,1,3,1,1] => [4,3,1,1,1,1] => 1100
[2,2,3,2,1,1] => [3,2,2,2,1,1] => 693
[3,1,3,2,1,1] => [3,3,2,1,1,1] => 990
[2,3,2,2,1,1] => [3,2,2,2,1,1] => 693
[3,2,2,2,1,1] => [3,2,2,2,1,1] => 693
[4,1,2,2,1,1] => [4,2,2,1,1,1] => 1232
[2,4,1,2,1,1] => [4,2,2,1,1,1] => 1232
[3,3,1,2,1,1] => [3,3,2,1,1,1] => 990
[4,2,1,2,1,1] => [4,2,2,1,1,1] => 1232
[5,1,1,2,1,1] => [5,2,1,1,1,1] => 924
[2,2,4,1,1,1] => [4,2,2,1,1,1] => 1232
[3,1,4,1,1,1] => [4,3,1,1,1,1] => 1100
[2,3,3,1,1,1] => [3,3,2,1,1,1] => 990
[3,2,3,1,1,1] => [3,3,2,1,1,1] => 990
[4,1,3,1,1,1] => [4,3,1,1,1,1] => 1100
[2,4,2,1,1,1] => [4,2,2,1,1,1] => 1232
[3,3,2,1,1,1] => [3,3,2,1,1,1] => 990
[4,2,2,1,1,1] => [4,2,2,1,1,1] => 1232
[5,1,2,1,1,1] => [5,2,1,1,1,1] => 924
[2,5,1,1,1,1] => [5,2,1,1,1,1] => 924
[3,4,1,1,1,1] => [4,3,1,1,1,1] => 1100
[4,3,1,1,1,1] => [4,3,1,1,1,1] => 1100
[5,2,1,1,1,1] => [5,2,1,1,1,1] => 924
[6,1,1,1,1,1] => [6,1,1,1,1,1] => 252
[2,2,2,2,2,2,1] => [2,2,2,2,2,2,1] => 429
[2,2,1,2,1,2,1,1] => [2,2,2,2,1,1,1,1] => 275
[2,2,1,1,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[2,1,2,1,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[2,1,2,1,2,1,1,2] => [2,2,2,2,1,1,1,1] => 275
[2,1,2,1,2,2,1,1] => [2,2,2,2,1,1,1,1] => 275
[2,1,2,1,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[2,1,1,2,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 154
[2,1,1,2,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[2,1,1,2,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[2,1,1,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1] => 154
[2,1,1,1,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 154
[2,1,1,1,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[2,1,1,1,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,2,1,2,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,2,1,1,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,2,1,1,1,2,1,1,2] => [2,2,2,1,1,1,1,1,1] => 154
[1,2,1,1,1,2,2,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,2,1,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,2,2,1,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,2,2,2,1,2,1,1] => [2,2,2,2,1,1,1,1] => 275
[1,2,2,1,2,1,1,2] => [2,2,2,2,1,1,1,1] => 275
[1,2,2,1,2,2,1,1] => [2,2,2,2,1,1,1,1] => 275
[1,2,1,2,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,2,1,2,2,1,1,2] => [2,2,2,2,1,1,1,1] => 275
[1,2,1,2,2,2,1,1] => [2,2,2,2,1,1,1,1] => 275
[1,2,1,2,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,2,1,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1] => 154
[1,2,1,1,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,2,1,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,2,1,1,1,2,1,2] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,2,1,1,2,1,1,2] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,2,1,1,2,2,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,2,2,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,2,2,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,2,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,2,1,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,1,2,1,1,1,2,2] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,1,2,1,1,2,1,2] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,1,2,1,2,1,1,2] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,1,2,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,1,2,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[2,1,1,1,1,1,1,3] => [3,2,1,1,1,1,1,1] => 231
[2,1,1,1,1,1,2,2] => [2,2,2,1,1,1,1,1] => 110
[2,1,1,1,1,2,1,2] => [2,2,2,1,1,1,1,1] => 110
[2,1,1,1,2,1,1,2] => [2,2,2,1,1,1,1,1] => 110
[2,1,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1] => 110
[2,1,2,1,1,1,1,2] => [2,2,2,1,1,1,1,1] => 110
[2,2,1,1,1,1,1,2] => [2,2,2,1,1,1,1,1] => 110
[3,1,1,1,1,1,1,2] => [3,2,1,1,1,1,1,1] => 231
[1,2,2,4,2,1] => [4,2,2,2,1,1] => 3080
[1,2,4,2,2,1] => [4,2,2,2,1,1] => 3080
[1,2,5,2,2] => [5,2,2,2,1] => 3520
[1,3,5,2,1] => [5,3,2,1,1] => 7700
[1,4,2,2,2,1] => [4,2,2,2,1,1] => 3080
[1,5,2,2,2] => [5,2,2,2,1] => 3520
[1,5,3,2,1] => [5,3,2,1,1] => 7700
[2,5,2,2,1] => [5,2,2,2,1] => 3520
[2,6,2,2] => [6,2,2,2] => 1925
[2,2,5,2,1] => [5,2,2,2,1] => 3520
[6,2,2,2] => [6,2,2,2] => 1925
[2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 297
[1,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1,1] => 275
[1,2,2,1,2,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,2,1,2,2,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,2,1,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 11
[9,2] => [9,2] => 44
[1,9,1] => [9,1,1] => 45
[10,2] => [10,2] => 54
[1,1,1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,2,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,2,2,2,3,1,1] => [3,2,2,2,1,1,1] => 1408
[1,2,2,3,1,2,1] => [3,2,2,2,1,1,1] => 1408
[1,2,2,4,1,1,1] => [4,2,2,1,1,1,1] => 2376
[1,2,3,1,2,2,1] => [3,2,2,2,1,1,1] => 1408
[1,2,3,1,3,1,1] => [3,3,2,1,1,1,1] => 1925
[1,2,3,2,1,2,1] => [3,2,2,2,1,1,1] => 1408
[1,2,4,1,1,2,1] => [4,2,2,1,1,1,1] => 2376
[1,2,3,2,2,1,1] => [3,2,2,2,1,1,1] => 1408
[1,2,3,3,1,1,1] => [3,3,2,1,1,1,1] => 1925
[1,2,4,2,1,1,1] => [4,2,2,1,1,1,1] => 2376
[1,2,5,1,1,1,1] => [5,2,1,1,1,1,1] => 1728
[1,3,1,2,2,2,1] => [3,2,2,2,1,1,1] => 1408
[1,3,1,3,1,2,1] => [3,3,2,1,1,1,1] => 1925
[1,3,1,3,2,1,1] => [3,3,2,1,1,1,1] => 1925
[1,3,2,1,3,1,1] => [3,3,2,1,1,1,1] => 1925
[1,4,1,1,2,2,1] => [4,2,2,1,1,1,1] => 2376
[1,4,1,1,3,1,1] => [4,3,1,1,1,1,1] => 2079
[1,3,2,2,1,2,1] => [3,2,2,2,1,1,1] => 1408
[1,3,3,1,1,2,1] => [3,3,2,1,1,1,1] => 1925
[1,4,1,2,1,2,1] => [4,2,2,1,1,1,1] => 2376
[1,4,2,1,1,2,1] => [4,2,2,1,1,1,1] => 2376
[1,5,1,1,1,2,1] => [5,2,1,1,1,1,1] => 1728
[1,3,2,3,1,1,1] => [3,3,2,1,1,1,1] => 1925
[1,3,3,1,2,1,1] => [3,3,2,1,1,1,1] => 1925
[1,3,4,1,1,1,1] => [4,3,1,1,1,1,1] => 2079
[1,4,1,2,2,1,1] => [4,2,2,1,1,1,1] => 2376
[1,4,1,3,1,1,1] => [4,3,1,1,1,1,1] => 2079
[1,5,1,1,2,1,1] => [5,2,1,1,1,1,1] => 1728
[1,4,2,2,1,1,1] => [4,2,2,1,1,1,1] => 2376
[1,4,3,1,1,1,1] => [4,3,1,1,1,1,1] => 2079
[1,5,2,1,1,1,1] => [5,2,1,1,1,1,1] => 1728
[1,6,1,1,1,1,1] => [6,1,1,1,1,1,1] => 462
[2,1,2,2,3,1,1] => [3,2,2,2,1,1,1] => 1408
[2,1,2,3,1,2,1] => [3,2,2,2,1,1,1] => 1408
[2,1,2,3,2,1,1] => [3,2,2,2,1,1,1] => 1408
[2,1,2,4,1,1,1] => [4,2,2,1,1,1,1] => 2376
[2,1,3,1,2,2,1] => [3,2,2,2,1,1,1] => 1408
[2,1,3,1,3,1,1] => [3,3,2,1,1,1,1] => 1925
[2,1,3,2,1,2,1] => [3,2,2,2,1,1,1] => 1408
[2,1,4,1,1,2,1] => [4,2,2,1,1,1,1] => 2376
[2,1,3,2,2,1,1] => [3,2,2,2,1,1,1] => 1408
[2,1,3,3,1,1,1] => [3,3,2,1,1,1,1] => 1925
[2,1,4,1,2,1,1] => [4,2,2,1,1,1,1] => 2376
[2,1,4,2,1,1,1] => [4,2,2,1,1,1,1] => 2376
[2,1,5,1,1,1,1] => [5,2,1,1,1,1,1] => 1728
[2,2,1,2,3,1,1] => [3,2,2,2,1,1,1] => 1408
[2,2,1,3,1,2,1] => [3,2,2,2,1,1,1] => 1408
[2,2,1,3,2,1,1] => [3,2,2,2,1,1,1] => 1408
[2,2,1,4,1,1,1] => [4,2,2,1,1,1,1] => 2376
[3,1,1,2,2,2,1] => [3,2,2,2,1,1,1] => 1408
[3,1,1,3,1,2,1] => [3,3,2,1,1,1,1] => 1925
[3,1,1,3,2,1,1] => [3,3,2,1,1,1,1] => 1925
[2,2,2,1,3,1,1] => [3,2,2,2,1,1,1] => 1408
[2,3,1,1,2,2,1] => [3,2,2,2,1,1,1] => 1408
[2,3,1,1,3,1,1] => [3,3,2,1,1,1,1] => 1925
[3,1,2,1,3,1,1] => [3,3,2,1,1,1,1] => 1925
[3,2,1,1,2,2,1] => [3,2,2,2,1,1,1] => 1408
[3,2,1,1,3,1,1] => [3,3,2,1,1,1,1] => 1925
[4,1,1,1,2,2,1] => [4,2,2,1,1,1,1] => 2376
[4,1,1,1,3,1,1] => [4,3,1,1,1,1,1] => 2079
[2,2,3,1,1,2,1] => [3,2,2,2,1,1,1] => 1408
[2,3,1,2,1,2,1] => [3,2,2,2,1,1,1] => 1408
[2,3,2,1,1,2,1] => [3,2,2,2,1,1,1] => 1408
[2,4,1,1,1,2,1] => [4,2,2,1,1,1,1] => 2376
[3,1,2,2,1,2,1] => [3,2,2,2,1,1,1] => 1408
[3,1,3,1,1,2,1] => [3,3,2,1,1,1,1] => 1925
[3,2,1,2,1,2,1] => [3,2,2,2,1,1,1] => 1408
[4,1,1,2,1,2,1] => [4,2,2,1,1,1,1] => 2376
[3,2,2,1,1,2,1] => [3,2,2,2,1,1,1] => 1408
[3,3,1,1,1,2,1] => [3,3,2,1,1,1,1] => 1925
[4,1,2,1,1,2,1] => [4,2,2,1,1,1,1] => 2376
[4,2,1,1,1,2,1] => [4,2,2,1,1,1,1] => 2376
[5,1,1,1,1,2,1] => [5,2,1,1,1,1,1] => 1728
[2,2,2,3,1,1,1] => [3,2,2,2,1,1,1] => 1408
[2,2,3,1,2,1,1] => [3,2,2,2,1,1,1] => 1408
[2,2,3,2,1,1,1] => [3,2,2,2,1,1,1] => 1408
[2,2,4,1,1,1,1] => [4,2,2,1,1,1,1] => 2376
[2,3,1,2,2,1,1] => [3,2,2,2,1,1,1] => 1408
[2,3,1,3,1,1,1] => [3,3,2,1,1,1,1] => 1925
[2,3,2,1,2,1,1] => [3,2,2,2,1,1,1] => 1408
[2,4,1,1,2,1,1] => [4,2,2,1,1,1,1] => 2376
[2,3,2,2,1,1,1] => [3,2,2,2,1,1,1] => 1408
[2,3,3,1,1,1,1] => [3,3,2,1,1,1,1] => 1925
[2,4,1,2,1,1,1] => [4,2,2,1,1,1,1] => 2376
[2,4,2,1,1,1,1] => [4,2,2,1,1,1,1] => 2376
[2,5,1,1,1,1,1] => [5,2,1,1,1,1,1] => 1728
[3,1,2,3,1,1,1] => [3,3,2,1,1,1,1] => 1925
[3,1,3,1,2,1,1] => [3,3,2,1,1,1,1] => 1925
[3,1,4,1,1,1,1] => [4,3,1,1,1,1,1] => 2079
[3,2,1,2,2,1,1] => [3,2,2,2,1,1,1] => 1408
[3,2,1,3,1,1,1] => [3,3,2,1,1,1,1] => 1925
[4,1,1,2,2,1,1] => [4,2,2,1,1,1,1] => 2376
[4,1,1,3,1,1,1] => [4,3,1,1,1,1,1] => 2079
[3,3,1,1,2,1,1] => [3,3,2,1,1,1,1] => 1925
[4,1,2,1,2,1,1] => [4,2,2,1,1,1,1] => 2376
[4,2,1,1,2,1,1] => [4,2,2,1,1,1,1] => 2376
[5,1,1,1,2,1,1] => [5,2,1,1,1,1,1] => 1728
[3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => 1408
[3,2,3,1,1,1,1] => [3,3,2,1,1,1,1] => 1925
[3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => 1925
[3,4,1,1,1,1,1] => [4,3,1,1,1,1,1] => 2079
[4,1,2,2,1,1,1] => [4,2,2,1,1,1,1] => 2376
[4,1,3,1,1,1,1] => [4,3,1,1,1,1,1] => 2079
[4,2,1,2,1,1,1] => [4,2,2,1,1,1,1] => 2376
[4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => 2376
[4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => 2079
[5,1,2,1,1,1,1] => [5,2,1,1,1,1,1] => 1728
[5,2,1,1,1,1,1] => [5,2,1,1,1,1,1] => 1728
[6,1,1,1,1,1,1] => [6,1,1,1,1,1,1] => 462
[11] => [11] => 1
[2,9] => [9,2] => 44
[1,1,2,2,4,1] => [4,2,2,1,1,1] => 1232
[1,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 11
[1,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,2,2,1,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 11
[1,1,1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 11
[1,1,1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1,1,1] => 11
[1,1,2,3,2,3] => [3,3,2,2,1,1] => 2673
[1,2,2,2,2,3] => [3,2,2,2,2,1] => 1155
[5,1,1,1,1,2] => [5,2,1,1,1,1] => 924
[1,1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1,1] => 10
[1,2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1] => 44
[1,1,1,1,1,1,1,1,1,1,1] => [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] => 45
[1,1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1,1] => 45
[1,1,1,1,1,5,1] => [5,1,1,1,1,1,1] => 210
[1,1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1,1] => 44
[1,1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => 45
[1,1,1,3,1,3,1] => [3,3,1,1,1,1,1] => 385
[1,1,1,5,1,1,1] => [5,1,1,1,1,1,1] => 210
[1,1,1,7,1] => [7,1,1,1,1] => 210
[1,1,1,4,1,2,1] => [4,2,1,1,1,1,1] => 594
[1,1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1] => 44
[1,1,1,2,1,4,1] => [4,2,1,1,1,1,1] => 594
[1,1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1] => 44
[1,1,1,2,3,2,1] => [3,2,2,1,1,1,1] => 550
[1,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => 45
[1,3,1,1,1,3,1] => [3,3,1,1,1,1,1] => 385
[1,3,1,3,1,1,1] => [3,3,1,1,1,1,1] => 385
[1,3,1,5,1] => [5,3,1,1,1] => 1540
[1,3,1,2,1,2,1] => [3,2,2,1,1,1,1] => 550
[1,5,1,1,1,1,1] => [5,1,1,1,1,1,1] => 210
[1,5,1,3,1] => [5,3,1,1,1] => 1540
[1,7,1,1,1] => [7,1,1,1,1] => 210
[1,6,1,2,1] => [6,2,1,1,1] => 924
[1,4,1,2,1,1,1] => [4,2,1,1,1,1,1] => 594
[1,4,1,4,1] => [4,4,1,1,1] => 825
[1,4,1,1,1,2,1] => [4,2,1,1,1,1,1] => 594
[1,4,3,2,1] => [4,3,2,1,1] => 2310
[1,2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 44
[1,2,1,2,1,3,1] => [3,2,2,1,1,1,1] => 550
[1,2,1,4,1,1,1] => [4,2,1,1,1,1,1] => 594
[1,2,1,6,1] => [6,2,1,1,1] => 924
[1,2,1,3,1,2,1] => [3,2,2,1,1,1,1] => 550
[1,2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1] => 44
[1,2,1,1,1,4,1] => [4,2,1,1,1,1,1] => 594
[1,2,1,1,3,2,1] => [3,2,2,1,1,1,1] => 550
[1,2,3,2,1,1,1] => [3,2,2,1,1,1,1] => 550
[1,2,3,4,1] => [4,3,2,1,1] => 2310
[1,2,3,1,1,2,1] => [3,2,2,1,1,1,1] => 550
[1,2,5,2,1] => [5,2,2,1,1] => 1540
[1,2,2,1,2,2,1] => [2,2,2,2,1,1,1] => 165
[1,4,3,4,1] => [4,4,3,1,1] => 11583
[1,4,5,2,1] => [5,4,2,1,1] => 21450
[1,2,5,4,1] => [5,4,2,1,1] => 21450
[1,1,9] => [9,1,1] => 45
[1,1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1,1] => 45
[1,1,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 11
[1,1,2,2,1,2,3] => [3,2,2,2,1,1,1] => 1408
[1,1,1,1,2,2,2,1,1] => [2,2,2,1,1,1,1,1,1] => 154
[1,1,1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 11
[1,1,1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 11
[1,1,1,2,2,2,3] => [3,2,2,2,1,1,1] => 1408
[1,6,4] => [6,4,1] => 693
[1,5,5] => [5,5,1] => 330
[1,4,6] => [6,4,1] => 693
[1,3,7] => [7,3,1] => 550
[1,2,8] => [8,2,1] => 231
[1,2,1,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,2,1,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,1,1,1,2,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 54
[1,1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1] => 44
[1,1,2,2,2,2,1] => [2,2,2,2,1,1,1] => 165
[1,1,2,2,2,1,1,1] => [2,2,2,1,1,1,1,1] => 110
[1,1,2,2,3,1,1] => [3,2,2,1,1,1,1] => 550
[1,1,2,2,1,2,1,1] => [2,2,2,1,1,1,1,1] => 110
[1,1,2,3,2,1,1] => [3,2,2,1,1,1,1] => 550
[1,1,2,1,2,2,1,1] => [2,2,2,1,1,1,1,1] => 110
[1,1,3,2,2,1,1] => [3,2,2,1,1,1,1] => 550
[1,1,1,2,2,2,1,1] => [2,2,2,1,1,1,1,1] => 110
[1,2,2,2,2,1,1] => [2,2,2,2,1,1,1] => 165
[1,1,2,2,2,4] => [4,2,2,2,1,1] => 3080
[1,1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 44
[1,1,2,5,1,1] => [5,2,1,1,1,1] => 924
[1,1,5,2,1,1] => [5,2,1,1,1,1] => 924
[1,1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1,1] => 44
[1,4,2,2,1,1] => [4,2,2,1,1,1] => 1232
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,2 2,1,5 2,0,0,6,5,3 2,0,0,0,9,0,0,0,8,7,0,0,0,0,0,6 2,0,0,0,0,8,0,0,0,0,0,0,0,18,8,0,0,0,0,4,6,0,0,0,0,0,0,0,0,0,0,0,0,0,18
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 2\ q + 2\ q^{2}$
$F_{4} = 2\ q + q^{2} + 5\ q^{3}$
$F_{5} = 2\ q + 6\ q^{4} + 5\ q^{5} + 3\ q^{6}$
$F_{6} = 2\ q + 9\ q^{5} + 8\ q^{9} + 7\ q^{10} + 6\ q^{16}$
$F_{7} = 2\ q + 8\ q^{6} + 18\ q^{14} + 8\ q^{15} + 4\ q^{20} + 6\ q^{21} + 18\ q^{35}$
$F_{8} = 2\ q + 9\ q^{7} + 2\ q^{14} + 17\ q^{20} + 9\ q^{21} + 12\ q^{28} + 9\ q^{35} + 3\ q^{42} + 9\ q^{56} + 26\ q^{64} + 18\ q^{70} + 12\ q^{90}$
$F_{9} = 2\ q + 10\ q^{8} + 23\ q^{27} + 10\ q^{28} + 8\ q^{42} + 22\ q^{48} + 10\ q^{56} + 5\ q^{70} + 7\ q^{84} + 36\ q^{105} + 13\ q^{120} + 36\ q^{162} + 18\ q^{168} + 32\ q^{189} + 24\ q^{216}$
$F_{10} = 2\ q + 11\ q^{9} + 30\ q^{35} + 11\ q^{36} + 2\ q^{42} + 37\ q^{75} + 11\ q^{84} + 17\ q^{90} + 11\ q^{126} + 48\ q^{160} + 7\ q^{210} + 18\ q^{225} + 9\ q^{252} + 26\ q^{288} + 10\ q^{300} + 66\ q^{315} + 42\ q^{350} + 20\ q^{448} + 36\ q^{450} + 32\ q^{525} + 42\ q^{567} + 24\ q^{768}$
Description
The number of standard Young tableaux of the partition.
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to partition
Description
Sends a composition to the partition obtained by sorting the entries.
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