Identifier
-
Mp00321:
Integer partitions
—2-conjugate⟶
Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000712: Integer partitions ⟶ ℤ
Values
[1] => [1] => [] => 1
[2] => [2] => [] => 1
[1,1] => [1,1] => [1] => 4
[3] => [2,1] => [1] => 4
[2,1] => [3] => [] => 1
[1,1,1] => [1,1,1] => [1,1] => 6
[4] => [2,2] => [2] => 10
[3,1] => [2,1,1] => [1,1] => 6
[2,2] => [4] => [] => 1
[2,1,1] => [3,1] => [1] => 4
[1,1,1,1] => [1,1,1,1] => [1,1,1] => 4
[5] => [2,2,1] => [2,1] => 20
[4,1] => [3,2] => [2] => 10
[3,2] => [4,1] => [1] => 4
[3,1,1] => [2,1,1,1] => [1,1,1] => 4
[2,2,1] => [5] => [] => 1
[2,1,1,1] => [3,1,1] => [1,1] => 6
[1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1] => 1
[6] => [2,2,2] => [2,2] => 20
[5,1] => [2,2,1,1] => [2,1,1] => 15
[4,2] => [4,2] => [2] => 10
[4,1,1] => [4,1,1] => [1,1] => 6
[3,3] => [3,2,1] => [2,1] => 20
[3,2,1] => [3,3] => [3] => 20
[3,1,1,1] => [2,1,1,1,1] => [1,1,1,1] => 1
[2,2,2] => [6] => [] => 1
[2,2,1,1] => [5,1] => [1] => 4
[2,1,1,1,1] => [3,1,1,1] => [1,1,1] => 4
[1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[7] => [2,2,2,1] => [2,2,1] => 20
[6,1] => [3,2,2] => [2,2] => 20
[5,2] => [4,2,1] => [2,1] => 20
[5,1,1] => [2,2,1,1,1] => [2,1,1,1] => 4
[4,3] => [4,3] => [3] => 20
[4,2,1] => [5,2] => [2] => 10
[4,1,1,1] => [4,1,1,1] => [1,1,1] => 4
[3,3,1] => [3,2,1,1] => [2,1,1] => 15
[3,2,2] => [6,1] => [1] => 4
[3,2,1,1] => [3,3,1] => [3,1] => 45
[3,1,1,1,1] => [2,1,1,1,1,1] => [1,1,1,1,1] => 0
[2,2,2,1] => [7] => [] => 1
[2,2,1,1,1] => [5,1,1] => [1,1] => 6
[2,1,1,1,1,1] => [3,1,1,1,1] => [1,1,1,1] => 1
[1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[8] => [2,2,2,2] => [2,2,2] => 10
[7,1] => [2,2,2,1,1] => [2,2,1,1] => 6
[6,2] => [4,2,2] => [2,2] => 20
[6,1,1] => [4,2,1,1] => [2,1,1] => 15
[5,3] => [3,2,2,1] => [2,2,1] => 20
[5,2,1] => [3,3,2] => [3,2] => 60
[5,1,1,1] => [2,2,1,1,1,1] => [2,1,1,1,1] => 0
[4,4] => [4,4] => [4] => 35
[4,3,1] => [4,3,1] => [3,1] => 45
[4,2,2] => [6,2] => [2] => 10
[4,2,1,1] => [6,1,1] => [1,1] => 6
[4,1,1,1,1] => [4,1,1,1,1] => [1,1,1,1] => 1
[3,3,2] => [5,2,1] => [2,1] => 20
[3,3,1,1] => [3,2,1,1,1] => [2,1,1,1] => 4
[3,2,2,1] => [5,3] => [3] => 20
[3,2,1,1,1] => [3,3,1,1] => [3,1,1] => 36
[3,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[2,2,2,2] => [8] => [] => 1
[2,2,2,1,1] => [7,1] => [1] => 4
[2,2,1,1,1,1] => [5,1,1,1] => [1,1,1] => 4
[2,1,1,1,1,1,1] => [3,1,1,1,1,1] => [1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[9] => [2,2,2,2,1] => [2,2,2,1] => 4
[8,1] => [3,2,2,2] => [2,2,2] => 10
[7,2] => [4,2,2,1] => [2,2,1] => 20
[7,1,1] => [2,2,2,1,1,1] => [2,2,1,1,1] => 0
[6,3] => [4,3,2] => [3,2] => 60
[6,2,1] => [5,2,2] => [2,2] => 20
[6,1,1,1] => [4,2,1,1,1] => [2,1,1,1] => 4
[5,4] => [4,4,1] => [4,1] => 84
[5,3,1] => [3,2,2,1,1] => [2,2,1,1] => 6
[5,2,2] => [6,2,1] => [2,1] => 20
[5,2,1,1] => [4,3,1,1] => [3,1,1] => 36
[5,1,1,1,1] => [2,2,1,1,1,1,1] => [2,1,1,1,1,1] => 0
[4,4,1] => [5,4] => [4] => 35
[4,3,2] => [6,3] => [3] => 20
[4,3,1,1] => [5,2,1,1] => [2,1,1] => 15
[4,2,2,1] => [7,2] => [2] => 10
[4,2,1,1,1] => [6,1,1,1] => [1,1,1] => 4
[4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,1] => 0
[3,3,3] => [3,3,2,1] => [3,2,1] => 64
[3,3,2,1] => [3,3,3] => [3,3] => 50
[3,3,1,1,1] => [3,2,1,1,1,1] => [2,1,1,1,1] => 0
[3,2,2,2] => [8,1] => [1] => 4
[3,2,2,1,1] => [5,3,1] => [3,1] => 45
[3,2,1,1,1,1] => [3,3,1,1,1] => [3,1,1,1] => 10
[3,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[2,2,2,2,1] => [9] => [] => 1
[2,2,2,1,1,1] => [7,1,1] => [1,1] => 6
[2,2,1,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1] => 1
[2,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[10] => [2,2,2,2,2] => [2,2,2,2] => 1
[9,1] => [2,2,2,2,1,1] => [2,2,2,1,1] => 0
[8,2] => [4,2,2,2] => [2,2,2] => 10
[8,1,1] => [4,2,2,1,1] => [2,2,1,1] => 6
[7,3] => [3,2,2,2,1] => [2,2,2,1] => 4
>>> Load all 1100 entries. <<<[7,2,1] => [3,3,2,2] => [3,2,2] => 36
[7,1,1,1] => [2,2,2,1,1,1,1] => [2,2,1,1,1,1] => 0
[6,4] => [4,4,2] => [4,2] => 126
[6,3,1] => [4,4,1,1] => [4,1,1] => 70
[6,2,2] => [6,2,2] => [2,2] => 20
[6,2,1,1] => [6,2,1,1] => [2,1,1] => 15
[6,1,1,1,1] => [4,2,1,1,1,1] => [2,1,1,1,1] => 0
[5,5] => [4,3,2,1] => [3,2,1] => 64
[5,4,1] => [4,3,3] => [3,3] => 50
[5,3,2] => [5,2,2,1] => [2,2,1] => 20
[5,3,1,1] => [3,2,2,1,1,1] => [2,2,1,1,1] => 0
[5,2,2,1] => [5,3,2] => [3,2] => 60
[5,2,1,1,1] => [4,3,1,1,1] => [3,1,1,1] => 10
[5,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 0
[4,4,2] => [6,4] => [4] => 35
[4,4,1,1] => [6,3,1] => [3,1] => 45
[4,3,3] => [5,4,1] => [4,1] => 84
[4,3,2,1] => [5,5] => [5] => 56
[4,3,1,1,1] => [5,2,1,1,1] => [2,1,1,1] => 4
[4,2,2,2] => [8,2] => [2] => 10
[4,2,2,1,1] => [8,1,1] => [1,1] => 6
[4,2,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1] => 1
[4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[3,3,3,1] => [3,3,2,1,1] => [3,2,1,1] => 20
[3,3,2,2] => [7,2,1] => [2,1] => 20
[3,3,2,1,1] => [3,3,3,1] => [3,3,1] => 60
[3,3,1,1,1,1] => [3,2,1,1,1,1,1] => [2,1,1,1,1,1] => 0
[3,2,2,2,1] => [7,3] => [3] => 20
[3,2,2,1,1,1] => [5,3,1,1] => [3,1,1] => 36
[3,2,1,1,1,1,1] => [3,3,1,1,1,1] => [3,1,1,1,1] => 0
[3,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2] => [10] => [] => 1
[2,2,2,2,1,1] => [9,1] => [1] => 4
[2,2,2,1,1,1,1] => [7,1,1,1] => [1,1,1] => 4
[2,2,1,1,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[11] => [2,2,2,2,2,1] => [2,2,2,2,1] => 0
[10,1] => [3,2,2,2,2] => [2,2,2,2] => 1
[9,2] => [4,2,2,2,1] => [2,2,2,1] => 4
[9,1,1] => [2,2,2,2,1,1,1] => [2,2,2,1,1,1] => 0
[8,3] => [4,3,2,2] => [3,2,2] => 36
[8,2,1] => [5,2,2,2] => [2,2,2] => 10
[8,1,1,1] => [4,2,2,1,1,1] => [2,2,1,1,1] => 0
[7,4] => [4,4,2,1] => [4,2,1] => 140
[7,3,1] => [3,2,2,2,1,1] => [2,2,2,1,1] => 0
[7,2,2] => [6,2,2,1] => [2,2,1] => 20
[7,2,1,1] => [4,4,1,1,1] => [4,1,1,1] => 20
[7,1,1,1,1] => [2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 0
[6,5] => [4,4,3] => [4,3] => 140
[6,4,1] => [5,4,2] => [4,2] => 126
[6,3,2] => [6,3,2] => [3,2] => 60
[6,3,1,1] => [5,2,2,1,1] => [2,2,1,1] => 6
[6,2,2,1] => [7,2,2] => [2,2] => 20
[6,2,1,1,1] => [6,2,1,1,1] => [2,1,1,1] => 4
[6,1,1,1,1,1] => [4,2,1,1,1,1,1] => [2,1,1,1,1,1] => 0
[5,5,1] => [4,3,2,1,1] => [3,2,1,1] => 20
[5,4,2] => [6,4,1] => [4,1] => 84
[5,4,1,1] => [4,3,3,1] => [3,3,1] => 60
[5,3,3] => [3,3,2,2,1] => [3,2,2,1] => 15
[5,3,2,1] => [3,3,3,2] => [3,3,2] => 45
[5,3,1,1,1] => [3,2,2,1,1,1,1] => [2,2,1,1,1,1] => 0
[5,2,2,2] => [8,2,1] => [2,1] => 20
[5,2,2,1,1] => [6,3,1,1] => [3,1,1] => 36
[5,2,1,1,1,1] => [4,3,1,1,1,1] => [3,1,1,1,1] => 0
[5,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 0
[4,4,3] => [6,5] => [5] => 56
[4,4,2,1] => [7,4] => [4] => 35
[4,4,1,1,1] => [7,2,1,1] => [2,1,1] => 15
[4,3,3,1] => [5,4,1,1] => [4,1,1] => 70
[4,3,2,2] => [8,3] => [3] => 20
[4,3,2,1,1] => [5,5,1] => [5,1] => 140
[4,3,1,1,1,1] => [5,2,1,1,1,1] => [2,1,1,1,1] => 0
[4,2,2,2,1] => [9,2] => [2] => 10
[4,2,2,1,1,1] => [8,1,1,1] => [1,1,1] => 4
[4,2,1,1,1,1,1] => [6,1,1,1,1,1] => [1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[3,3,3,2] => [5,3,2,1] => [3,2,1] => 64
[3,3,3,1,1] => [3,3,2,1,1,1] => [3,2,1,1,1] => 0
[3,3,2,2,1] => [5,3,3] => [3,3] => 50
[3,3,2,1,1,1] => [3,3,3,1,1] => [3,3,1,1] => 20
[3,3,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 0
[3,2,2,2,2] => [10,1] => [1] => 4
[3,2,2,2,1,1] => [7,3,1] => [3,1] => 45
[3,2,2,1,1,1,1] => [5,3,1,1,1] => [3,1,1,1] => 10
[3,2,1,1,1,1,1,1] => [3,3,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,1] => [11] => [] => 1
[2,2,2,2,1,1,1] => [9,1,1] => [1,1] => 6
[2,2,2,1,1,1,1,1] => [7,1,1,1,1] => [1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[12] => [2,2,2,2,2,2] => [2,2,2,2,2] => 0
[11,1] => [2,2,2,2,2,1,1] => [2,2,2,2,1,1] => 0
[10,2] => [4,2,2,2,2] => [2,2,2,2] => 1
[10,1,1] => [4,2,2,2,1,1] => [2,2,2,1,1] => 0
[9,3] => [3,2,2,2,2,1] => [2,2,2,2,1] => 0
[9,2,1] => [3,3,2,2,2] => [3,2,2,2] => 4
[9,1,1,1] => [2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 0
[8,4] => [4,4,2,2] => [4,2,2] => 84
[8,3,1] => [4,4,2,1,1] => [4,2,1,1] => 45
[8,2,2] => [6,2,2,2] => [2,2,2] => 10
[8,2,1,1] => [6,2,2,1,1] => [2,2,1,1] => 6
[8,1,1,1,1] => [4,2,2,1,1,1,1] => [2,2,1,1,1,1] => 0
[7,5] => [4,3,2,2,1] => [3,2,2,1] => 15
[7,4,1] => [4,3,3,2] => [3,3,2] => 45
[7,3,2] => [5,2,2,2,1] => [2,2,2,1] => 4
[7,3,1,1] => [3,2,2,2,1,1,1] => [2,2,2,1,1,1] => 0
[7,2,2,1] => [5,3,2,2] => [3,2,2] => 36
[7,2,1,1,1] => [4,4,1,1,1,1] => [4,1,1,1,1] => 0
[7,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 0
[6,6] => [4,4,4] => [4,4] => 105
[6,5,1] => [4,4,3,1] => [4,3,1] => 175
[6,4,2] => [6,4,2] => [4,2] => 126
[6,4,1,1] => [6,4,1,1] => [4,1,1] => 70
[6,3,3] => [5,4,2,1] => [4,2,1] => 140
[6,3,2,1] => [5,5,2] => [5,2] => 224
[6,3,1,1,1] => [5,2,2,1,1,1] => [2,2,1,1,1] => 0
[6,2,2,2] => [8,2,2] => [2,2] => 20
[6,2,2,1,1] => [8,2,1,1] => [2,1,1] => 15
[6,2,1,1,1,1] => [6,2,1,1,1,1] => [2,1,1,1,1] => 0
[6,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 0
[5,5,2] => [6,3,2,1] => [3,2,1] => 64
[5,5,1,1] => [4,3,2,1,1,1] => [3,2,1,1,1] => 0
[5,4,3] => [5,4,3] => [4,3] => 140
[5,4,2,1] => [6,3,3] => [3,3] => 50
[5,4,1,1,1] => [5,4,1,1,1] => [4,1,1,1] => 20
[5,3,3,1] => [3,3,2,2,1,1] => [3,2,2,1,1] => 0
[5,3,2,2] => [7,2,2,1] => [2,2,1] => 20
[5,3,2,1,1] => [4,3,3,1,1] => [3,3,1,1] => 20
[5,3,1,1,1,1] => [3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 0
[5,2,2,2,1] => [7,3,2] => [3,2] => 60
[5,2,2,1,1,1] => [6,3,1,1,1] => [3,1,1,1] => 10
[5,2,1,1,1,1,1] => [4,3,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 0
[4,4,4] => [6,6] => [6] => 84
[4,4,3,1] => [6,5,1] => [5,1] => 140
[4,4,2,2] => [8,4] => [4] => 35
[4,4,2,1,1] => [8,3,1] => [3,1] => 45
[4,4,1,1,1,1] => [7,2,1,1,1] => [2,1,1,1] => 4
[4,3,3,2] => [7,4,1] => [4,1] => 84
[4,3,3,1,1] => [5,3,2,1,1] => [3,2,1,1] => 20
[4,3,2,2,1] => [7,5] => [5] => 56
[4,3,2,1,1,1] => [5,5,1,1] => [5,1,1] => 120
[4,3,1,1,1,1,1] => [5,2,1,1,1,1,1] => [2,1,1,1,1,1] => 0
[4,2,2,2,2] => [10,2] => [2] => 10
[4,2,2,2,1,1] => [10,1,1] => [1,1] => 6
[4,2,2,1,1,1,1] => [8,1,1,1,1] => [1,1,1,1] => 1
[4,2,1,1,1,1,1,1] => [6,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[3,3,3,3] => [3,3,3,2,1] => [3,3,2,1] => 20
[3,3,3,2,1] => [3,3,3,3] => [3,3,3] => 20
[3,3,3,1,1,1] => [3,3,2,1,1,1,1] => [3,2,1,1,1,1] => 0
[3,3,2,2,2] => [9,2,1] => [2,1] => 20
[3,3,2,2,1,1] => [5,3,3,1] => [3,3,1] => 60
[3,3,2,1,1,1,1] => [3,3,3,1,1,1] => [3,3,1,1,1] => 0
[3,3,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 0
[3,2,2,2,2,1] => [9,3] => [3] => 20
[3,2,2,2,1,1,1] => [7,3,1,1] => [3,1,1] => 36
[3,2,2,1,1,1,1,1] => [5,3,1,1,1,1] => [3,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2] => [12] => [] => 1
[2,2,2,2,2,1,1] => [11,1] => [1] => 4
[2,2,2,2,1,1,1,1] => [9,1,1,1] => [1,1,1] => 4
[2,2,2,1,1,1,1,1,1] => [7,1,1,1,1,1] => [1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 0
[13] => [2,2,2,2,2,2,1] => [2,2,2,2,2,1] => 0
[12,1] => [3,2,2,2,2,2] => [2,2,2,2,2] => 0
[11,2] => [4,2,2,2,2,1] => [2,2,2,2,1] => 0
[11,1,1] => [2,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 0
[10,3] => [4,3,2,2,2] => [3,2,2,2] => 4
[10,2,1] => [5,2,2,2,2] => [2,2,2,2] => 1
[10,1,1,1] => [4,2,2,2,1,1,1] => [2,2,2,1,1,1] => 0
[9,4] => [4,4,2,2,1] => [4,2,2,1] => 36
[9,3,1] => [3,2,2,2,2,1,1] => [2,2,2,2,1,1] => 0
[9,2,2] => [6,2,2,2,1] => [2,2,2,1] => 4
[9,2,1,1] => [4,4,2,1,1,1] => [4,2,1,1,1] => 0
[9,1,1,1,1] => [2,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 0
[8,5] => [4,4,3,2] => [4,3,2] => 140
[8,4,1] => [5,4,2,2] => [4,2,2] => 84
[8,3,2] => [6,3,2,2] => [3,2,2] => 36
[8,3,1,1] => [5,2,2,2,1,1] => [2,2,2,1,1] => 0
[8,2,2,1] => [7,2,2,2] => [2,2,2] => 10
[8,2,1,1,1] => [6,2,2,1,1,1] => [2,2,1,1,1] => 0
[8,1,1,1,1,1] => [4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 0
[7,6] => [4,4,4,1] => [4,4,1] => 140
[7,5,1] => [4,3,2,2,1,1] => [3,2,2,1,1] => 0
[7,4,2] => [6,4,2,1] => [4,2,1] => 140
[7,4,1,1] => [4,4,3,1,1] => [4,3,1,1] => 60
[7,3,3] => [3,3,2,2,2,1] => [3,2,2,2,1] => 0
[7,3,2,1] => [3,3,3,2,2] => [3,3,2,2] => 6
[7,3,1,1,1] => [3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 0
[7,2,2,2] => [8,2,2,1] => [2,2,1] => 20
[7,2,2,1,1] => [6,4,1,1,1] => [4,1,1,1] => 20
[7,2,1,1,1,1] => [4,4,1,1,1,1,1] => [4,1,1,1,1,1] => 0
[7,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 0
[6,6,1] => [5,4,4] => [4,4] => 105
[6,5,2] => [6,4,3] => [4,3] => 140
[6,5,1,1] => [6,3,2,1,1] => [3,2,1,1] => 20
[6,4,3] => [6,5,2] => [5,2] => 224
[6,4,2,1] => [7,4,2] => [4,2] => 126
[6,4,1,1,1] => [7,2,2,1,1] => [2,2,1,1] => 6
[6,3,3,1] => [5,4,2,1,1] => [4,2,1,1] => 45
[6,3,2,2] => [8,3,2] => [3,2] => 60
[6,3,2,1,1] => [6,5,1,1] => [5,1,1] => 120
[6,3,1,1,1,1] => [5,2,2,1,1,1,1] => [2,2,1,1,1,1] => 0
[6,2,2,2,1] => [9,2,2] => [2,2] => 20
[6,2,2,1,1,1] => [8,2,1,1,1] => [2,1,1,1] => 4
[6,2,1,1,1,1,1] => [6,2,1,1,1,1,1] => [2,1,1,1,1,1] => 0
[6,1,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 0
[5,5,3] => [4,3,3,2,1] => [3,3,2,1] => 20
[5,5,2,1] => [4,3,3,3] => [3,3,3] => 20
[5,5,1,1,1] => [4,3,2,1,1,1,1] => [3,2,1,1,1,1] => 0
[5,4,4] => [6,6,1] => [6,1] => 216
[5,4,3,1] => [5,4,3,1] => [4,3,1] => 175
[5,4,2,2] => [8,4,1] => [4,1] => 84
[5,4,2,1,1] => [6,3,3,1] => [3,3,1] => 60
[5,4,1,1,1,1] => [5,4,1,1,1,1] => [4,1,1,1,1] => 0
[5,3,3,2] => [5,3,2,2,1] => [3,2,2,1] => 15
[5,3,3,1,1] => [3,3,2,2,1,1,1] => [3,2,2,1,1,1] => 0
[5,3,2,2,1] => [5,3,3,2] => [3,3,2] => 45
[5,3,2,1,1,1] => [4,3,3,1,1,1] => [3,3,1,1,1] => 0
[5,3,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 0
[5,2,2,2,2] => [10,2,1] => [2,1] => 20
[5,2,2,2,1,1] => [8,3,1,1] => [3,1,1] => 36
[5,2,2,1,1,1,1] => [6,3,1,1,1,1] => [3,1,1,1,1] => 0
[5,2,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 0
[4,4,4,1] => [7,6] => [6] => 84
[4,4,3,2] => [8,5] => [5] => 56
[4,4,3,1,1] => [7,4,1,1] => [4,1,1] => 70
[4,4,2,2,1] => [9,4] => [4] => 35
[4,4,2,1,1,1] => [9,2,1,1] => [2,1,1] => 15
[4,4,1,1,1,1,1] => [7,2,1,1,1,1] => [2,1,1,1,1] => 0
[4,3,3,3] => [5,5,2,1] => [5,2,1] => 256
[4,3,3,2,1] => [5,5,3] => [5,3] => 280
[4,3,3,1,1,1] => [5,3,2,1,1,1] => [3,2,1,1,1] => 0
[4,3,2,2,2] => [10,3] => [3] => 20
[4,3,2,2,1,1] => [7,5,1] => [5,1] => 140
[4,3,2,1,1,1,1] => [5,5,1,1,1] => [5,1,1,1] => 35
[4,3,1,1,1,1,1,1] => [5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 0
[4,2,2,2,2,1] => [11,2] => [2] => 10
[4,2,2,2,1,1,1] => [10,1,1,1] => [1,1,1] => 4
[4,2,2,1,1,1,1,1] => [8,1,1,1,1,1] => [1,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1] => [6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[3,3,3,3,1] => [3,3,3,2,1,1] => [3,3,2,1,1] => 0
[3,3,3,2,2] => [7,3,2,1] => [3,2,1] => 64
[3,3,3,2,1,1] => [3,3,3,3,1] => [3,3,3,1] => 10
[3,3,3,1,1,1,1] => [3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 0
[3,3,2,2,2,1] => [7,3,3] => [3,3] => 50
[3,3,2,2,1,1,1] => [5,3,3,1,1] => [3,3,1,1] => 20
[3,3,2,1,1,1,1,1] => [3,3,3,1,1,1,1] => [3,3,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 0
[3,2,2,2,2,2] => [12,1] => [1] => 4
[3,2,2,2,2,1,1] => [9,3,1] => [3,1] => 45
[3,2,2,2,1,1,1,1] => [7,3,1,1,1] => [3,1,1,1] => 10
[3,2,2,1,1,1,1,1,1] => [5,3,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2,1] => [13] => [] => 1
[2,2,2,2,2,1,1,1] => [11,1,1] => [1,1] => 6
[2,2,2,2,1,1,1,1,1] => [9,1,1,1,1] => [1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1,1] => [7,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => 0
[14] => [2,2,2,2,2,2,2] => [2,2,2,2,2,2] => 0
[13,1] => [2,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 0
[12,2] => [4,2,2,2,2,2] => [2,2,2,2,2] => 0
[12,1,1] => [4,2,2,2,2,1,1] => [2,2,2,2,1,1] => 0
[11,3] => [3,2,2,2,2,2,1] => [2,2,2,2,2,1] => 0
[11,2,1] => [3,3,2,2,2,2] => [3,2,2,2,2] => 0
[11,1,1,1] => [2,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 0
[10,4] => [4,4,2,2,2] => [4,2,2,2] => 10
[10,3,1] => [4,4,2,2,1,1] => [4,2,2,1,1] => 0
[10,2,2] => [6,2,2,2,2] => [2,2,2,2] => 1
[10,2,1,1] => [6,2,2,2,1,1] => [2,2,2,1,1] => 0
[10,1,1,1,1] => [4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 0
[9,5] => [4,3,2,2,2,1] => [3,2,2,2,1] => 0
[9,4,1] => [4,3,3,2,2] => [3,3,2,2] => 6
[9,3,2] => [5,2,2,2,2,1] => [2,2,2,2,1] => 0
[9,3,1,1] => [3,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 0
[9,2,2,1] => [5,3,2,2,2] => [3,2,2,2] => 4
[9,2,1,1,1] => [4,4,2,1,1,1,1] => [4,2,1,1,1,1] => 0
[9,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 0
[8,6] => [4,4,4,2] => [4,4,2] => 126
[8,5,1] => [4,4,4,1,1] => [4,4,1,1] => 50
[8,4,2] => [6,4,2,2] => [4,2,2] => 84
[8,4,1,1] => [6,4,2,1,1] => [4,2,1,1] => 45
[8,3,3] => [5,4,2,2,1] => [4,2,2,1] => 36
[8,3,2,1] => [5,5,2,2] => [5,2,2] => 160
[8,3,1,1,1] => [5,2,2,2,1,1,1] => [2,2,2,1,1,1] => 0
[8,2,2,2] => [8,2,2,2] => [2,2,2] => 10
[8,2,2,1,1] => [8,2,2,1,1] => [2,2,1,1] => 6
[8,2,1,1,1,1] => [6,2,2,1,1,1,1] => [2,2,1,1,1,1] => 0
[8,1,1,1,1,1,1] => [4,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 0
[7,7] => [4,4,3,2,1] => [4,3,2,1] => 64
[7,6,1] => [4,4,3,3] => [4,3,3] => 70
[7,5,2] => [6,3,2,2,1] => [3,2,2,1] => 15
[7,5,1,1] => [4,3,2,2,1,1,1] => [3,2,2,1,1,1] => 0
[7,4,3] => [5,4,3,2] => [4,3,2] => 140
[7,4,2,1] => [6,3,3,2] => [3,3,2] => 45
[7,4,1,1,1] => [5,4,2,1,1,1] => [4,2,1,1,1] => 0
[7,3,3,1] => [3,3,2,2,2,1,1] => [3,2,2,2,1,1] => 0
[7,3,2,2] => [7,2,2,2,1] => [2,2,2,1] => 4
[7,3,2,1,1] => [4,4,3,1,1,1] => [4,3,1,1,1] => 0
[7,3,1,1,1,1] => [3,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 0
[7,2,2,2,1] => [7,3,2,2] => [3,2,2] => 36
[7,2,2,1,1,1] => [6,4,1,1,1,1] => [4,1,1,1,1] => 0
[7,2,1,1,1,1,1] => [4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 0
[7,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 0
[6,6,2] => [6,4,4] => [4,4] => 105
[6,6,1,1] => [6,4,3,1] => [4,3,1] => 175
[6,5,3] => [5,4,4,1] => [4,4,1] => 140
[6,5,2,1] => [5,5,4] => [5,4] => 280
[6,5,1,1,1] => [6,3,2,1,1,1] => [3,2,1,1,1] => 0
[6,4,4] => [6,6,2] => [6,2] => 360
[6,4,3,1] => [6,6,1,1] => [6,1,1] => 189
[6,4,2,2] => [8,4,2] => [4,2] => 126
[6,4,2,1,1] => [8,4,1,1] => [4,1,1] => 70
[6,4,1,1,1,1] => [7,2,2,1,1,1] => [2,2,1,1,1] => 0
[6,3,3,2] => [7,4,2,1] => [4,2,1] => 140
[6,3,3,1,1] => [5,3,2,2,1,1] => [3,2,2,1,1] => 0
[6,3,2,2,1] => [7,5,2] => [5,2] => 224
[6,3,2,1,1,1] => [6,5,1,1,1] => [5,1,1,1] => 35
[6,3,1,1,1,1,1] => [5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 0
[6,2,2,2,2] => [10,2,2] => [2,2] => 20
[6,2,2,2,1,1] => [10,2,1,1] => [2,1,1] => 15
[6,2,2,1,1,1,1] => [8,2,1,1,1,1] => [2,1,1,1,1] => 0
[6,2,1,1,1,1,1,1] => [6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 0
[6,1,1,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 0
[5,5,4] => [6,5,2,1] => [5,2,1] => 256
[5,5,3,1] => [4,3,3,2,1,1] => [3,3,2,1,1] => 0
[5,5,2,2] => [8,3,2,1] => [3,2,1] => 64
[5,5,2,1,1] => [4,3,3,3,1] => [3,3,3,1] => 10
[5,5,1,1,1,1] => [4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 0
[5,4,4,1] => [6,5,3] => [5,3] => 280
[5,4,3,2] => [7,4,3] => [4,3] => 140
[5,4,3,1,1] => [5,4,3,1,1] => [4,3,1,1] => 60
[5,4,2,2,1] => [8,3,3] => [3,3] => 50
[5,4,2,1,1,1] => [7,4,1,1,1] => [4,1,1,1] => 20
[5,4,1,1,1,1,1] => [5,4,1,1,1,1,1] => [4,1,1,1,1,1] => 0
[5,3,3,3] => [3,3,3,2,2,1] => [3,3,2,2,1] => 0
[5,3,3,2,1] => [3,3,3,3,2] => [3,3,3,2] => 4
[5,3,3,1,1,1] => [3,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => 0
[5,3,2,2,2] => [9,2,2,1] => [2,2,1] => 20
[5,3,2,2,1,1] => [6,3,3,1,1] => [3,3,1,1] => 20
[5,3,2,1,1,1,1] => [4,3,3,1,1,1,1] => [3,3,1,1,1,1] => 0
[5,3,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 0
[5,2,2,2,2,1] => [9,3,2] => [3,2] => 60
[5,2,2,2,1,1,1] => [8,3,1,1,1] => [3,1,1,1] => 10
[5,2,2,1,1,1,1,1] => [6,3,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[5,2,1,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 0
[4,4,4,2] => [8,6] => [6] => 84
[4,4,4,1,1] => [8,5,1] => [5,1] => 140
[4,4,3,3] => [7,6,1] => [6,1] => 216
[4,4,3,2,1] => [7,7] => [7] => 120
[4,4,3,1,1,1] => [7,3,2,1,1] => [3,2,1,1] => 20
[4,4,2,2,2] => [10,4] => [4] => 35
[4,4,2,2,1,1] => [10,3,1] => [3,1] => 45
[4,4,2,1,1,1,1] => [9,2,1,1,1] => [2,1,1,1] => 4
[4,4,1,1,1,1,1,1] => [7,2,1,1,1,1,1] => [2,1,1,1,1,1] => 0
[4,3,3,3,1] => [5,5,2,1,1] => [5,2,1,1] => 84
[4,3,3,2,2] => [9,4,1] => [4,1] => 84
[4,3,3,2,1,1] => [5,5,3,1] => [5,3,1] => 360
[4,3,3,1,1,1,1] => [5,3,2,1,1,1,1] => [3,2,1,1,1,1] => 0
[4,3,2,2,2,1] => [9,5] => [5] => 56
[4,3,2,2,1,1,1] => [7,5,1,1] => [5,1,1] => 120
[4,3,2,1,1,1,1,1] => [5,5,1,1,1,1] => [5,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1] => [5,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 0
[4,2,2,2,2,2] => [12,2] => [2] => 10
[4,2,2,2,2,1,1] => [12,1,1] => [1,1] => 6
[4,2,2,2,1,1,1,1] => [10,1,1,1,1] => [1,1,1,1] => 1
[4,2,2,1,1,1,1,1,1] => [8,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[3,3,3,3,2] => [5,3,3,2,1] => [3,3,2,1] => 20
[3,3,3,3,1,1] => [3,3,3,2,1,1,1] => [3,3,2,1,1,1] => 0
[3,3,3,2,2,1] => [5,3,3,3] => [3,3,3] => 20
[3,3,3,2,1,1,1] => [3,3,3,3,1,1] => [3,3,3,1,1] => 0
[3,3,3,1,1,1,1,1] => [3,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => 0
[3,3,2,2,2,2] => [11,2,1] => [2,1] => 20
[3,3,2,2,2,1,1] => [7,3,3,1] => [3,3,1] => 60
[3,3,2,2,1,1,1,1] => [5,3,3,1,1,1] => [3,3,1,1,1] => 0
[3,3,2,1,1,1,1,1,1] => [3,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 0
[3,2,2,2,2,2,1] => [11,3] => [3] => 20
[3,2,2,2,2,1,1,1] => [9,3,1,1] => [3,1,1] => 36
[3,2,2,2,1,1,1,1,1] => [7,3,1,1,1,1] => [3,1,1,1,1] => 0
[3,2,2,1,1,1,1,1,1,1] => [5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2,2] => [14] => [] => 1
[2,2,2,2,2,2,1,1] => [13,1] => [1] => 4
[2,2,2,2,2,1,1,1,1] => [11,1,1,1] => [1,1,1] => 4
[2,2,2,2,1,1,1,1,1,1] => [9,1,1,1,1,1] => [1,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 0
[14,1] => [3,2,2,2,2,2,2] => [2,2,2,2,2,2] => 0
[13,2] => [4,2,2,2,2,2,1] => [2,2,2,2,2,1] => 0
[12,3] => [4,3,2,2,2,2] => [3,2,2,2,2] => 0
[12,2,1] => [5,2,2,2,2,2] => [2,2,2,2,2] => 0
[12,1,1,1] => [4,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 0
[11,4] => [4,4,2,2,2,1] => [4,2,2,2,1] => 0
[11,3,1] => [3,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 0
[11,2,2] => [6,2,2,2,2,1] => [2,2,2,2,1] => 0
[11,2,1,1] => [4,4,2,2,1,1,1] => [4,2,2,1,1,1] => 0
[10,5] => [4,4,3,2,2] => [4,3,2,2] => 20
[10,4,1] => [5,4,2,2,2] => [4,2,2,2] => 10
[10,3,2] => [6,3,2,2,2] => [3,2,2,2] => 4
[10,3,1,1] => [5,2,2,2,2,1,1] => [2,2,2,2,1,1] => 0
[10,2,2,1] => [7,2,2,2,2] => [2,2,2,2] => 1
[10,2,1,1,1] => [6,2,2,2,1,1,1] => [2,2,2,1,1,1] => 0
[10,1,1,1,1,1] => [4,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 0
[9,6] => [4,4,4,2,1] => [4,4,2,1] => 60
[9,5,1] => [4,3,2,2,2,1,1] => [3,2,2,2,1,1] => 0
[9,4,2] => [6,4,2,2,1] => [4,2,2,1] => 36
[9,4,1,1] => [4,4,4,1,1,1] => [4,4,1,1,1] => 0
[9,3,3] => [3,3,2,2,2,2,1] => [3,2,2,2,2,1] => 0
[9,3,2,1] => [3,3,3,2,2,2] => [3,3,2,2,2] => 0
[9,3,1,1,1] => [3,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 0
[9,2,2,2] => [8,2,2,2,1] => [2,2,2,1] => 4
[9,2,2,1,1] => [6,4,2,1,1,1] => [4,2,1,1,1] => 0
[9,2,1,1,1,1] => [4,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => 0
[8,7] => [4,4,4,3] => [4,4,3] => 84
[8,6,1] => [5,4,4,2] => [4,4,2] => 126
[8,5,2] => [6,4,3,2] => [4,3,2] => 140
[8,5,1,1] => [6,3,2,2,1,1] => [3,2,2,1,1] => 0
[8,4,3] => [6,5,2,2] => [5,2,2] => 160
[8,4,2,1] => [7,4,2,2] => [4,2,2] => 84
[8,4,1,1,1] => [7,2,2,2,1,1] => [2,2,2,1,1] => 0
[8,3,3,1] => [5,4,2,2,1,1] => [4,2,2,1,1] => 0
[8,3,2,2] => [8,3,2,2] => [3,2,2] => 36
[8,3,2,1,1] => [6,6,1,1,1] => [6,1,1,1] => 56
[8,3,1,1,1,1] => [5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 0
[8,2,2,2,1] => [9,2,2,2] => [2,2,2] => 10
[8,2,2,1,1,1] => [8,2,2,1,1,1] => [2,2,1,1,1] => 0
[8,2,1,1,1,1,1] => [6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 0
[8,1,1,1,1,1,1,1] => [4,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 0
[7,7,1] => [4,4,3,2,1,1] => [4,3,2,1,1] => 0
[7,6,2] => [6,4,4,1] => [4,4,1] => 140
[7,6,1,1] => [4,4,3,3,1] => [4,3,3,1] => 36
[7,5,3] => [4,3,3,2,2,1] => [3,3,2,2,1] => 0
[7,5,2,1] => [4,3,3,3,2] => [3,3,3,2] => 4
[7,5,1,1,1] => [4,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => 0
[7,4,4] => [6,6,2,1] => [6,2,1] => 420
[7,4,3,1] => [5,4,4,1,1] => [4,4,1,1] => 50
[7,4,2,2] => [8,4,2,1] => [4,2,1] => 140
[7,4,2,1,1] => [6,4,3,1,1] => [4,3,1,1] => 60
[7,4,1,1,1,1] => [5,4,2,1,1,1,1] => [4,2,1,1,1,1] => 0
[7,3,3,2] => [5,3,2,2,2,1] => [3,2,2,2,1] => 0
[7,3,3,1,1] => [3,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => 0
[7,3,2,2,1] => [5,3,3,2,2] => [3,3,2,2] => 6
[7,3,2,1,1,1] => [4,4,3,1,1,1,1] => [4,3,1,1,1,1] => 0
[7,3,1,1,1,1,1] => [3,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 0
[7,2,2,2,2] => [10,2,2,1] => [2,2,1] => 20
[7,2,2,2,1,1] => [8,4,1,1,1] => [4,1,1,1] => 20
[7,2,2,1,1,1,1] => [6,4,1,1,1,1,1] => [4,1,1,1,1,1] => 0
[7,2,1,1,1,1,1,1] => [4,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => 0
[6,6,3] => [6,5,4] => [5,4] => 280
[6,6,2,1] => [7,4,4] => [4,4] => 105
[6,6,1,1,1] => [8,3,2,1,1] => [3,2,1,1] => 20
[6,5,4] => [6,6,3] => [6,3] => 480
[6,5,3,1] => [6,5,2,1,1] => [5,2,1,1] => 84
[6,5,2,2] => [8,4,3] => [4,3] => 140
[6,5,2,1,1] => [6,5,3,1] => [5,3,1] => 360
[6,5,1,1,1,1] => [6,3,2,1,1,1,1] => [3,2,1,1,1,1] => 0
[6,4,4,1] => [7,6,2] => [6,2] => 360
[6,4,3,2] => [8,5,2] => [5,2] => 224
[6,4,3,1,1] => [7,4,2,1,1] => [4,2,1,1] => 45
[6,4,2,2,1] => [9,4,2] => [4,2] => 126
[6,4,2,1,1,1] => [9,2,2,1,1] => [2,2,1,1] => 6
[6,4,1,1,1,1,1] => [7,2,2,1,1,1,1] => [2,2,1,1,1,1] => 0
[6,3,3,3] => [5,5,2,2,1] => [5,2,2,1] => 70
[6,3,3,2,1] => [5,5,3,2] => [5,3,2] => 300
[6,3,3,1,1,1] => [5,3,2,2,1,1,1] => [3,2,2,1,1,1] => 0
[6,3,2,2,2] => [10,3,2] => [3,2] => 60
[6,3,2,2,1,1] => [8,5,1,1] => [5,1,1] => 120
[6,3,2,1,1,1,1] => [6,5,1,1,1,1] => [5,1,1,1,1] => 0
[6,3,1,1,1,1,1,1] => [5,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 0
[6,2,2,2,2,1] => [11,2,2] => [2,2] => 20
[6,2,2,2,1,1,1] => [10,2,1,1,1] => [2,1,1,1] => 4
[6,2,2,1,1,1,1,1] => [8,2,1,1,1,1,1] => [2,1,1,1,1,1] => 0
[6,2,1,1,1,1,1,1,1] => [6,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 0
[6,1,1,1,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 0
[5,5,5] => [5,4,3,2,1] => [4,3,2,1] => 64
[5,5,4,1] => [5,4,3,3] => [4,3,3] => 70
[5,5,3,2] => [6,3,3,2,1] => [3,3,2,1] => 20
[5,5,3,1,1] => [4,3,3,2,1,1,1] => [3,3,2,1,1,1] => 0
[5,5,2,2,1] => [6,3,3,3] => [3,3,3] => 20
[5,5,2,1,1,1] => [5,4,3,1,1,1] => [4,3,1,1,1] => 0
[5,5,1,1,1,1,1] => [4,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => 0
[5,4,4,2] => [8,6,1] => [6,1] => 216
[5,4,4,1,1] => [7,4,3,1] => [4,3,1] => 175
[5,4,3,3] => [5,5,4,1] => [5,4,1] => 384
[5,4,3,2,1] => [5,5,5] => [5,5] => 196
[5,4,3,1,1,1] => [5,5,2,1,1,1] => [5,2,1,1,1] => 0
[5,4,2,2,2] => [10,4,1] => [4,1] => 84
[5,4,2,2,1,1] => [8,3,3,1] => [3,3,1] => 60
[5,4,2,1,1,1,1] => [7,4,1,1,1,1] => [4,1,1,1,1] => 0
[5,4,1,1,1,1,1,1] => [5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 0
[5,3,3,3,1] => [3,3,3,2,2,1,1] => [3,3,2,2,1,1] => 0
[5,3,3,2,2] => [7,3,2,2,1] => [3,2,2,1] => 15
[5,3,3,2,1,1] => [4,3,3,3,1,1] => [3,3,3,1,1] => 0
[5,3,3,1,1,1,1] => [3,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => 0
[5,3,2,2,2,1] => [7,3,3,2] => [3,3,2] => 45
[5,3,2,2,1,1,1] => [6,3,3,1,1,1] => [3,3,1,1,1] => 0
[5,3,2,1,1,1,1,1] => [4,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => 0
[5,3,1,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 0
[5,2,2,2,2,2] => [12,2,1] => [2,1] => 20
[5,2,2,2,2,1,1] => [10,3,1,1] => [3,1,1] => 36
[5,2,2,2,1,1,1,1] => [8,3,1,1,1,1] => [3,1,1,1,1] => 0
[5,2,2,1,1,1,1,1,1] => [6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 0
[5,2,1,1,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => 0
[4,4,4,3] => [8,7] => [7] => 120
[4,4,4,2,1] => [9,6] => [6] => 84
[4,4,4,1,1,1] => [9,4,1,1] => [4,1,1] => 70
[4,4,3,3,1] => [7,6,1,1] => [6,1,1] => 189
[4,4,3,2,2] => [10,5] => [5] => 56
[4,4,3,2,1,1] => [7,7,1] => [7,1] => 315
[4,4,3,1,1,1,1] => [7,3,2,1,1,1] => [3,2,1,1,1] => 0
[4,4,2,2,2,1] => [11,4] => [4] => 35
[4,4,2,2,1,1,1] => [11,2,1,1] => [2,1,1] => 15
[4,4,2,1,1,1,1,1] => [9,2,1,1,1,1] => [2,1,1,1,1] => 0
[4,4,1,1,1,1,1,1,1] => [7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 0
[4,3,3,3,2] => [7,5,2,1] => [5,2,1] => 256
[4,3,3,3,1,1] => [5,3,3,2,1,1] => [3,3,2,1,1] => 0
[4,3,3,2,2,1] => [7,5,3] => [5,3] => 280
[4,3,3,2,1,1,1] => [5,5,3,1,1] => [5,3,1,1] => 126
[4,3,3,1,1,1,1,1] => [5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 0
[4,3,2,2,2,2] => [12,3] => [3] => 20
[4,3,2,2,2,1,1] => [9,5,1] => [5,1] => 140
[4,3,2,2,1,1,1,1] => [7,5,1,1,1] => [5,1,1,1] => 35
[4,3,2,1,1,1,1,1,1] => [5,5,1,1,1,1,1] => [5,1,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1,1] => [5,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 0
[4,2,2,2,2,2,1] => [13,2] => [2] => 10
[4,2,2,2,2,1,1,1] => [12,1,1,1] => [1,1,1] => 4
[4,2,2,2,1,1,1,1,1] => [10,1,1,1,1,1] => [1,1,1,1,1] => 0
[4,2,2,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 0
[3,3,3,3,3] => [3,3,3,3,2,1] => [3,3,3,2,1] => 0
[3,3,3,3,2,1] => [3,3,3,3,3] => [3,3,3,3] => 1
[3,3,3,3,1,1,1] => [3,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => 0
[3,3,3,2,2,2] => [9,3,2,1] => [3,2,1] => 64
[3,3,3,2,2,1,1] => [5,3,3,3,1] => [3,3,3,1] => 10
[3,3,3,2,1,1,1,1] => [3,3,3,3,1,1,1] => [3,3,3,1,1,1] => 0
[3,3,3,1,1,1,1,1,1] => [3,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => 0
[3,3,2,2,2,2,1] => [9,3,3] => [3,3] => 50
[3,3,2,2,2,1,1,1] => [7,3,3,1,1] => [3,3,1,1] => 20
[3,3,2,2,1,1,1,1,1] => [5,3,3,1,1,1,1] => [3,3,1,1,1,1] => 0
[3,3,2,1,1,1,1,1,1,1] => [3,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 0
[3,2,2,2,2,2,2] => [14,1] => [1] => 4
[3,2,2,2,2,2,1,1] => [11,3,1] => [3,1] => 45
[3,2,2,2,2,1,1,1,1] => [9,3,1,1,1] => [3,1,1,1] => 10
[3,2,2,2,1,1,1,1,1,1] => [7,3,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[3,2,2,1,1,1,1,1,1,1,1] => [5,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2,2,1] => [15] => [] => 1
[2,2,2,2,2,2,1,1,1] => [13,1,1] => [1,1] => 6
[2,2,2,2,2,1,1,1,1,1] => [11,1,1,1,1] => [1,1,1,1] => 1
[2,2,2,2,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => 0
[14,2] => [4,2,2,2,2,2,2] => [2,2,2,2,2,2] => 0
[14,1,1] => [4,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 0
[12,4] => [4,4,2,2,2,2] => [4,2,2,2,2] => 0
[12,3,1] => [4,4,2,2,2,1,1] => [4,2,2,2,1,1] => 0
[12,2,2] => [6,2,2,2,2,2] => [2,2,2,2,2] => 0
[12,2,1,1] => [6,2,2,2,2,1,1] => [2,2,2,2,1,1] => 0
[12,1,1,1,1] => [4,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 0
[11,5] => [4,3,2,2,2,2,1] => [3,2,2,2,2,1] => 0
[11,4,1] => [4,3,3,2,2,2] => [3,3,2,2,2] => 0
[11,3,2] => [5,2,2,2,2,2,1] => [2,2,2,2,2,1] => 0
[11,2,2,1] => [5,3,2,2,2,2] => [3,2,2,2,2] => 0
[11,2,1,1,1] => [4,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => 0
[10,6] => [4,4,4,2,2] => [4,4,2,2] => 20
[10,5,1] => [4,4,4,2,1,1] => [4,4,2,1,1] => 0
[10,4,2] => [6,4,2,2,2] => [4,2,2,2] => 10
[10,4,1,1] => [6,4,2,2,1,1] => [4,2,2,1,1] => 0
[10,3,3] => [5,4,2,2,2,1] => [4,2,2,2,1] => 0
[10,3,2,1] => [5,5,2,2,2] => [5,2,2,2] => 20
[10,3,1,1,1] => [5,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 0
[10,2,2,2] => [8,2,2,2,2] => [2,2,2,2] => 1
[10,2,2,1,1] => [8,2,2,2,1,1] => [2,2,2,1,1] => 0
[10,2,1,1,1,1] => [6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 0
[10,1,1,1,1,1,1] => [4,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 0
[9,7] => [4,4,3,2,2,1] => [4,3,2,2,1] => 0
[9,6,1] => [4,4,3,3,2] => [4,3,3,2] => 15
[9,5,2] => [6,3,2,2,2,1] => [3,2,2,2,1] => 0
[9,5,1,1] => [4,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => 0
[9,4,3] => [5,4,3,2,2] => [4,3,2,2] => 20
[9,4,2,1] => [6,3,3,2,2] => [3,3,2,2] => 6
[9,4,1,1,1] => [5,4,2,2,1,1,1] => [4,2,2,1,1,1] => 0
[9,3,2,2] => [7,2,2,2,2,1] => [2,2,2,2,1] => 0
[9,3,2,1,1] => [4,4,4,1,1,1,1] => [4,4,1,1,1,1] => 0
[9,2,2,2,1] => [7,3,2,2,2] => [3,2,2,2] => 4
[9,2,2,1,1,1] => [6,4,2,1,1,1,1] => [4,2,1,1,1,1] => 0
[9,2,1,1,1,1,1] => [4,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => 0
[8,8] => [4,4,4,4] => [4,4,4] => 35
[8,7,1] => [4,4,4,3,1] => [4,4,3,1] => 45
[8,6,2] => [6,4,4,2] => [4,4,2] => 126
[8,6,1,1] => [6,4,4,1,1] => [4,4,1,1] => 50
[8,5,3] => [5,4,4,2,1] => [4,4,2,1] => 60
[8,5,2,1] => [5,5,4,2] => [5,4,2] => 360
[8,5,1,1,1] => [6,3,2,2,1,1,1] => [3,2,2,1,1,1] => 0
[8,4,4] => [6,6,2,2] => [6,2,2] => 270
[8,4,3,1] => [6,6,2,1,1] => [6,2,1,1] => 140
[8,4,2,2] => [8,4,2,2] => [4,2,2] => 84
[8,4,2,1,1] => [8,4,2,1,1] => [4,2,1,1] => 45
[8,4,1,1,1,1] => [7,2,2,2,1,1,1] => [2,2,2,1,1,1] => 0
[8,3,3,2] => [7,4,2,2,1] => [4,2,2,1] => 36
[8,3,3,1,1] => [5,3,2,2,2,1,1] => [3,2,2,2,1,1] => 0
[8,3,2,2,1] => [7,5,2,2] => [5,2,2] => 160
[8,3,2,1,1,1] => [6,6,1,1,1,1] => [6,1,1,1,1] => 0
[8,3,1,1,1,1,1] => [5,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 0
[8,2,2,2,2] => [10,2,2,2] => [2,2,2] => 10
[8,2,2,2,1,1] => [10,2,2,1,1] => [2,2,1,1] => 6
[8,2,2,1,1,1,1] => [8,2,2,1,1,1,1] => [2,2,1,1,1,1] => 0
[8,2,1,1,1,1,1,1] => [6,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 0
[8,1,1,1,1,1,1,1,1] => [4,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 0
[7,7,2] => [6,4,3,2,1] => [4,3,2,1] => 64
[7,7,1,1] => [4,4,3,2,1,1,1] => [4,3,2,1,1,1] => 0
[7,6,3] => [5,4,4,3] => [4,4,3] => 84
[7,6,2,1] => [6,4,3,3] => [4,3,3] => 70
[7,6,1,1,1] => [6,5,2,1,1,1] => [5,2,1,1,1] => 0
[7,5,4] => [6,5,2,2,1] => [5,2,2,1] => 70
[7,5,3,1] => [4,3,3,2,2,1,1] => [3,3,2,2,1,1] => 0
[7,5,2,2] => [8,3,2,2,1] => [3,2,2,1] => 15
[7,5,2,1,1] => [4,4,3,3,1,1] => [4,3,3,1,1] => 0
[7,5,1,1,1,1] => [4,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => 0
[7,4,4,1] => [6,5,3,2] => [5,3,2] => 300
[7,4,3,2] => [7,4,3,2] => [4,3,2] => 140
[7,4,3,1,1] => [5,4,4,1,1,1] => [4,4,1,1,1] => 0
[7,4,2,2,1] => [8,3,3,2] => [3,3,2] => 45
[7,4,2,1,1,1] => [7,4,2,1,1,1] => [4,2,1,1,1] => 0
[7,4,1,1,1,1,1] => [5,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => 0
[7,3,2,2,2] => [9,2,2,2,1] => [2,2,2,1] => 4
[7,3,2,2,1,1] => [6,4,3,1,1,1] => [4,3,1,1,1] => 0
[7,3,2,1,1,1,1] => [4,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => 0
[7,2,2,2,2,1] => [9,3,2,2] => [3,2,2] => 36
[7,2,2,2,1,1,1] => [8,4,1,1,1,1] => [4,1,1,1,1] => 0
[7,2,2,1,1,1,1,1] => [6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 0
[7,2,1,1,1,1,1,1,1] => [4,4,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => 0
[6,6,4] => [6,6,4] => [6,4] => 540
[6,6,3,1] => [6,6,3,1] => [6,3,1] => 630
[6,6,2,2] => [8,4,4] => [4,4] => 105
[6,6,2,1,1] => [8,4,3,1] => [4,3,1] => 175
[6,6,1,1,1,1] => [8,3,2,1,1,1] => [3,2,1,1,1] => 0
[6,5,5] => [6,5,4,1] => [5,4,1] => 384
[6,5,4,1] => [6,5,5] => [5,5] => 196
[6,5,3,2] => [7,4,4,1] => [4,4,1] => 140
[6,5,3,1,1] => [6,3,3,2,1,1] => [3,3,2,1,1] => 0
[6,5,2,2,1] => [7,5,4] => [5,4] => 280
[6,5,2,1,1,1] => [7,6,1,1,1] => [6,1,1,1] => 56
[6,5,1,1,1,1,1] => [6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 0
[6,4,4,2] => [8,6,2] => [6,2] => 360
[6,4,4,1,1] => [8,6,1,1] => [6,1,1] => 189
[6,4,3,3] => [7,6,2,1] => [6,2,1] => 420
[6,4,3,2,1] => [7,7,2] => [7,2] => 540
[6,4,3,1,1,1] => [7,3,2,2,1,1] => [3,2,2,1,1] => 0
[6,4,2,2,2] => [10,4,2] => [4,2] => 126
[6,4,2,2,1,1] => [10,4,1,1] => [4,1,1] => 70
[6,4,2,1,1,1,1] => [9,2,2,1,1,1] => [2,2,1,1,1] => 0
[6,4,1,1,1,1,1,1] => [7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 0
[6,3,3,3,1] => [5,5,2,2,1,1] => [5,2,2,1,1] => 0
[6,3,3,2,2] => [9,4,2,1] => [4,2,1] => 140
[6,3,3,2,1,1] => [6,5,3,1,1] => [5,3,1,1] => 126
[6,3,3,1,1,1,1] => [5,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => 0
[6,3,2,2,2,1] => [9,5,2] => [5,2] => 224
[6,3,2,2,1,1,1] => [8,5,1,1,1] => [5,1,1,1] => 35
[6,3,2,1,1,1,1,1] => [6,5,1,1,1,1,1] => [5,1,1,1,1,1] => 0
[6,3,1,1,1,1,1,1,1] => [5,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 0
[6,2,2,2,2,2] => [12,2,2] => [2,2] => 20
[6,2,2,2,2,1,1] => [12,2,1,1] => [2,1,1] => 15
[6,2,2,2,1,1,1,1] => [10,2,1,1,1,1] => [2,1,1,1,1] => 0
[6,2,2,1,1,1,1,1,1] => [8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 0
[6,2,1,1,1,1,1,1,1,1] => [6,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 0
[6,1,1,1,1,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 0
[5,5,5,1] => [5,4,3,2,1,1] => [4,3,2,1,1] => 0
[5,5,4,2] => [8,5,2,1] => [5,2,1] => 256
[5,5,4,1,1] => [5,4,3,3,1] => [4,3,3,1] => 36
[5,5,3,3] => [4,3,3,3,2,1] => [3,3,3,2,1] => 0
[5,5,3,2,1] => [4,3,3,3,3] => [3,3,3,3] => 1
[5,5,3,1,1,1] => [4,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => 0
[5,5,2,2,2] => [10,3,2,1] => [3,2,1] => 64
[5,5,2,2,1,1] => [6,3,3,3,1] => [3,3,3,1] => 10
[5,5,2,1,1,1,1] => [5,4,3,1,1,1,1] => [4,3,1,1,1,1] => 0
[5,5,1,1,1,1,1,1] => [4,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => 0
[5,4,4,3] => [7,6,3] => [6,3] => 480
[5,4,4,2,1] => [8,5,3] => [5,3] => 280
[5,4,4,1,1,1] => [7,4,3,1,1] => [4,3,1,1] => 60
[5,4,3,3,1] => [5,5,4,1,1] => [5,4,1,1] => 140
[5,4,3,2,2] => [9,4,3] => [4,3] => 140
[5,4,3,2,1,1] => [5,5,5,1] => [5,5,1] => 280
[5,4,3,1,1,1,1] => [5,5,2,1,1,1,1] => [5,2,1,1,1,1] => 0
[5,4,2,2,2,1] => [10,3,3] => [3,3] => 50
[5,4,2,2,1,1,1] => [9,4,1,1,1] => [4,1,1,1] => 20
[5,4,2,1,1,1,1,1] => [7,4,1,1,1,1,1] => [4,1,1,1,1,1] => 0
[5,4,1,1,1,1,1,1,1] => [5,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => 0
[5,3,3,3,2] => [5,3,3,2,2,1] => [3,3,2,2,1] => 0
[5,3,3,2,2,1] => [5,3,3,3,2] => [3,3,3,2] => 4
[5,3,3,2,1,1,1] => [4,3,3,3,1,1,1] => [3,3,3,1,1,1] => 0
[5,3,2,2,2,2] => [11,2,2,1] => [2,2,1] => 20
[5,3,2,2,2,1,1] => [8,3,3,1,1] => [3,3,1,1] => 20
[5,3,2,2,1,1,1,1] => [6,3,3,1,1,1,1] => [3,3,1,1,1,1] => 0
[5,3,2,1,1,1,1,1,1] => [4,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => 0
[5,2,2,2,2,2,1] => [11,3,2] => [3,2] => 60
[5,2,2,2,2,1,1,1] => [10,3,1,1,1] => [3,1,1,1] => 10
[5,2,2,2,1,1,1,1,1] => [8,3,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[5,2,2,1,1,1,1,1,1,1] => [6,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 0
[5,2,1,1,1,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => 0
[4,4,4,4] => [8,8] => [8] => 165
[4,4,4,3,1] => [8,7,1] => [7,1] => 315
[4,4,4,2,2] => [10,6] => [6] => 84
[4,4,4,2,1,1] => [10,5,1] => [5,1] => 140
[4,4,4,1,1,1,1] => [9,3,2,1,1] => [3,2,1,1] => 20
[4,4,3,3,2] => [9,6,1] => [6,1] => 216
[4,4,3,3,1,1] => [7,5,2,1,1] => [5,2,1,1] => 84
[4,4,3,2,2,1] => [9,7] => [7] => 120
[4,4,3,2,1,1,1] => [7,7,1,1] => [7,1,1] => 280
[4,4,3,1,1,1,1,1] => [7,3,2,1,1,1,1] => [3,2,1,1,1,1] => 0
[4,4,2,2,2,2] => [12,4] => [4] => 35
[4,4,2,2,2,1,1] => [12,3,1] => [3,1] => 45
[4,4,2,2,1,1,1,1] => [11,2,1,1,1] => [2,1,1,1] => 4
[4,4,2,1,1,1,1,1,1] => [9,2,1,1,1,1,1] => [2,1,1,1,1,1] => 0
[4,4,1,1,1,1,1,1,1,1] => [7,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 0
[4,3,3,3,3] => [5,5,3,2,1] => [5,3,2,1] => 140
[4,3,3,3,2,1] => [5,5,3,3] => [5,3,3] => 160
[4,3,3,3,1,1,1] => [5,3,3,2,1,1,1] => [3,3,2,1,1,1] => 0
[4,3,3,2,2,2] => [11,4,1] => [4,1] => 84
[4,3,3,2,2,1,1] => [7,5,3,1] => [5,3,1] => 360
[4,3,3,2,1,1,1,1] => [5,5,3,1,1,1] => [5,3,1,1,1] => 0
[4,3,3,1,1,1,1,1,1] => [5,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => 0
[4,3,2,2,2,2,1] => [11,5] => [5] => 56
[4,3,2,2,2,1,1,1] => [9,5,1,1] => [5,1,1] => 120
[4,3,2,2,1,1,1,1,1] => [7,5,1,1,1,1] => [5,1,1,1,1] => 0
[4,3,2,1,1,1,1,1,1,1] => [5,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1,1,1] => [5,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 0
[4,2,2,2,2,2,2] => [14,2] => [2] => 10
[4,2,2,2,2,2,1,1] => [14,1,1] => [1,1] => 6
[4,2,2,2,2,1,1,1,1] => [12,1,1,1,1] => [1,1,1,1] => 1
[4,2,2,2,1,1,1,1,1,1] => [10,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[4,2,2,1,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => 0
[3,3,3,3,2,2] => [7,3,3,2,1] => [3,3,2,1] => 20
[3,3,3,2,2,2,1] => [7,3,3,3] => [3,3,3] => 20
[3,3,3,2,2,1,1,1] => [5,3,3,3,1,1] => [3,3,3,1,1] => 0
[3,3,2,2,2,2,2] => [13,2,1] => [2,1] => 20
[3,3,2,2,2,2,1,1] => [9,3,3,1] => [3,3,1] => 60
[3,3,2,2,2,1,1,1,1] => [7,3,3,1,1,1] => [3,3,1,1,1] => 0
[3,3,2,2,1,1,1,1,1,1] => [5,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => 0
[3,2,2,2,2,2,2,1] => [13,3] => [3] => 20
[3,2,2,2,2,2,1,1,1] => [11,3,1,1] => [3,1,1] => 36
[3,2,2,2,2,1,1,1,1,1] => [9,3,1,1,1,1] => [3,1,1,1,1] => 0
[3,2,2,2,1,1,1,1,1,1,1] => [7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 0
[3,2,2,1,1,1,1,1,1,1,1,1] => [5,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2,2,2] => [16] => [] => 1
[2,2,2,2,2,2,2,1,1] => [15,1] => [1] => 4
[2,2,2,2,2,2,1,1,1,1] => [13,1,1,1] => [1,1,1] => 4
[2,2,2,2,2,1,1,1,1,1,1] => [11,1,1,1,1,1] => [1,1,1,1,1] => 0
[2,2,2,2,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 0
[14,2,1] => [5,2,2,2,2,2,2] => [2,2,2,2,2,2] => 0
[13,2,2] => [6,2,2,2,2,2,1] => [2,2,2,2,2,1] => 0
[12,4,1] => [5,4,2,2,2,2] => [4,2,2,2,2] => 0
[12,3,2] => [6,3,2,2,2,2] => [3,2,2,2,2] => 0
[12,3,1,1] => [5,2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 0
[12,2,2,1] => [7,2,2,2,2,2] => [2,2,2,2,2] => 0
[12,2,1,1,1] => [6,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1] => 0
[11,4,2] => [6,4,2,2,2,1] => [4,2,2,2,1] => 0
[11,2,2,2] => [8,2,2,2,2,1] => [2,2,2,2,1] => 0
[11,2,2,1,1] => [6,4,2,2,1,1,1] => [4,2,2,1,1,1] => 0
[10,6,1] => [5,4,4,2,2] => [4,4,2,2] => 20
[10,5,2] => [6,4,3,2,2] => [4,3,2,2] => 20
[10,5,1,1] => [6,3,2,2,2,1,1] => [3,2,2,2,1,1] => 0
[10,4,3] => [6,5,2,2,2] => [5,2,2,2] => 20
[10,4,2,1] => [7,4,2,2,2] => [4,2,2,2] => 10
[10,4,1,1,1] => [7,2,2,2,2,1,1] => [2,2,2,2,1,1] => 0
[10,3,3,1] => [5,4,2,2,2,1,1] => [4,2,2,2,1,1] => 0
[10,3,2,2] => [8,3,2,2,2] => [3,2,2,2] => 4
[10,3,2,1,1] => [6,6,2,1,1,1] => [6,2,1,1,1] => 0
[10,3,1,1,1,1] => [5,2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 0
[10,2,2,2,1] => [9,2,2,2,2] => [2,2,2,2] => 1
[10,2,2,1,1,1] => [8,2,2,2,1,1,1] => [2,2,2,1,1,1] => 0
[10,2,1,1,1,1,1] => [6,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1] => 0
[9,6,2] => [6,4,4,2,1] => [4,4,2,1] => 60
[9,4,4] => [6,6,2,2,1] => [6,2,2,1] => 120
[9,4,3,1] => [5,4,4,2,1,1] => [4,4,2,1,1] => 0
[9,4,2,2] => [8,4,2,2,1] => [4,2,2,1] => 36
[9,4,2,1,1] => [6,4,4,1,1,1] => [4,4,1,1,1] => 0
[9,4,1,1,1,1] => [5,4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => 0
[9,3,3,2] => [5,3,2,2,2,2,1] => [3,2,2,2,2,1] => 0
[9,3,2,2,1] => [5,3,3,2,2,2] => [3,3,2,2,2] => 0
[9,2,2,2,2] => [10,2,2,2,1] => [2,2,2,1] => 4
[9,2,2,2,1,1] => [8,4,2,1,1,1] => [4,2,1,1,1] => 0
[9,2,2,1,1,1,1] => [6,4,2,1,1,1,1,1] => [4,2,1,1,1,1,1] => 0
[8,8,1] => [5,4,4,4] => [4,4,4] => 35
[8,7,2] => [6,4,4,3] => [4,4,3] => 84
[8,7,1,1] => [6,4,3,2,1,1] => [4,3,2,1,1] => 0
[8,6,3] => [6,5,4,2] => [5,4,2] => 360
[8,6,2,1] => [7,4,4,2] => [4,4,2] => 126
[8,6,1,1,1] => [8,3,2,2,1,1] => [3,2,2,1,1] => 0
[8,5,4] => [6,6,3,2] => [6,3,2] => 540
[8,5,3,1] => [6,5,2,2,1,1] => [5,2,2,1,1] => 0
[8,5,2,2] => [8,4,3,2] => [4,3,2] => 140
[8,5,2,1,1] => [6,6,3,1,1] => [6,3,1,1] => 224
[8,5,1,1,1,1] => [6,3,2,2,1,1,1,1] => [3,2,2,1,1,1,1] => 0
[8,4,4,1] => [7,6,2,2] => [6,2,2] => 270
[8,4,3,2] => [8,5,2,2] => [5,2,2] => 160
[8,4,3,1,1] => [7,4,2,2,1,1] => [4,2,2,1,1] => 0
[8,4,2,2,1] => [9,4,2,2] => [4,2,2] => 84
[8,4,2,1,1,1] => [9,2,2,2,1,1] => [2,2,2,1,1] => 0
[8,4,1,1,1,1,1] => [7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 0
[8,3,3,3] => [5,5,2,2,2,1] => [5,2,2,2,1] => 0
[8,3,3,2,1] => [5,5,3,2,2] => [5,3,2,2] => 45
[8,3,3,1,1,1] => [5,3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => 0
[8,3,2,2,2] => [10,3,2,2] => [3,2,2] => 36
[8,3,2,2,1,1] => [8,6,1,1,1] => [6,1,1,1] => 56
[8,3,2,1,1,1,1] => [6,6,1,1,1,1,1] => [6,1,1,1,1,1] => 0
[8,3,1,1,1,1,1,1] => [5,2,2,2,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 0
[8,2,2,2,2,1] => [11,2,2,2] => [2,2,2] => 10
[8,2,2,2,1,1,1] => [10,2,2,1,1,1] => [2,2,1,1,1] => 0
[8,2,2,1,1,1,1,1] => [8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 0
[8,2,1,1,1,1,1,1,1] => [6,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 0
[7,6,4] => [6,6,4,1] => [6,4,1] => 756
[7,6,3,1] => [5,4,4,3,1] => [4,4,3,1] => 45
[7,6,2,2] => [8,4,4,1] => [4,4,1] => 140
[7,6,2,1,1] => [6,4,3,3,1] => [4,3,3,1] => 36
[7,6,1,1,1,1] => [6,5,2,1,1,1,1] => [5,2,1,1,1,1] => 0
[7,5,5] => [5,4,3,2,2,1] => [4,3,2,2,1] => 0
[7,5,4,1] => [5,4,3,3,2] => [4,3,3,2] => 15
[7,5,3,2] => [6,3,3,2,2,1] => [3,3,2,2,1] => 0
[7,5,2,2,1] => [6,3,3,3,2] => [3,3,3,2] => 4
[7,5,2,1,1,1] => [5,4,4,1,1,1,1] => [4,4,1,1,1,1] => 0
[7,4,4,2] => [8,6,2,1] => [6,2,1] => 420
[7,4,4,1,1] => [7,4,4,1,1] => [4,4,1,1] => 50
[7,4,3,3] => [5,5,4,2,1] => [5,4,2,1] => 175
[7,4,3,2,1] => [5,5,5,2] => [5,5,2] => 280
[7,4,3,1,1,1] => [5,5,2,2,1,1,1] => [5,2,2,1,1,1] => 0
[7,4,2,2,2] => [10,4,2,1] => [4,2,1] => 140
[7,4,2,2,1,1] => [8,4,3,1,1] => [4,3,1,1] => 60
[7,4,2,1,1,1,1] => [7,4,2,1,1,1,1] => [4,2,1,1,1,1] => 0
[7,4,1,1,1,1,1,1] => [5,4,2,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1] => 0
[7,3,3,2,2] => [7,3,2,2,2,1] => [3,2,2,2,1] => 0
[7,3,2,2,2,1] => [7,3,3,2,2] => [3,3,2,2] => 6
[7,3,2,2,1,1,1] => [6,4,3,1,1,1,1] => [4,3,1,1,1,1] => 0
[7,2,2,2,2,2] => [12,2,2,1] => [2,2,1] => 20
[7,2,2,2,2,1,1] => [10,4,1,1,1] => [4,1,1,1] => 20
[7,2,2,2,1,1,1,1] => [8,4,1,1,1,1,1] => [4,1,1,1,1,1] => 0
[7,2,2,1,1,1,1,1,1] => [6,4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1] => 0
[6,6,5] => [6,6,5] => [6,5] => 504
[6,6,4,1] => [7,6,4] => [6,4] => 540
[6,6,3,2] => [8,5,4] => [5,4] => 280
[6,6,3,1,1] => [8,5,2,1,1] => [5,2,1,1] => 84
[6,6,2,2,1] => [9,4,4] => [4,4] => 105
[6,6,2,1,1,1] => [10,3,2,1,1] => [3,2,1,1] => 20
[6,6,1,1,1,1,1] => [8,3,2,1,1,1,1] => [3,2,1,1,1,1] => 0
[6,5,5,1] => [6,5,4,1,1] => [5,4,1,1] => 140
[6,5,4,2] => [8,6,3] => [6,3] => 480
[6,5,4,1,1] => [6,5,5,1] => [5,5,1] => 280
[6,5,3,3] => [6,5,3,2,1] => [5,3,2,1] => 140
[6,5,3,2,1] => [6,5,3,3] => [5,3,3] => 160
[6,5,3,1,1,1] => [6,3,3,2,1,1,1] => [3,3,2,1,1,1] => 0
[6,5,2,2,2] => [10,4,3] => [4,3] => 140
[6,5,2,2,1,1] => [8,5,3,1] => [5,3,1] => 360
[6,5,2,1,1,1,1] => [7,6,1,1,1,1] => [6,1,1,1,1] => 0
[6,5,1,1,1,1,1,1] => [6,3,2,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1] => 0
[6,4,4,3] => [8,7,2] => [7,2] => 540
[6,4,4,2,1] => [9,6,2] => [6,2] => 360
[6,4,4,1,1,1] => [9,4,2,1,1] => [4,2,1,1] => 45
[6,4,3,3,1] => [7,6,2,1,1] => [6,2,1,1] => 140
[6,4,3,2,2] => [10,5,2] => [5,2] => 224
[6,4,3,2,1,1] => [8,7,1,1] => [7,1,1] => 280
[6,4,3,1,1,1,1] => [7,3,2,2,1,1,1] => [3,2,2,1,1,1] => 0
[6,4,2,2,2,1] => [11,4,2] => [4,2] => 126
[6,4,2,2,1,1,1] => [11,2,2,1,1] => [2,2,1,1] => 6
[6,4,2,1,1,1,1,1] => [9,2,2,1,1,1,1] => [2,2,1,1,1,1] => 0
[6,4,1,1,1,1,1,1,1] => [7,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 0
[6,3,3,3,2] => [7,5,2,2,1] => [5,2,2,1] => 70
[6,3,3,3,1,1] => [5,3,3,2,2,1,1] => [3,3,2,2,1,1] => 0
[6,3,3,2,2,1] => [7,5,3,2] => [5,3,2] => 300
[6,3,3,2,1,1,1] => [6,5,3,1,1,1] => [5,3,1,1,1] => 0
[6,3,3,1,1,1,1,1] => [5,3,2,2,1,1,1,1,1] => [3,2,2,1,1,1,1,1] => 0
[6,3,2,2,2,2] => [12,3,2] => [3,2] => 60
[6,3,2,2,2,1,1] => [10,5,1,1] => [5,1,1] => 120
[6,3,2,2,1,1,1,1] => [8,5,1,1,1,1] => [5,1,1,1,1] => 0
[6,3,2,1,1,1,1,1,1] => [6,5,1,1,1,1,1,1] => [5,1,1,1,1,1,1] => 0
[6,3,1,1,1,1,1,1,1,1] => [5,2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 0
[6,2,2,2,2,2,1] => [13,2,2] => [2,2] => 20
[6,2,2,2,2,1,1,1] => [12,2,1,1,1] => [2,1,1,1] => 4
[6,2,2,2,1,1,1,1,1] => [10,2,1,1,1,1,1] => [2,1,1,1,1,1] => 0
[6,2,2,1,1,1,1,1,1,1] => [8,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 0
[6,2,1,1,1,1,1,1,1,1,1] => [6,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 0
[5,5,5,2] => [7,4,3,2,1] => [4,3,2,1] => 64
[5,5,5,1,1] => [5,4,3,2,1,1,1] => [4,3,2,1,1,1] => 0
[5,5,4,3] => [5,5,4,3] => [5,4,3] => 256
[5,5,4,2,1] => [7,4,3,3] => [4,3,3] => 70
[5,5,4,1,1,1] => [5,4,3,3,1,1] => [4,3,3,1,1] => 0
[5,5,3,2,2] => [8,3,3,2,1] => [3,3,2,1] => 20
[5,5,2,2,2,1] => [8,3,3,3] => [3,3,3] => 20
[5,5,2,2,1,1,1] => [7,4,3,1,1,1] => [4,3,1,1,1] => 0
[5,5,2,1,1,1,1,1] => [5,4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => 0
[5,4,4,4] => [8,8,1] => [8,1] => 440
[5,4,4,3,1] => [7,6,3,1] => [6,3,1] => 630
[5,4,4,2,2] => [10,6,1] => [6,1] => 216
[5,4,4,2,1,1] => [9,4,3,1] => [4,3,1] => 175
[5,4,4,1,1,1,1] => [7,5,2,1,1,1] => [5,2,1,1,1] => 0
[5,4,3,3,2] => [7,5,4,1] => [5,4,1] => 384
[5,4,3,3,1,1] => [5,5,4,1,1,1] => [5,4,1,1,1] => 0
[5,4,3,2,2,1] => [7,5,5] => [5,5] => 196
[5,4,3,2,1,1,1] => [5,5,5,1,1] => [5,5,1,1] => 105
[5,4,3,1,1,1,1,1] => [5,5,2,1,1,1,1,1] => [5,2,1,1,1,1,1] => 0
[5,4,2,2,2,2] => [12,4,1] => [4,1] => 84
[5,4,2,2,2,1,1] => [10,3,3,1] => [3,3,1] => 60
[5,4,2,2,1,1,1,1] => [9,4,1,1,1,1] => [4,1,1,1,1] => 0
[5,4,2,1,1,1,1,1,1] => [7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 0
[5,4,1,1,1,1,1,1,1,1] => [5,4,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => 0
[5,3,3,2,2,2] => [9,3,2,2,1] => [3,2,2,1] => 15
[5,3,3,2,2,1,1] => [6,3,3,3,1,1] => [3,3,3,1,1] => 0
[5,3,2,2,2,2,1] => [9,3,3,2] => [3,3,2] => 45
[5,3,2,2,2,1,1,1] => [8,3,3,1,1,1] => [3,3,1,1,1] => 0
[5,3,2,2,1,1,1,1,1] => [6,3,3,1,1,1,1,1] => [3,3,1,1,1,1,1] => 0
[5,2,2,2,2,2,2] => [14,2,1] => [2,1] => 20
[5,2,2,2,2,2,1,1] => [12,3,1,1] => [3,1,1] => 36
[5,2,2,2,2,1,1,1,1] => [10,3,1,1,1,1] => [3,1,1,1,1] => 0
[5,2,2,2,1,1,1,1,1,1] => [8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 0
[5,2,2,1,1,1,1,1,1,1,1] => [6,3,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => 0
[4,4,4,4,1] => [9,8] => [8] => 165
[4,4,4,3,2] => [10,7] => [7] => 120
[4,4,4,3,1,1] => [9,6,1,1] => [6,1,1] => 189
[4,4,4,2,2,1] => [11,6] => [6] => 84
[4,4,4,2,1,1,1] => [11,4,1,1] => [4,1,1] => 70
[4,4,4,1,1,1,1,1] => [9,3,2,1,1,1] => [3,2,1,1,1] => 0
[4,4,3,3,3] => [7,7,2,1] => [7,2,1] => 640
[4,4,3,3,2,1] => [7,7,3] => [7,3] => 750
[4,4,3,3,1,1,1] => [7,3,3,2,1,1] => [3,3,2,1,1] => 0
[4,4,3,2,2,2] => [12,5] => [5] => 56
[4,4,3,2,2,1,1] => [9,7,1] => [7,1] => 315
[4,4,3,2,1,1,1,1] => [7,7,1,1,1] => [7,1,1,1] => 84
[4,4,3,1,1,1,1,1,1] => [7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 0
[4,4,2,2,2,2,1] => [13,4] => [4] => 35
[4,4,2,2,2,1,1,1] => [13,2,1,1] => [2,1,1] => 15
[4,4,2,2,1,1,1,1,1] => [11,2,1,1,1,1] => [2,1,1,1,1] => 0
[4,4,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 0
[4,4,1,1,1,1,1,1,1,1,1] => [7,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 0
[4,3,3,3,3,1] => [5,5,3,2,1,1] => [5,3,2,1,1] => 0
[4,3,3,3,2,2] => [9,5,2,1] => [5,2,1] => 256
[4,3,3,3,2,1,1] => [5,5,3,3,1] => [5,3,3,1] => 84
[4,3,3,3,1,1,1,1] => [5,3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => 0
[4,3,3,2,2,2,1] => [9,5,3] => [5,3] => 280
[4,3,3,2,2,1,1,1] => [7,5,3,1,1] => [5,3,1,1] => 126
[4,3,3,2,1,1,1,1,1] => [5,5,3,1,1,1,1] => [5,3,1,1,1,1] => 0
[4,3,3,1,1,1,1,1,1,1] => [5,3,2,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => 0
[4,3,2,2,2,2,2] => [14,3] => [3] => 20
[4,3,2,2,2,2,1,1] => [11,5,1] => [5,1] => 140
[4,3,2,2,2,1,1,1,1] => [9,5,1,1,1] => [5,1,1,1] => 35
[4,3,2,2,1,1,1,1,1,1] => [7,5,1,1,1,1,1] => [5,1,1,1,1,1] => 0
[4,3,2,1,1,1,1,1,1,1,1] => [5,5,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1,1,1,1] => [5,2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 0
[4,2,2,2,2,2,2,1] => [15,2] => [2] => 10
[4,2,2,2,2,2,1,1,1] => [14,1,1,1] => [1,1,1] => 4
[4,2,2,2,2,1,1,1,1,1] => [12,1,1,1,1,1] => [1,1,1,1,1] => 0
[4,2,2,2,1,1,1,1,1,1,1] => [10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 0
[4,2,2,1,1,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 0
[4,2,1,1,1,1,1,1,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 0
[3,3,3,3,3,2] => [5,3,3,3,2,1] => [3,3,3,2,1] => 0
[3,3,3,3,2,2,1] => [5,3,3,3,3] => [3,3,3,3] => 1
[3,3,3,2,2,2,2] => [11,3,2,1] => [3,2,1] => 64
[3,3,3,2,2,2,1,1] => [7,3,3,3,1] => [3,3,3,1] => 10
[3,3,3,2,2,1,1,1,1] => [5,3,3,3,1,1,1] => [3,3,3,1,1,1] => 0
[3,3,2,2,2,2,2,1] => [11,3,3] => [3,3] => 50
[3,3,2,2,2,2,1,1,1] => [9,3,3,1,1] => [3,3,1,1] => 20
[3,3,2,2,2,1,1,1,1,1] => [7,3,3,1,1,1,1] => [3,3,1,1,1,1] => 0
[3,3,2,2,1,1,1,1,1,1,1] => [5,3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => 0
[3,2,2,2,2,2,2,2] => [16,1] => [1] => 4
[3,2,2,2,2,2,2,1,1] => [13,3,1] => [3,1] => 45
[3,2,2,2,2,2,1,1,1,1] => [11,3,1,1,1] => [3,1,1,1] => 10
[3,2,2,2,2,1,1,1,1,1,1] => [9,3,1,1,1,1,1] => [3,1,1,1,1,1] => 0
[3,2,2,2,1,1,1,1,1,1,1,1] => [7,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 0
[3,2,2,1,1,1,1,1,1,1,1,1,1] => [5,3,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2,2,2,1] => [17] => [] => 1
[2,2,2,2,2,2,2,1,1,1] => [15,1,1] => [1,1] => 6
[2,2,2,2,2,2,1,1,1,1,1] => [13,1,1,1,1] => [1,1,1,1] => 1
[2,2,2,2,2,1,1,1,1,1,1,1] => [11,1,1,1,1,1,1] => [1,1,1,1,1,1] => 0
[2,2,2,2,1,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => 0
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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:
1,0,0,1 1,0,0,1,0,1 1,0,0,2,0,1,0,0,0,1 2,0,0,2,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1 1,2,0,0,2,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,3
$F_{1} = q$
$F_{2} = q + q^{4}$
$F_{3} = q + q^{4} + q^{6}$
$F_{4} = q + 2\ q^{4} + q^{6} + q^{10}$
$F_{5} = 2\ q + 2\ q^{4} + q^{6} + q^{10} + q^{20}$
$F_{6} = 1 + 2\ q + 2\ q^{4} + q^{6} + q^{10} + q^{15} + 3\ q^{20}$
$F_{7} = 2 + 2\ q + 3\ q^{4} + q^{6} + q^{10} + q^{15} + 4\ q^{20} + q^{45}$
$F_{8} = 4 + 2\ q + 3\ q^{4} + 2\ q^{6} + 2\ q^{10} + q^{15} + 4\ q^{20} + q^{35} + q^{36} + q^{45} + q^{60}$
$F_{9} = 7 + 2\ q + 4\ q^{4} + 2\ q^{6} + 3\ q^{10} + q^{15} + 4\ q^{20} + q^{35} + q^{36} + q^{45} + q^{50} + q^{60} + q^{64} + q^{84}$
$F_{10} = 12 + 3\ q + 4\ q^{4} + 2\ q^{6} + 3\ q^{10} + q^{15} + 5\ q^{20} + q^{35} + 2\ q^{36} + q^{45} + q^{50} + q^{56} + 2\ q^{60} + q^{64} + q^{70} + q^{84} + q^{126}$
$F_{11} = 19 + 3\ q + 4\ q^{4} + 2\ q^{6} + 3\ q^{10} + 2\ q^{15} + 7\ q^{20} + q^{35} + 2\ q^{36} + 2\ q^{45} + q^{50} + q^{56} + 2\ q^{60} + q^{64} + q^{70} + q^{84} + q^{126} + 3\ q^{140}$
$F_{12} = 30 + 3\ q + 5\ q^{4} + 2\ q^{6} + 3\ q^{10} + 2\ q^{15} + 9\ q^{20} + q^{35} + 2\ q^{36} + 3\ q^{45} + q^{50} + q^{56} + 2\ q^{60} + q^{64} + q^{70} + 3\ q^{84} + q^{105} + q^{120} + q^{126} + 3\ q^{140} + q^{175} + q^{224}$
$F_{13} = 44 + 3\ q + 5\ q^{4} + 3\ q^{6} + 4\ q^{10} + 2\ q^{15} + 9\ q^{20} + 2\ q^{35} + 3\ q^{36} + 3\ q^{45} + q^{50} + q^{56} + 3\ q^{60} + q^{64} + q^{70} + 3\ q^{84} + q^{105} + q^{120} + q^{126} + 5\ q^{140} + q^{175} + q^{216} + q^{224} + q^{256} + q^{280}$
Description
The number of semistandard Young tableau of given shape, with entries at most 4.
This is also the dimension of the corresponding irreducible representation of $GL_4$.
This is also the dimension of the corresponding irreducible representation of $GL_4$.
Map
2-conjugate
Description
Return a partition with the same number of odd parts and number of even parts interchanged with the number of cells with zero leg and odd arm length.
This is a special case of an involution that preserves the sequence of non-zero remainders of the parts under division by $s$ and interchanges the number of parts divisible by $s$ and the number of cells with zero leg length and arm length congruent to $s-1$ modulo $s$.
In particular, for $s=1$ the involution is conjugation, hence the name.
This is a special case of an involution that preserves the sequence of non-zero remainders of the parts under division by $s$ and interchanges the number of parts divisible by $s$ and the number of cells with zero leg length and arm length congruent to $s-1$ modulo $s$.
In particular, for $s=1$ the involution is conjugation, hence the name.
Map
first row removal
Description
Removes the first entry of an integer partition
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