Identifier
-
Mp00040:
Integer compositions
—to partition⟶
Integer partitions
St000814: Integer partitions ⟶ ℤ
Values
[1] => [1] => 1
[1,1] => [1,1] => 2
[2] => [2] => 1
[1,1,1] => [1,1,1] => 4
[1,2] => [2,1] => 2
[2,1] => [2,1] => 2
[3] => [3] => 1
[1,1,1,1] => [1,1,1,1] => 10
[1,1,2] => [2,1,1] => 5
[1,2,1] => [2,1,1] => 5
[1,3] => [3,1] => 2
[2,1,1] => [2,1,1] => 5
[2,2] => [2,2] => 3
[3,1] => [3,1] => 2
[4] => [4] => 1
[1,1,1,1,1] => [1,1,1,1,1] => 26
[1,1,1,2] => [2,1,1,1] => 13
[1,1,2,1] => [2,1,1,1] => 13
[1,1,3] => [3,1,1] => 5
[1,2,1,1] => [2,1,1,1] => 13
[1,2,2] => [2,2,1] => 7
[1,3,1] => [3,1,1] => 5
[1,4] => [4,1] => 2
[2,1,1,1] => [2,1,1,1] => 13
[2,1,2] => [2,2,1] => 7
[2,2,1] => [2,2,1] => 7
[2,3] => [3,2] => 3
[3,1,1] => [3,1,1] => 5
[3,2] => [3,2] => 3
[4,1] => [4,1] => 2
[5] => [5] => 1
[1,1,1,1,1,1] => [1,1,1,1,1,1] => 76
[1,1,1,1,2] => [2,1,1,1,1] => 38
[1,1,1,2,1] => [2,1,1,1,1] => 38
[1,1,1,3] => [3,1,1,1] => 14
[1,1,2,1,1] => [2,1,1,1,1] => 38
[1,1,2,2] => [2,2,1,1] => 20
[1,1,3,1] => [3,1,1,1] => 14
[1,1,4] => [4,1,1] => 5
[1,2,1,1,1] => [2,1,1,1,1] => 38
[1,2,1,2] => [2,2,1,1] => 20
[1,2,2,1] => [2,2,1,1] => 20
[1,2,3] => [3,2,1] => 8
[1,3,1,1] => [3,1,1,1] => 14
[1,3,2] => [3,2,1] => 8
[1,4,1] => [4,1,1] => 5
[1,5] => [5,1] => 2
[2,1,1,1,1] => [2,1,1,1,1] => 38
[2,1,1,2] => [2,2,1,1] => 20
[2,1,2,1] => [2,2,1,1] => 20
[2,1,3] => [3,2,1] => 8
[2,2,1,1] => [2,2,1,1] => 20
[2,2,2] => [2,2,2] => 11
[2,3,1] => [3,2,1] => 8
[2,4] => [4,2] => 3
[3,1,1,1] => [3,1,1,1] => 14
[3,1,2] => [3,2,1] => 8
[3,2,1] => [3,2,1] => 8
[3,3] => [3,3] => 4
[4,1,1] => [4,1,1] => 5
[4,2] => [4,2] => 3
[5,1] => [5,1] => 2
[6] => [6] => 1
[1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => 232
[1,1,1,1,1,2] => [2,1,1,1,1,1] => 116
[1,1,1,1,2,1] => [2,1,1,1,1,1] => 116
[1,1,1,1,3] => [3,1,1,1,1] => 42
[1,1,1,2,1,1] => [2,1,1,1,1,1] => 116
[1,1,1,2,2] => [2,2,1,1,1] => 60
[1,1,1,3,1] => [3,1,1,1,1] => 42
[1,1,1,4] => [4,1,1,1] => 14
[1,1,2,1,1,1] => [2,1,1,1,1,1] => 116
[1,1,2,1,2] => [2,2,1,1,1] => 60
[1,1,2,2,1] => [2,2,1,1,1] => 60
[1,1,2,3] => [3,2,1,1] => 23
[1,1,3,1,1] => [3,1,1,1,1] => 42
[1,1,3,2] => [3,2,1,1] => 23
[1,1,4,1] => [4,1,1,1] => 14
[1,1,5] => [5,1,1] => 5
[1,2,1,1,1,1] => [2,1,1,1,1,1] => 116
[1,2,1,1,2] => [2,2,1,1,1] => 60
[1,2,1,2,1] => [2,2,1,1,1] => 60
[1,2,1,3] => [3,2,1,1] => 23
[1,2,2,1,1] => [2,2,1,1,1] => 60
[1,2,2,2] => [2,2,2,1] => 32
[1,2,3,1] => [3,2,1,1] => 23
[1,2,4] => [4,2,1] => 8
[1,3,1,1,1] => [3,1,1,1,1] => 42
[1,3,1,2] => [3,2,1,1] => 23
[1,3,2,1] => [3,2,1,1] => 23
[1,3,3] => [3,3,1] => 10
[1,4,1,1] => [4,1,1,1] => 14
[1,4,2] => [4,2,1] => 8
[1,5,1] => [5,1,1] => 5
[1,6] => [6,1] => 2
[2,1,1,1,1,1] => [2,1,1,1,1,1] => 116
[2,1,1,1,2] => [2,2,1,1,1] => 60
[2,1,1,2,1] => [2,2,1,1,1] => 60
[2,1,1,3] => [3,2,1,1] => 23
[2,1,2,1,1] => [2,2,1,1,1] => 60
[2,1,2,2] => [2,2,2,1] => 32
>>> Load all 1884 entries. <<<[2,1,3,1] => [3,2,1,1] => 23
[2,1,4] => [4,2,1] => 8
[2,2,1,1,1] => [2,2,1,1,1] => 60
[2,2,1,2] => [2,2,2,1] => 32
[2,2,2,1] => [2,2,2,1] => 32
[2,2,3] => [3,2,2] => 13
[2,3,1,1] => [3,2,1,1] => 23
[2,3,2] => [3,2,2] => 13
[2,4,1] => [4,2,1] => 8
[2,5] => [5,2] => 3
[3,1,1,1,1] => [3,1,1,1,1] => 42
[3,1,1,2] => [3,2,1,1] => 23
[3,1,2,1] => [3,2,1,1] => 23
[3,1,3] => [3,3,1] => 10
[3,2,1,1] => [3,2,1,1] => 23
[3,2,2] => [3,2,2] => 13
[3,3,1] => [3,3,1] => 10
[3,4] => [4,3] => 4
[4,1,1,1] => [4,1,1,1] => 14
[4,1,2] => [4,2,1] => 8
[4,2,1] => [4,2,1] => 8
[4,3] => [4,3] => 4
[5,1,1] => [5,1,1] => 5
[5,2] => [5,2] => 3
[6,1] => [6,1] => 2
[7] => [7] => 1
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => 764
[1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => 382
[1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => 382
[1,1,1,1,1,3] => [3,1,1,1,1,1] => 136
[1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => 382
[1,1,1,1,2,2] => [2,2,1,1,1,1] => 196
[1,1,1,1,3,1] => [3,1,1,1,1,1] => 136
[1,1,1,1,4] => [4,1,1,1,1] => 43
[1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => 382
[1,1,1,2,1,2] => [2,2,1,1,1,1] => 196
[1,1,1,2,2,1] => [2,2,1,1,1,1] => 196
[1,1,1,2,3] => [3,2,1,1,1] => 73
[1,1,1,3,1,1] => [3,1,1,1,1,1] => 136
[1,1,1,3,2] => [3,2,1,1,1] => 73
[1,1,1,4,1] => [4,1,1,1,1] => 43
[1,1,1,5] => [5,1,1,1] => 14
[1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => 382
[1,1,2,1,1,2] => [2,2,1,1,1,1] => 196
[1,1,2,1,2,1] => [2,2,1,1,1,1] => 196
[1,1,2,1,3] => [3,2,1,1,1] => 73
[1,1,2,2,1,1] => [2,2,1,1,1,1] => 196
[1,1,2,2,2] => [2,2,2,1,1] => 103
[1,1,2,3,1] => [3,2,1,1,1] => 73
[1,1,2,4] => [4,2,1,1] => 24
[1,1,3,1,1,1] => [3,1,1,1,1,1] => 136
[1,1,3,1,2] => [3,2,1,1,1] => 73
[1,1,3,2,1] => [3,2,1,1,1] => 73
[1,1,3,3] => [3,3,1,1] => 30
[1,1,4,1,1] => [4,1,1,1,1] => 43
[1,1,4,2] => [4,2,1,1] => 24
[1,1,5,1] => [5,1,1,1] => 14
[1,1,6] => [6,1,1] => 5
[1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => 382
[1,2,1,1,1,2] => [2,2,1,1,1,1] => 196
[1,2,1,1,2,1] => [2,2,1,1,1,1] => 196
[1,2,1,1,3] => [3,2,1,1,1] => 73
[1,2,1,2,1,1] => [2,2,1,1,1,1] => 196
[1,2,1,2,2] => [2,2,2,1,1] => 103
[1,2,1,3,1] => [3,2,1,1,1] => 73
[1,2,1,4] => [4,2,1,1] => 24
[1,2,2,1,1,1] => [2,2,1,1,1,1] => 196
[1,2,2,1,2] => [2,2,2,1,1] => 103
[1,2,2,2,1] => [2,2,2,1,1] => 103
[1,2,2,3] => [3,2,2,1] => 40
[1,2,3,1,1] => [3,2,1,1,1] => 73
[1,2,3,2] => [3,2,2,1] => 40
[1,2,4,1] => [4,2,1,1] => 24
[1,2,5] => [5,2,1] => 8
[1,3,1,1,1,1] => [3,1,1,1,1,1] => 136
[1,3,1,1,2] => [3,2,1,1,1] => 73
[1,3,1,2,1] => [3,2,1,1,1] => 73
[1,3,1,3] => [3,3,1,1] => 30
[1,3,2,1,1] => [3,2,1,1,1] => 73
[1,3,2,2] => [3,2,2,1] => 40
[1,3,3,1] => [3,3,1,1] => 30
[1,3,4] => [4,3,1] => 11
[1,4,1,1,1] => [4,1,1,1,1] => 43
[1,4,1,2] => [4,2,1,1] => 24
[1,4,2,1] => [4,2,1,1] => 24
[1,4,3] => [4,3,1] => 11
[1,5,1,1] => [5,1,1,1] => 14
[1,5,2] => [5,2,1] => 8
[1,6,1] => [6,1,1] => 5
[1,7] => [7,1] => 2
[2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => 382
[2,1,1,1,1,2] => [2,2,1,1,1,1] => 196
[2,1,1,1,2,1] => [2,2,1,1,1,1] => 196
[2,1,1,1,3] => [3,2,1,1,1] => 73
[2,1,1,2,1,1] => [2,2,1,1,1,1] => 196
[2,1,1,2,2] => [2,2,2,1,1] => 103
[2,1,1,3,1] => [3,2,1,1,1] => 73
[2,1,1,4] => [4,2,1,1] => 24
[2,1,2,1,1,1] => [2,2,1,1,1,1] => 196
[2,1,2,1,2] => [2,2,2,1,1] => 103
[2,1,2,2,1] => [2,2,2,1,1] => 103
[2,1,2,3] => [3,2,2,1] => 40
[2,1,3,1,1] => [3,2,1,1,1] => 73
[2,1,3,2] => [3,2,2,1] => 40
[2,1,4,1] => [4,2,1,1] => 24
[2,1,5] => [5,2,1] => 8
[2,2,1,1,1,1] => [2,2,1,1,1,1] => 196
[2,2,1,1,2] => [2,2,2,1,1] => 103
[2,2,1,2,1] => [2,2,2,1,1] => 103
[2,2,1,3] => [3,2,2,1] => 40
[2,2,2,1,1] => [2,2,2,1,1] => 103
[2,2,2,2] => [2,2,2,2] => 56
[2,2,3,1] => [3,2,2,1] => 40
[2,2,4] => [4,2,2] => 14
[2,3,1,1,1] => [3,2,1,1,1] => 73
[2,3,1,2] => [3,2,2,1] => 40
[2,3,2,1] => [3,2,2,1] => 40
[2,3,3] => [3,3,2] => 17
[2,4,1,1] => [4,2,1,1] => 24
[2,4,2] => [4,2,2] => 14
[2,5,1] => [5,2,1] => 8
[2,6] => [6,2] => 3
[3,1,1,1,1,1] => [3,1,1,1,1,1] => 136
[3,1,1,1,2] => [3,2,1,1,1] => 73
[3,1,1,2,1] => [3,2,1,1,1] => 73
[3,1,1,3] => [3,3,1,1] => 30
[3,1,2,1,1] => [3,2,1,1,1] => 73
[3,1,2,2] => [3,2,2,1] => 40
[3,1,3,1] => [3,3,1,1] => 30
[3,1,4] => [4,3,1] => 11
[3,2,1,1,1] => [3,2,1,1,1] => 73
[3,2,1,2] => [3,2,2,1] => 40
[3,2,2,1] => [3,2,2,1] => 40
[3,2,3] => [3,3,2] => 17
[3,3,1,1] => [3,3,1,1] => 30
[3,3,2] => [3,3,2] => 17
[3,4,1] => [4,3,1] => 11
[3,5] => [5,3] => 4
[4,1,1,1,1] => [4,1,1,1,1] => 43
[4,1,1,2] => [4,2,1,1] => 24
[4,1,2,1] => [4,2,1,1] => 24
[4,1,3] => [4,3,1] => 11
[4,2,1,1] => [4,2,1,1] => 24
[4,2,2] => [4,2,2] => 14
[4,3,1] => [4,3,1] => 11
[4,4] => [4,4] => 5
[5,1,1,1] => [5,1,1,1] => 14
[5,1,2] => [5,2,1] => 8
[5,2,1] => [5,2,1] => 8
[5,3] => [5,3] => 4
[6,1,1] => [6,1,1] => 5
[6,2] => [6,2] => 3
[7,1] => [7,1] => 2
[8] => [8] => 1
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => 2620
[1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => 1310
[1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => 1310
[1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => 462
[1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1] => 1310
[1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => 668
[1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => 462
[1,1,1,1,1,4] => [4,1,1,1,1,1] => 141
[1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1] => 1310
[1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => 668
[1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => 668
[1,1,1,1,2,3] => [3,2,1,1,1,1] => 244
[1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => 462
[1,1,1,1,3,2] => [3,2,1,1,1,1] => 244
[1,1,1,1,4,1] => [4,1,1,1,1,1] => 141
[1,1,1,1,5] => [5,1,1,1,1] => 43
[1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1310
[1,1,1,2,1,1,2] => [2,2,1,1,1,1,1] => 668
[1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => 668
[1,1,1,2,1,3] => [3,2,1,1,1,1] => 244
[1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => 668
[1,1,1,2,2,2] => [2,2,2,1,1,1] => 347
[1,1,1,2,3,1] => [3,2,1,1,1,1] => 244
[1,1,1,2,4] => [4,2,1,1,1] => 77
[1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => 462
[1,1,1,3,1,2] => [3,2,1,1,1,1] => 244
[1,1,1,3,2,1] => [3,2,1,1,1,1] => 244
[1,1,1,3,3] => [3,3,1,1,1] => 96
[1,1,1,4,1,1] => [4,1,1,1,1,1] => 141
[1,1,1,4,2] => [4,2,1,1,1] => 77
[1,1,1,5,1] => [5,1,1,1,1] => 43
[1,1,1,6] => [6,1,1,1] => 14
[1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1310
[1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => 668
[1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => 668
[1,1,2,1,1,3] => [3,2,1,1,1,1] => 244
[1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => 668
[1,1,2,1,2,2] => [2,2,2,1,1,1] => 347
[1,1,2,1,3,1] => [3,2,1,1,1,1] => 244
[1,1,2,1,4] => [4,2,1,1,1] => 77
[1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => 668
[1,1,2,2,1,2] => [2,2,2,1,1,1] => 347
[1,1,2,2,2,1] => [2,2,2,1,1,1] => 347
[1,1,2,2,3] => [3,2,2,1,1] => 131
[1,1,2,3,1,1] => [3,2,1,1,1,1] => 244
[1,1,2,3,2] => [3,2,2,1,1] => 131
[1,1,2,4,1] => [4,2,1,1,1] => 77
[1,1,2,5] => [5,2,1,1] => 24
[1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => 462
[1,1,3,1,1,2] => [3,2,1,1,1,1] => 244
[1,1,3,1,2,1] => [3,2,1,1,1,1] => 244
[1,1,3,1,3] => [3,3,1,1,1] => 96
[1,1,3,2,1,1] => [3,2,1,1,1,1] => 244
[1,1,3,2,2] => [3,2,2,1,1] => 131
[1,1,3,3,1] => [3,3,1,1,1] => 96
[1,1,3,4] => [4,3,1,1] => 33
[1,1,4,1,1,1] => [4,1,1,1,1,1] => 141
[1,1,4,1,2] => [4,2,1,1,1] => 77
[1,1,4,2,1] => [4,2,1,1,1] => 77
[1,1,4,3] => [4,3,1,1] => 33
[1,1,5,1,1] => [5,1,1,1,1] => 43
[1,1,5,2] => [5,2,1,1] => 24
[1,1,6,1] => [6,1,1,1] => 14
[1,1,7] => [7,1,1] => 5
[1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1310
[1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => 668
[1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => 668
[1,2,1,1,1,3] => [3,2,1,1,1,1] => 244
[1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => 668
[1,2,1,1,2,2] => [2,2,2,1,1,1] => 347
[1,2,1,1,3,1] => [3,2,1,1,1,1] => 244
[1,2,1,1,4] => [4,2,1,1,1] => 77
[1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => 668
[1,2,1,2,1,2] => [2,2,2,1,1,1] => 347
[1,2,1,2,2,1] => [2,2,2,1,1,1] => 347
[1,2,1,2,3] => [3,2,2,1,1] => 131
[1,2,1,3,1,1] => [3,2,1,1,1,1] => 244
[1,2,1,3,2] => [3,2,2,1,1] => 131
[1,2,1,4,1] => [4,2,1,1,1] => 77
[1,2,1,5] => [5,2,1,1] => 24
[1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => 668
[1,2,2,1,1,2] => [2,2,2,1,1,1] => 347
[1,2,2,1,2,1] => [2,2,2,1,1,1] => 347
[1,2,2,1,3] => [3,2,2,1,1] => 131
[1,2,2,2,1,1] => [2,2,2,1,1,1] => 347
[1,2,2,2,2] => [2,2,2,2,1] => 184
[1,2,2,3,1] => [3,2,2,1,1] => 131
[1,2,2,4] => [4,2,2,1] => 43
[1,2,3,1,1,1] => [3,2,1,1,1,1] => 244
[1,2,3,1,2] => [3,2,2,1,1] => 131
[1,2,3,2,1] => [3,2,2,1,1] => 131
[1,2,3,3] => [3,3,2,1] => 53
[1,2,4,1,1] => [4,2,1,1,1] => 77
[1,2,4,2] => [4,2,2,1] => 43
[1,2,5,1] => [5,2,1,1] => 24
[1,2,6] => [6,2,1] => 8
[1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => 462
[1,3,1,1,1,2] => [3,2,1,1,1,1] => 244
[1,3,1,1,2,1] => [3,2,1,1,1,1] => 244
[1,3,1,1,3] => [3,3,1,1,1] => 96
[1,3,1,2,1,1] => [3,2,1,1,1,1] => 244
[1,3,1,2,2] => [3,2,2,1,1] => 131
[1,3,1,3,1] => [3,3,1,1,1] => 96
[1,3,1,4] => [4,3,1,1] => 33
[1,3,2,1,1,1] => [3,2,1,1,1,1] => 244
[1,3,2,1,2] => [3,2,2,1,1] => 131
[1,3,2,2,1] => [3,2,2,1,1] => 131
[1,3,2,3] => [3,3,2,1] => 53
[1,3,3,1,1] => [3,3,1,1,1] => 96
[1,3,3,2] => [3,3,2,1] => 53
[1,3,4,1] => [4,3,1,1] => 33
[1,3,5] => [5,3,1] => 11
[1,4,1,1,1,1] => [4,1,1,1,1,1] => 141
[1,4,1,1,2] => [4,2,1,1,1] => 77
[1,4,1,2,1] => [4,2,1,1,1] => 77
[1,4,1,3] => [4,3,1,1] => 33
[1,4,2,1,1] => [4,2,1,1,1] => 77
[1,4,2,2] => [4,2,2,1] => 43
[1,4,3,1] => [4,3,1,1] => 33
[1,4,4] => [4,4,1] => 13
[1,5,1,1,1] => [5,1,1,1,1] => 43
[1,5,1,2] => [5,2,1,1] => 24
[1,5,2,1] => [5,2,1,1] => 24
[1,5,3] => [5,3,1] => 11
[1,6,1,1] => [6,1,1,1] => 14
[1,6,2] => [6,2,1] => 8
[1,7,1] => [7,1,1] => 5
[1,8] => [8,1] => 2
[2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => 1310
[2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => 668
[2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => 668
[2,1,1,1,1,3] => [3,2,1,1,1,1] => 244
[2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => 668
[2,1,1,1,2,2] => [2,2,2,1,1,1] => 347
[2,1,1,1,3,1] => [3,2,1,1,1,1] => 244
[2,1,1,1,4] => [4,2,1,1,1] => 77
[2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => 668
[2,1,1,2,1,2] => [2,2,2,1,1,1] => 347
[2,1,1,2,2,1] => [2,2,2,1,1,1] => 347
[2,1,1,2,3] => [3,2,2,1,1] => 131
[2,1,1,3,1,1] => [3,2,1,1,1,1] => 244
[2,1,1,3,2] => [3,2,2,1,1] => 131
[2,1,1,4,1] => [4,2,1,1,1] => 77
[2,1,1,5] => [5,2,1,1] => 24
[2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => 668
[2,1,2,1,1,2] => [2,2,2,1,1,1] => 347
[2,1,2,1,2,1] => [2,2,2,1,1,1] => 347
[2,1,2,1,3] => [3,2,2,1,1] => 131
[2,1,2,2,1,1] => [2,2,2,1,1,1] => 347
[2,1,2,2,2] => [2,2,2,2,1] => 184
[2,1,2,3,1] => [3,2,2,1,1] => 131
[2,1,2,4] => [4,2,2,1] => 43
[2,1,3,1,1,1] => [3,2,1,1,1,1] => 244
[2,1,3,1,2] => [3,2,2,1,1] => 131
[2,1,3,2,1] => [3,2,2,1,1] => 131
[2,1,3,3] => [3,3,2,1] => 53
[2,1,4,1,1] => [4,2,1,1,1] => 77
[2,1,4,2] => [4,2,2,1] => 43
[2,1,5,1] => [5,2,1,1] => 24
[2,1,6] => [6,2,1] => 8
[2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => 668
[2,2,1,1,1,2] => [2,2,2,1,1,1] => 347
[2,2,1,1,2,1] => [2,2,2,1,1,1] => 347
[2,2,1,1,3] => [3,2,2,1,1] => 131
[2,2,1,2,1,1] => [2,2,2,1,1,1] => 347
[2,2,1,2,2] => [2,2,2,2,1] => 184
[2,2,1,3,1] => [3,2,2,1,1] => 131
[2,2,1,4] => [4,2,2,1] => 43
[2,2,2,1,1,1] => [2,2,2,1,1,1] => 347
[2,2,2,1,2] => [2,2,2,2,1] => 184
[2,2,2,2,1] => [2,2,2,2,1] => 184
[2,2,2,3] => [3,2,2,2] => 72
[2,2,3,1,1] => [3,2,2,1,1] => 131
[2,2,3,2] => [3,2,2,2] => 72
[2,2,4,1] => [4,2,2,1] => 43
[2,2,5] => [5,2,2] => 14
[2,3,1,1,1,1] => [3,2,1,1,1,1] => 244
[2,3,1,1,2] => [3,2,2,1,1] => 131
[2,3,1,2,1] => [3,2,2,1,1] => 131
[2,3,1,3] => [3,3,2,1] => 53
[2,3,2,1,1] => [3,2,2,1,1] => 131
[2,3,2,2] => [3,2,2,2] => 72
[2,3,3,1] => [3,3,2,1] => 53
[2,3,4] => [4,3,2] => 19
[2,4,1,1,1] => [4,2,1,1,1] => 77
[2,4,1,2] => [4,2,2,1] => 43
[2,4,2,1] => [4,2,2,1] => 43
[2,4,3] => [4,3,2] => 19
[2,5,1,1] => [5,2,1,1] => 24
[2,5,2] => [5,2,2] => 14
[2,6,1] => [6,2,1] => 8
[2,7] => [7,2] => 3
[3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => 462
[3,1,1,1,1,2] => [3,2,1,1,1,1] => 244
[3,1,1,1,2,1] => [3,2,1,1,1,1] => 244
[3,1,1,1,3] => [3,3,1,1,1] => 96
[3,1,1,2,1,1] => [3,2,1,1,1,1] => 244
[3,1,1,2,2] => [3,2,2,1,1] => 131
[3,1,1,3,1] => [3,3,1,1,1] => 96
[3,1,1,4] => [4,3,1,1] => 33
[3,1,2,1,1,1] => [3,2,1,1,1,1] => 244
[3,1,2,1,2] => [3,2,2,1,1] => 131
[3,1,2,2,1] => [3,2,2,1,1] => 131
[3,1,2,3] => [3,3,2,1] => 53
[3,1,3,1,1] => [3,3,1,1,1] => 96
[3,1,3,2] => [3,3,2,1] => 53
[3,1,4,1] => [4,3,1,1] => 33
[3,1,5] => [5,3,1] => 11
[3,2,1,1,1,1] => [3,2,1,1,1,1] => 244
[3,2,1,1,2] => [3,2,2,1,1] => 131
[3,2,1,2,1] => [3,2,2,1,1] => 131
[3,2,1,3] => [3,3,2,1] => 53
[3,2,2,1,1] => [3,2,2,1,1] => 131
[3,2,2,2] => [3,2,2,2] => 72
[3,2,3,1] => [3,3,2,1] => 53
[3,2,4] => [4,3,2] => 19
[3,3,1,1,1] => [3,3,1,1,1] => 96
[3,3,1,2] => [3,3,2,1] => 53
[3,3,2,1] => [3,3,2,1] => 53
[3,3,3] => [3,3,3] => 23
[3,4,1,1] => [4,3,1,1] => 33
[3,4,2] => [4,3,2] => 19
[3,5,1] => [5,3,1] => 11
[3,6] => [6,3] => 4
[4,1,1,1,1,1] => [4,1,1,1,1,1] => 141
[4,1,1,1,2] => [4,2,1,1,1] => 77
[4,1,1,2,1] => [4,2,1,1,1] => 77
[4,1,1,3] => [4,3,1,1] => 33
[4,1,2,1,1] => [4,2,1,1,1] => 77
[4,1,2,2] => [4,2,2,1] => 43
[4,1,3,1] => [4,3,1,1] => 33
[4,1,4] => [4,4,1] => 13
[4,2,1,1,1] => [4,2,1,1,1] => 77
[4,2,1,2] => [4,2,2,1] => 43
[4,2,2,1] => [4,2,2,1] => 43
[4,2,3] => [4,3,2] => 19
[4,3,1,1] => [4,3,1,1] => 33
[4,3,2] => [4,3,2] => 19
[4,4,1] => [4,4,1] => 13
[4,5] => [5,4] => 5
[5,1,1,1,1] => [5,1,1,1,1] => 43
[5,1,1,2] => [5,2,1,1] => 24
[5,1,2,1] => [5,2,1,1] => 24
[5,1,3] => [5,3,1] => 11
[5,2,1,1] => [5,2,1,1] => 24
[5,2,2] => [5,2,2] => 14
[5,3,1] => [5,3,1] => 11
[5,4] => [5,4] => 5
[6,1,1,1] => [6,1,1,1] => 14
[6,1,2] => [6,2,1] => 8
[6,2,1] => [6,2,1] => 8
[6,3] => [6,3] => 4
[7,1,1] => [7,1,1] => 5
[7,2] => [7,2] => 3
[8,1] => [8,1] => 2
[9] => [9] => 1
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => 9496
[1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1] => 4748
[1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => 4748
[1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => 1660
[1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1] => 4748
[1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1] => 2412
[1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => 1660
[1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => 492
[1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => 4748
[1,1,1,1,1,2,1,2] => [2,2,1,1,1,1,1,1] => 2412
[1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1] => 2412
[1,1,1,1,1,2,3] => [3,2,1,1,1,1,1] => 868
[1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => 1660
[1,1,1,1,1,3,2] => [3,2,1,1,1,1,1] => 868
[1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => 492
[1,1,1,1,1,5] => [5,1,1,1,1,1] => 142
[1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 4748
[1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1] => 2412
[1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1] => 2412
[1,1,1,1,2,1,3] => [3,2,1,1,1,1,1] => 868
[1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1] => 2412
[1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => 1244
[1,1,1,1,2,3,1] => [3,2,1,1,1,1,1] => 868
[1,1,1,1,2,4] => [4,2,1,1,1,1] => 265
[1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1] => 1660
[1,1,1,1,3,1,2] => [3,2,1,1,1,1,1] => 868
[1,1,1,1,3,2,1] => [3,2,1,1,1,1,1] => 868
[1,1,1,1,3,3] => [3,3,1,1,1,1] => 332
[1,1,1,1,4,1,1] => [4,1,1,1,1,1,1] => 492
[1,1,1,1,4,2] => [4,2,1,1,1,1] => 265
[1,1,1,1,5,1] => [5,1,1,1,1,1] => 142
[1,1,1,1,6] => [6,1,1,1,1] => 43
[1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 4748
[1,1,1,2,1,1,1,2] => [2,2,1,1,1,1,1,1] => 2412
[1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1] => 2412
[1,1,1,2,1,1,3] => [3,2,1,1,1,1,1] => 868
[1,1,1,2,1,2,1,1] => [2,2,1,1,1,1,1,1] => 2412
[1,1,1,2,1,2,2] => [2,2,2,1,1,1,1] => 1244
[1,1,1,2,1,3,1] => [3,2,1,1,1,1,1] => 868
[1,1,1,2,1,4] => [4,2,1,1,1,1] => 265
[1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1] => 2412
[1,1,1,2,2,1,2] => [2,2,2,1,1,1,1] => 1244
[1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => 1244
[1,1,1,2,2,3] => [3,2,2,1,1,1] => 460
[1,1,1,2,3,1,1] => [3,2,1,1,1,1,1] => 868
[1,1,1,2,3,2] => [3,2,2,1,1,1] => 460
[1,1,1,2,4,1] => [4,2,1,1,1,1] => 265
[1,1,1,2,5] => [5,2,1,1,1] => 78
[1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => 1660
[1,1,1,3,1,1,2] => [3,2,1,1,1,1,1] => 868
[1,1,1,3,1,2,1] => [3,2,1,1,1,1,1] => 868
[1,1,1,3,1,3] => [3,3,1,1,1,1] => 332
[1,1,1,3,2,1,1] => [3,2,1,1,1,1,1] => 868
[1,1,1,3,2,2] => [3,2,2,1,1,1] => 460
[1,1,1,3,3,1] => [3,3,1,1,1,1] => 332
[1,1,1,3,4] => [4,3,1,1,1] => 109
[1,1,1,4,1,1,1] => [4,1,1,1,1,1,1] => 492
[1,1,1,4,1,2] => [4,2,1,1,1,1] => 265
[1,1,1,4,2,1] => [4,2,1,1,1,1] => 265
[1,1,1,4,3] => [4,3,1,1,1] => 109
[1,1,1,5,1,1] => [5,1,1,1,1,1] => 142
[1,1,1,5,2] => [5,2,1,1,1] => 78
[1,1,1,6,1] => [6,1,1,1,1] => 43
[1,1,1,7] => [7,1,1,1] => 14
[1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 4748
[1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 2412
[1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 2412
[1,1,2,1,1,1,3] => [3,2,1,1,1,1,1] => 868
[1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => 2412
[1,1,2,1,1,2,2] => [2,2,2,1,1,1,1] => 1244
[1,1,2,1,1,3,1] => [3,2,1,1,1,1,1] => 868
[1,1,2,1,1,4] => [4,2,1,1,1,1] => 265
[1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => 2412
[1,1,2,1,2,1,2] => [2,2,2,1,1,1,1] => 1244
[1,1,2,1,2,2,1] => [2,2,2,1,1,1,1] => 1244
[1,1,2,1,2,3] => [3,2,2,1,1,1] => 460
[1,1,2,1,3,1,1] => [3,2,1,1,1,1,1] => 868
[1,1,2,1,3,2] => [3,2,2,1,1,1] => 460
[1,1,2,1,4,1] => [4,2,1,1,1,1] => 265
[1,1,2,1,5] => [5,2,1,1,1] => 78
[1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => 2412
[1,1,2,2,1,1,2] => [2,2,2,1,1,1,1] => 1244
[1,1,2,2,1,2,1] => [2,2,2,1,1,1,1] => 1244
[1,1,2,2,1,3] => [3,2,2,1,1,1] => 460
[1,1,2,2,2,1,1] => [2,2,2,1,1,1,1] => 1244
[1,1,2,2,2,2] => [2,2,2,2,1,1] => 652
[1,1,2,2,3,1] => [3,2,2,1,1,1] => 460
[1,1,2,2,4] => [4,2,2,1,1] => 145
[1,1,2,3,1,1,1] => [3,2,1,1,1,1,1] => 868
[1,1,2,3,1,2] => [3,2,2,1,1,1] => 460
[1,1,2,3,2,1] => [3,2,2,1,1,1] => 460
[1,1,2,3,3] => [3,3,2,1,1] => 180
[1,1,2,4,1,1] => [4,2,1,1,1,1] => 265
[1,1,2,4,2] => [4,2,2,1,1] => 145
[1,1,2,5,1] => [5,2,1,1,1] => 78
[1,1,2,6] => [6,2,1,1] => 24
[1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 1660
[1,1,3,1,1,1,2] => [3,2,1,1,1,1,1] => 868
[1,1,3,1,1,2,1] => [3,2,1,1,1,1,1] => 868
[1,1,3,1,1,3] => [3,3,1,1,1,1] => 332
[1,1,3,1,2,1,1] => [3,2,1,1,1,1,1] => 868
[1,1,3,1,2,2] => [3,2,2,1,1,1] => 460
[1,1,3,1,3,1] => [3,3,1,1,1,1] => 332
[1,1,3,1,4] => [4,3,1,1,1] => 109
[1,1,3,2,1,1,1] => [3,2,1,1,1,1,1] => 868
[1,1,3,2,1,2] => [3,2,2,1,1,1] => 460
[1,1,3,2,2,1] => [3,2,2,1,1,1] => 460
[1,1,3,2,3] => [3,3,2,1,1] => 180
[1,1,3,3,1,1] => [3,3,1,1,1,1] => 332
[1,1,3,3,2] => [3,3,2,1,1] => 180
[1,1,3,4,1] => [4,3,1,1,1] => 109
[1,1,3,5] => [5,3,1,1] => 34
[1,1,4,1,1,1,1] => [4,1,1,1,1,1,1] => 492
[1,1,4,1,1,2] => [4,2,1,1,1,1] => 265
[1,1,4,1,2,1] => [4,2,1,1,1,1] => 265
[1,1,4,1,3] => [4,3,1,1,1] => 109
[1,1,4,2,1,1] => [4,2,1,1,1,1] => 265
[1,1,4,2,2] => [4,2,2,1,1] => 145
[1,1,4,3,1] => [4,3,1,1,1] => 109
[1,1,4,4] => [4,4,1,1] => 40
[1,1,5,1,1,1] => [5,1,1,1,1,1] => 142
[1,1,5,1,2] => [5,2,1,1,1] => 78
[1,1,5,2,1] => [5,2,1,1,1] => 78
[1,1,5,3] => [5,3,1,1] => 34
[1,1,6,1,1] => [6,1,1,1,1] => 43
[1,1,6,2] => [6,2,1,1] => 24
[1,1,7,1] => [7,1,1,1] => 14
[1,1,8] => [8,1,1] => 5
[1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 4748
[1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 2412
[1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 2412
[1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => 868
[1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => 2412
[1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => 1244
[1,2,1,1,1,3,1] => [3,2,1,1,1,1,1] => 868
[1,2,1,1,1,4] => [4,2,1,1,1,1] => 265
[1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => 2412
[1,2,1,1,2,1,2] => [2,2,2,1,1,1,1] => 1244
[1,2,1,1,2,2,1] => [2,2,2,1,1,1,1] => 1244
[1,2,1,1,2,3] => [3,2,2,1,1,1] => 460
[1,2,1,1,3,1,1] => [3,2,1,1,1,1,1] => 868
[1,2,1,1,3,2] => [3,2,2,1,1,1] => 460
[1,2,1,1,4,1] => [4,2,1,1,1,1] => 265
[1,2,1,1,5] => [5,2,1,1,1] => 78
[1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => 2412
[1,2,1,2,1,1,2] => [2,2,2,1,1,1,1] => 1244
[1,2,1,2,1,2,1] => [2,2,2,1,1,1,1] => 1244
[1,2,1,2,1,3] => [3,2,2,1,1,1] => 460
[1,2,1,2,2,1,1] => [2,2,2,1,1,1,1] => 1244
[1,2,1,2,2,2] => [2,2,2,2,1,1] => 652
[1,2,1,2,3,1] => [3,2,2,1,1,1] => 460
[1,2,1,2,4] => [4,2,2,1,1] => 145
[1,2,1,3,1,1,1] => [3,2,1,1,1,1,1] => 868
[1,2,1,3,1,2] => [3,2,2,1,1,1] => 460
[1,2,1,3,2,1] => [3,2,2,1,1,1] => 460
[1,2,1,3,3] => [3,3,2,1,1] => 180
[1,2,1,4,1,1] => [4,2,1,1,1,1] => 265
[1,2,1,4,2] => [4,2,2,1,1] => 145
[1,2,1,5,1] => [5,2,1,1,1] => 78
[1,2,1,6] => [6,2,1,1] => 24
[1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 2412
[1,2,2,1,1,1,2] => [2,2,2,1,1,1,1] => 1244
[1,2,2,1,1,2,1] => [2,2,2,1,1,1,1] => 1244
[1,2,2,1,1,3] => [3,2,2,1,1,1] => 460
[1,2,2,1,2,1,1] => [2,2,2,1,1,1,1] => 1244
[1,2,2,1,2,2] => [2,2,2,2,1,1] => 652
[1,2,2,1,3,1] => [3,2,2,1,1,1] => 460
[1,2,2,1,4] => [4,2,2,1,1] => 145
[1,2,2,2,1,1,1] => [2,2,2,1,1,1,1] => 1244
[1,2,2,2,1,2] => [2,2,2,2,1,1] => 652
[1,2,2,2,2,1] => [2,2,2,2,1,1] => 652
[1,2,2,2,3] => [3,2,2,2,1] => 248
[1,2,2,3,1,1] => [3,2,2,1,1,1] => 460
[1,2,2,3,2] => [3,2,2,2,1] => 248
[1,2,2,4,1] => [4,2,2,1,1] => 145
[1,2,2,5] => [5,2,2,1] => 44
[1,2,3,1,1,1,1] => [3,2,1,1,1,1,1] => 868
[1,2,3,1,1,2] => [3,2,2,1,1,1] => 460
[1,2,3,1,2,1] => [3,2,2,1,1,1] => 460
[1,2,3,1,3] => [3,3,2,1,1] => 180
[1,2,3,2,1,1] => [3,2,2,1,1,1] => 460
[1,2,3,2,2] => [3,2,2,2,1] => 248
[1,2,3,3,1] => [3,3,2,1,1] => 180
[1,2,3,4] => [4,3,2,1] => 61
[1,2,4,1,1,1] => [4,2,1,1,1,1] => 265
[1,2,4,1,2] => [4,2,2,1,1] => 145
[1,2,4,2,1] => [4,2,2,1,1] => 145
[1,2,4,3] => [4,3,2,1] => 61
[1,2,5,1,1] => [5,2,1,1,1] => 78
[1,2,5,2] => [5,2,2,1] => 44
[1,2,6,1] => [6,2,1,1] => 24
[1,2,7] => [7,2,1] => 8
[1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 1660
[1,3,1,1,1,1,2] => [3,2,1,1,1,1,1] => 868
[1,3,1,1,1,2,1] => [3,2,1,1,1,1,1] => 868
[1,3,1,1,1,3] => [3,3,1,1,1,1] => 332
[1,3,1,1,2,1,1] => [3,2,1,1,1,1,1] => 868
[1,3,1,1,2,2] => [3,2,2,1,1,1] => 460
[1,3,1,1,3,1] => [3,3,1,1,1,1] => 332
[1,3,1,1,4] => [4,3,1,1,1] => 109
[1,3,1,2,1,1,1] => [3,2,1,1,1,1,1] => 868
[1,3,1,2,1,2] => [3,2,2,1,1,1] => 460
[1,3,1,2,2,1] => [3,2,2,1,1,1] => 460
[1,3,1,2,3] => [3,3,2,1,1] => 180
[1,3,1,3,1,1] => [3,3,1,1,1,1] => 332
[1,3,1,3,2] => [3,3,2,1,1] => 180
[1,3,1,4,1] => [4,3,1,1,1] => 109
[1,3,1,5] => [5,3,1,1] => 34
[1,3,2,1,1,1,1] => [3,2,1,1,1,1,1] => 868
[1,3,2,1,1,2] => [3,2,2,1,1,1] => 460
[1,3,2,1,2,1] => [3,2,2,1,1,1] => 460
[1,3,2,1,3] => [3,3,2,1,1] => 180
[1,3,2,2,1,1] => [3,2,2,1,1,1] => 460
[1,3,2,2,2] => [3,2,2,2,1] => 248
[1,3,2,3,1] => [3,3,2,1,1] => 180
[1,3,2,4] => [4,3,2,1] => 61
[1,3,3,1,1,1] => [3,3,1,1,1,1] => 332
[1,3,3,1,2] => [3,3,2,1,1] => 180
[1,3,3,2,1] => [3,3,2,1,1] => 180
[1,3,3,3] => [3,3,3,1] => 74
[1,3,4,1,1] => [4,3,1,1,1] => 109
[1,3,4,2] => [4,3,2,1] => 61
[1,3,5,1] => [5,3,1,1] => 34
[1,3,6] => [6,3,1] => 11
[1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => 492
[1,4,1,1,1,2] => [4,2,1,1,1,1] => 265
[1,4,1,1,2,1] => [4,2,1,1,1,1] => 265
[1,4,1,1,3] => [4,3,1,1,1] => 109
[1,4,1,2,1,1] => [4,2,1,1,1,1] => 265
[1,4,1,2,2] => [4,2,2,1,1] => 145
[1,4,1,3,1] => [4,3,1,1,1] => 109
[1,4,1,4] => [4,4,1,1] => 40
[1,4,2,1,1,1] => [4,2,1,1,1,1] => 265
[1,4,2,1,2] => [4,2,2,1,1] => 145
[1,4,2,2,1] => [4,2,2,1,1] => 145
[1,4,2,3] => [4,3,2,1] => 61
[1,4,3,1,1] => [4,3,1,1,1] => 109
[1,4,3,2] => [4,3,2,1] => 61
[1,4,4,1] => [4,4,1,1] => 40
[1,4,5] => [5,4,1] => 14
[1,5,1,1,1,1] => [5,1,1,1,1,1] => 142
[1,5,1,1,2] => [5,2,1,1,1] => 78
[1,5,1,2,1] => [5,2,1,1,1] => 78
[1,5,1,3] => [5,3,1,1] => 34
[1,5,2,1,1] => [5,2,1,1,1] => 78
[1,5,2,2] => [5,2,2,1] => 44
[1,5,3,1] => [5,3,1,1] => 34
[1,5,4] => [5,4,1] => 14
[1,6,1,1,1] => [6,1,1,1,1] => 43
[1,6,1,2] => [6,2,1,1] => 24
[1,6,2,1] => [6,2,1,1] => 24
[1,6,3] => [6,3,1] => 11
[1,7,1,1] => [7,1,1,1] => 14
[1,7,2] => [7,2,1] => 8
[1,8,1] => [8,1,1] => 5
[1,9] => [9,1] => 2
[2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => 4748
[2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => 2412
[2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => 2412
[2,1,1,1,1,1,3] => [3,2,1,1,1,1,1] => 868
[2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => 2412
[2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => 1244
[2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => 868
[2,1,1,1,1,4] => [4,2,1,1,1,1] => 265
[2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => 2412
[2,1,1,1,2,1,2] => [2,2,2,1,1,1,1] => 1244
[2,1,1,1,2,2,1] => [2,2,2,1,1,1,1] => 1244
[2,1,1,1,2,3] => [3,2,2,1,1,1] => 460
[2,1,1,1,3,1,1] => [3,2,1,1,1,1,1] => 868
[2,1,1,1,3,2] => [3,2,2,1,1,1] => 460
[2,1,1,1,4,1] => [4,2,1,1,1,1] => 265
[2,1,1,1,5] => [5,2,1,1,1] => 78
[2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => 2412
[2,1,1,2,1,1,2] => [2,2,2,1,1,1,1] => 1244
[2,1,1,2,1,2,1] => [2,2,2,1,1,1,1] => 1244
[2,1,1,2,1,3] => [3,2,2,1,1,1] => 460
[2,1,1,2,2,1,1] => [2,2,2,1,1,1,1] => 1244
[2,1,1,2,2,2] => [2,2,2,2,1,1] => 652
[2,1,1,2,3,1] => [3,2,2,1,1,1] => 460
[2,1,1,2,4] => [4,2,2,1,1] => 145
[2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => 868
[2,1,1,3,1,2] => [3,2,2,1,1,1] => 460
[2,1,1,3,2,1] => [3,2,2,1,1,1] => 460
[2,1,1,3,3] => [3,3,2,1,1] => 180
[2,1,1,4,1,1] => [4,2,1,1,1,1] => 265
[2,1,1,4,2] => [4,2,2,1,1] => 145
[2,1,1,5,1] => [5,2,1,1,1] => 78
[2,1,1,6] => [6,2,1,1] => 24
[2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 2412
[2,1,2,1,1,1,2] => [2,2,2,1,1,1,1] => 1244
[2,1,2,1,1,2,1] => [2,2,2,1,1,1,1] => 1244
[2,1,2,1,1,3] => [3,2,2,1,1,1] => 460
[2,1,2,1,2,1,1] => [2,2,2,1,1,1,1] => 1244
[2,1,2,1,2,2] => [2,2,2,2,1,1] => 652
[2,1,2,1,3,1] => [3,2,2,1,1,1] => 460
[2,1,2,1,4] => [4,2,2,1,1] => 145
[2,1,2,2,1,1,1] => [2,2,2,1,1,1,1] => 1244
[2,1,2,2,1,2] => [2,2,2,2,1,1] => 652
[2,1,2,2,2,1] => [2,2,2,2,1,1] => 652
[2,1,2,2,3] => [3,2,2,2,1] => 248
[2,1,2,3,1,1] => [3,2,2,1,1,1] => 460
[2,1,2,3,2] => [3,2,2,2,1] => 248
[2,1,2,4,1] => [4,2,2,1,1] => 145
[2,1,2,5] => [5,2,2,1] => 44
[2,1,3,1,1,1,1] => [3,2,1,1,1,1,1] => 868
[2,1,3,1,1,2] => [3,2,2,1,1,1] => 460
[2,1,3,1,2,1] => [3,2,2,1,1,1] => 460
[2,1,3,1,3] => [3,3,2,1,1] => 180
[2,1,3,2,1,1] => [3,2,2,1,1,1] => 460
[2,1,3,2,2] => [3,2,2,2,1] => 248
[2,1,3,3,1] => [3,3,2,1,1] => 180
[2,1,3,4] => [4,3,2,1] => 61
[2,1,4,1,1,1] => [4,2,1,1,1,1] => 265
[2,1,4,1,2] => [4,2,2,1,1] => 145
[2,1,4,2,1] => [4,2,2,1,1] => 145
[2,1,4,3] => [4,3,2,1] => 61
[2,1,5,1,1] => [5,2,1,1,1] => 78
[2,1,5,2] => [5,2,2,1] => 44
[2,1,6,1] => [6,2,1,1] => 24
[2,1,7] => [7,2,1] => 8
[2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => 2412
[2,2,1,1,1,1,2] => [2,2,2,1,1,1,1] => 1244
[2,2,1,1,1,2,1] => [2,2,2,1,1,1,1] => 1244
[2,2,1,1,1,3] => [3,2,2,1,1,1] => 460
[2,2,1,1,2,1,1] => [2,2,2,1,1,1,1] => 1244
[2,2,1,1,2,2] => [2,2,2,2,1,1] => 652
[2,2,1,1,3,1] => [3,2,2,1,1,1] => 460
[2,2,1,1,4] => [4,2,2,1,1] => 145
[2,2,1,2,1,1,1] => [2,2,2,1,1,1,1] => 1244
[2,2,1,2,1,2] => [2,2,2,2,1,1] => 652
[2,2,1,2,2,1] => [2,2,2,2,1,1] => 652
[2,2,1,2,3] => [3,2,2,2,1] => 248
[2,2,1,3,1,1] => [3,2,2,1,1,1] => 460
[2,2,1,3,2] => [3,2,2,2,1] => 248
[2,2,1,4,1] => [4,2,2,1,1] => 145
[2,2,1,5] => [5,2,2,1] => 44
[2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => 1244
[2,2,2,1,1,2] => [2,2,2,2,1,1] => 652
[2,2,2,1,2,1] => [2,2,2,2,1,1] => 652
[2,2,2,1,3] => [3,2,2,2,1] => 248
[2,2,2,2,1,1] => [2,2,2,2,1,1] => 652
[2,2,2,2,2] => [2,2,2,2,2] => 348
[2,2,2,3,1] => [3,2,2,2,1] => 248
[2,2,2,4] => [4,2,2,2] => 81
[2,2,3,1,1,1] => [3,2,2,1,1,1] => 460
[2,2,3,1,2] => [3,2,2,2,1] => 248
[2,2,3,2,1] => [3,2,2,2,1] => 248
[2,2,3,3] => [3,3,2,2] => 100
[2,2,4,1,1] => [4,2,2,1,1] => 145
[2,2,4,2] => [4,2,2,2] => 81
[2,2,5,1] => [5,2,2,1] => 44
[2,2,6] => [6,2,2] => 14
[2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => 868
[2,3,1,1,1,2] => [3,2,2,1,1,1] => 460
[2,3,1,1,2,1] => [3,2,2,1,1,1] => 460
[2,3,1,1,3] => [3,3,2,1,1] => 180
[2,3,1,2,1,1] => [3,2,2,1,1,1] => 460
[2,3,1,2,2] => [3,2,2,2,1] => 248
[2,3,1,3,1] => [3,3,2,1,1] => 180
[2,3,1,4] => [4,3,2,1] => 61
[2,3,2,1,1,1] => [3,2,2,1,1,1] => 460
[2,3,2,1,2] => [3,2,2,2,1] => 248
[2,3,2,2,1] => [3,2,2,2,1] => 248
[2,3,2,3] => [3,3,2,2] => 100
[2,3,3,1,1] => [3,3,2,1,1] => 180
[2,3,3,2] => [3,3,2,2] => 100
[2,3,4,1] => [4,3,2,1] => 61
[2,3,5] => [5,3,2] => 20
[2,4,1,1,1,1] => [4,2,1,1,1,1] => 265
[2,4,1,1,2] => [4,2,2,1,1] => 145
[2,4,1,2,1] => [4,2,2,1,1] => 145
[2,4,1,3] => [4,3,2,1] => 61
[2,4,2,1,1] => [4,2,2,1,1] => 145
[2,4,2,2] => [4,2,2,2] => 81
[2,4,3,1] => [4,3,2,1] => 61
[2,4,4] => [4,4,2] => 23
[2,5,1,1,1] => [5,2,1,1,1] => 78
[2,5,1,2] => [5,2,2,1] => 44
[2,5,2,1] => [5,2,2,1] => 44
[2,5,3] => [5,3,2] => 20
[2,6,1,1] => [6,2,1,1] => 24
[2,6,2] => [6,2,2] => 14
[2,7,1] => [7,2,1] => 8
[2,8] => [8,2] => 3
[3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => 1660
[3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => 868
[3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => 868
[3,1,1,1,1,3] => [3,3,1,1,1,1] => 332
[3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => 868
[3,1,1,1,2,2] => [3,2,2,1,1,1] => 460
[3,1,1,1,3,1] => [3,3,1,1,1,1] => 332
[3,1,1,1,4] => [4,3,1,1,1] => 109
[3,1,1,2,1,1,1] => [3,2,1,1,1,1,1] => 868
[3,1,1,2,1,2] => [3,2,2,1,1,1] => 460
[3,1,1,2,2,1] => [3,2,2,1,1,1] => 460
[3,1,1,2,3] => [3,3,2,1,1] => 180
[3,1,1,3,1,1] => [3,3,1,1,1,1] => 332
[3,1,1,3,2] => [3,3,2,1,1] => 180
[3,1,1,4,1] => [4,3,1,1,1] => 109
[3,1,1,5] => [5,3,1,1] => 34
[3,1,2,1,1,1,1] => [3,2,1,1,1,1,1] => 868
[3,1,2,1,1,2] => [3,2,2,1,1,1] => 460
[3,1,2,1,2,1] => [3,2,2,1,1,1] => 460
[3,1,2,1,3] => [3,3,2,1,1] => 180
[3,1,2,2,1,1] => [3,2,2,1,1,1] => 460
[3,1,2,2,2] => [3,2,2,2,1] => 248
[3,1,2,3,1] => [3,3,2,1,1] => 180
[3,1,2,4] => [4,3,2,1] => 61
[3,1,3,1,1,1] => [3,3,1,1,1,1] => 332
[3,1,3,1,2] => [3,3,2,1,1] => 180
[3,1,3,2,1] => [3,3,2,1,1] => 180
[3,1,3,3] => [3,3,3,1] => 74
[3,1,4,1,1] => [4,3,1,1,1] => 109
[3,1,4,2] => [4,3,2,1] => 61
[3,1,5,1] => [5,3,1,1] => 34
[3,1,6] => [6,3,1] => 11
[3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => 868
[3,2,1,1,1,2] => [3,2,2,1,1,1] => 460
[3,2,1,1,2,1] => [3,2,2,1,1,1] => 460
[3,2,1,1,3] => [3,3,2,1,1] => 180
[3,2,1,2,1,1] => [3,2,2,1,1,1] => 460
[3,2,1,2,2] => [3,2,2,2,1] => 248
[3,2,1,3,1] => [3,3,2,1,1] => 180
[3,2,1,4] => [4,3,2,1] => 61
[3,2,2,1,1,1] => [3,2,2,1,1,1] => 460
[3,2,2,1,2] => [3,2,2,2,1] => 248
[3,2,2,2,1] => [3,2,2,2,1] => 248
[3,2,2,3] => [3,3,2,2] => 100
[3,2,3,1,1] => [3,3,2,1,1] => 180
[3,2,3,2] => [3,3,2,2] => 100
[3,2,4,1] => [4,3,2,1] => 61
[3,2,5] => [5,3,2] => 20
[3,3,1,1,1,1] => [3,3,1,1,1,1] => 332
[3,3,1,1,2] => [3,3,2,1,1] => 180
[3,3,1,2,1] => [3,3,2,1,1] => 180
[3,3,1,3] => [3,3,3,1] => 74
[3,3,2,1,1] => [3,3,2,1,1] => 180
[3,3,2,2] => [3,3,2,2] => 100
[3,3,3,1] => [3,3,3,1] => 74
[3,3,4] => [4,3,3] => 27
[3,4,1,1,1] => [4,3,1,1,1] => 109
[3,4,1,2] => [4,3,2,1] => 61
[3,4,2,1] => [4,3,2,1] => 61
[3,4,3] => [4,3,3] => 27
[3,5,1,1] => [5,3,1,1] => 34
[3,5,2] => [5,3,2] => 20
[3,6,1] => [6,3,1] => 11
[3,7] => [7,3] => 4
[4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => 492
[4,1,1,1,1,2] => [4,2,1,1,1,1] => 265
[4,1,1,1,2,1] => [4,2,1,1,1,1] => 265
[4,1,1,1,3] => [4,3,1,1,1] => 109
[4,1,1,2,1,1] => [4,2,1,1,1,1] => 265
[4,1,1,2,2] => [4,2,2,1,1] => 145
[4,1,1,3,1] => [4,3,1,1,1] => 109
[4,1,1,4] => [4,4,1,1] => 40
[4,1,2,1,1,1] => [4,2,1,1,1,1] => 265
[4,1,2,1,2] => [4,2,2,1,1] => 145
[4,1,2,2,1] => [4,2,2,1,1] => 145
[4,1,2,3] => [4,3,2,1] => 61
[4,1,3,1,1] => [4,3,1,1,1] => 109
[4,1,3,2] => [4,3,2,1] => 61
[4,1,4,1] => [4,4,1,1] => 40
[4,1,5] => [5,4,1] => 14
[4,2,1,1,1,1] => [4,2,1,1,1,1] => 265
[4,2,1,1,2] => [4,2,2,1,1] => 145
[4,2,1,2,1] => [4,2,2,1,1] => 145
[4,2,1,3] => [4,3,2,1] => 61
[4,2,2,1,1] => [4,2,2,1,1] => 145
[4,2,2,2] => [4,2,2,2] => 81
[4,2,3,1] => [4,3,2,1] => 61
[4,2,4] => [4,4,2] => 23
[4,3,1,1,1] => [4,3,1,1,1] => 109
[4,3,1,2] => [4,3,2,1] => 61
[4,3,2,1] => [4,3,2,1] => 61
[4,3,3] => [4,3,3] => 27
[4,4,1,1] => [4,4,1,1] => 40
[4,4,2] => [4,4,2] => 23
[4,5,1] => [5,4,1] => 14
[4,6] => [6,4] => 5
[5,1,1,1,1,1] => [5,1,1,1,1,1] => 142
[5,1,1,1,2] => [5,2,1,1,1] => 78
[5,1,1,2,1] => [5,2,1,1,1] => 78
[5,1,1,3] => [5,3,1,1] => 34
[5,1,2,1,1] => [5,2,1,1,1] => 78
[5,1,2,2] => [5,2,2,1] => 44
[5,1,3,1] => [5,3,1,1] => 34
[5,1,4] => [5,4,1] => 14
[5,2,1,1,1] => [5,2,1,1,1] => 78
[5,2,1,2] => [5,2,2,1] => 44
[5,2,2,1] => [5,2,2,1] => 44
[5,2,3] => [5,3,2] => 20
[5,3,1,1] => [5,3,1,1] => 34
[5,3,2] => [5,3,2] => 20
[5,4,1] => [5,4,1] => 14
[5,5] => [5,5] => 6
[6,1,1,1,1] => [6,1,1,1,1] => 43
[6,1,1,2] => [6,2,1,1] => 24
[6,1,2,1] => [6,2,1,1] => 24
[6,1,3] => [6,3,1] => 11
[6,2,1,1] => [6,2,1,1] => 24
[6,2,2] => [6,2,2] => 14
[6,3,1] => [6,3,1] => 11
[6,4] => [6,4] => 5
[7,1,1,1] => [7,1,1,1] => 14
[7,1,2] => [7,2,1] => 8
[7,2,1] => [7,2,1] => 8
[7,3] => [7,3] => 4
[8,1,1] => [8,1,1] => 5
[8,2] => [8,2] => 3
[9,1] => [9,1] => 2
[10] => [10] => 1
[1,10] => [10,1] => 2
[1,8,1,1] => [8,1,1,1] => 14
[1,7,2,1] => [7,2,1,1] => 24
[1,6,3,1] => [6,3,1,1] => 34
[1,5,4,1] => [5,4,1,1] => 43
[1,4,5,1] => [5,4,1,1] => 43
[1,3,6,1] => [6,3,1,1] => 34
[1,2,7,1] => [7,2,1,1] => 24
[1,1,8,1] => [8,1,1,1] => 14
[10,1] => [10,1] => 2
[1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1] => 140152
[1,1,1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,1,1,1,1,3,3] => [3,3,1,1,1,1,1,1] => 4600
[1,1,1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,1,1,2,2,2,2] => [2,2,2,2,1,1,1,1] => 9340
[1,1,1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,1,1,2,1,2,3] => [3,2,2,1,1,1,1,1] => 6508
[1,1,1,1,3,3,1,1] => [3,3,1,1,1,1,1,1] => 4600
[1,1,1,1,3,2,1,2] => [3,2,2,1,1,1,1,1] => 6508
[1,1,1,1,3,1,1,3] => [3,3,1,1,1,1,1,1] => 4600
[1,1,1,1,4,4] => [4,4,1,1,1,1] => 470
[1,1,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,2,2,1,1,2,2] => [2,2,2,2,1,1,1,1] => 9340
[1,1,2,2,2,2,1,1] => [2,2,2,2,1,1,1,1] => 9340
[1,1,2,2,2,1,1,2] => [2,2,2,2,1,1,1,1] => 9340
[1,1,2,2,3,3] => [3,3,2,2,1,1] => 1306
[1,1,2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,2,1,1,2,2,2] => [2,2,2,2,1,1,1,1] => 9340
[1,1,2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,2,1,1,1,2,3] => [3,2,2,1,1,1,1,1] => 6508
[1,1,2,1,2,3,1,1] => [3,2,2,1,1,1,1,1] => 6508
[1,1,2,1,2,2,1,2] => [2,2,2,2,1,1,1,1] => 9340
[1,1,2,1,2,1,1,3] => [3,2,2,1,1,1,1,1] => 6508
[1,1,2,1,3,4] => [4,3,2,1,1,1] => 765
[1,1,3,3,1,1,1,1] => [3,3,1,1,1,1,1,1] => 4600
[1,1,3,3,2,2] => [3,3,2,2,1,1] => 1306
[1,1,3,2,1,2,1,1] => [3,2,2,1,1,1,1,1] => 6508
[1,1,3,2,1,1,1,2] => [3,2,2,1,1,1,1,1] => 6508
[1,1,3,2,2,3] => [3,3,2,2,1,1] => 1306
[1,1,3,1,1,3,1,1] => [3,3,1,1,1,1,1,1] => 4600
[1,1,3,1,1,2,1,2] => [3,2,2,1,1,1,1,1] => 6508
[1,1,3,1,1,1,1,3] => [3,3,1,1,1,1,1,1] => 4600
[1,1,3,1,2,4] => [4,3,2,1,1,1] => 765
[1,1,4,4,1,1] => [4,4,1,1,1,1] => 470
[1,1,4,3,1,2] => [4,3,2,1,1,1] => 765
[1,1,4,2,1,3] => [4,3,2,1,1,1] => 765
[1,1,4,1,1,4] => [4,4,1,1,1,1] => 470
[1,1,5,5] => [5,5,1,1] => 50
[2,2,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[2,2,1,1,1,1,2,2] => [2,2,2,2,1,1,1,1] => 9340
[2,2,1,1,2,2,1,1] => [2,2,2,2,1,1,1,1] => 9340
[2,2,1,1,2,1,1,2] => [2,2,2,2,1,1,1,1] => 9340
[2,2,1,1,3,3] => [3,3,2,2,1,1] => 1306
[2,2,2,2,1,1,1,1] => [2,2,2,2,1,1,1,1] => 9340
[2,2,2,2,2,2] => [2,2,2,2,2,2] => 2578
[2,2,2,1,1,2,1,1] => [2,2,2,2,1,1,1,1] => 9340
[2,2,2,1,1,1,1,2] => [2,2,2,2,1,1,1,1] => 9340
[2,2,2,1,2,3] => [3,2,2,2,2,1] => 1824
[2,2,3,3,1,1] => [3,3,2,2,1,1] => 1306
[2,2,3,2,1,2] => [3,2,2,2,2,1] => 1824
[2,2,3,1,1,3] => [3,3,2,2,1,1] => 1306
[2,2,4,4] => [4,4,2,2] => 146
[2,1,1,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[2,1,1,2,1,1,2,2] => [2,2,2,2,1,1,1,1] => 9340
[2,1,1,2,2,2,1,1] => [2,2,2,2,1,1,1,1] => 9340
[2,1,1,2,2,1,1,2] => [2,2,2,2,1,1,1,1] => 9340
[2,1,1,2,3,3] => [3,3,2,2,1,1] => 1306
[2,1,1,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[2,1,1,1,1,2,2,2] => [2,2,2,2,1,1,1,1] => 9340
[2,1,1,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[2,1,1,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 35420
[2,1,1,1,1,1,2,3] => [3,2,2,1,1,1,1,1] => 6508
[2,1,1,1,2,3,1,1] => [3,2,2,1,1,1,1,1] => 6508
[2,1,1,1,2,2,1,2] => [2,2,2,2,1,1,1,1] => 9340
[2,1,1,1,2,1,1,3] => [3,2,2,1,1,1,1,1] => 6508
[2,1,1,1,3,4] => [4,3,2,1,1,1] => 765
[2,1,2,3,1,1,1,1] => [3,2,2,1,1,1,1,1] => 6508
[2,1,2,3,2,2] => [3,2,2,2,2,1] => 1824
[2,1,2,2,1,2,1,1] => [2,2,2,2,1,1,1,1] => 9340
[2,1,2,2,1,1,1,2] => [2,2,2,2,1,1,1,1] => 9340
[2,1,2,2,2,3] => [3,2,2,2,2,1] => 1824
[2,1,2,1,1,3,1,1] => [3,2,2,1,1,1,1,1] => 6508
[2,1,2,1,1,2,1,2] => [2,2,2,2,1,1,1,1] => 9340
[2,1,2,1,1,1,1,3] => [3,2,2,1,1,1,1,1] => 6508
[2,1,2,1,2,4] => [4,2,2,2,1,1] => 1046
[2,1,3,4,1,1] => [4,3,2,1,1,1] => 765
[2,1,3,3,1,2] => [3,3,2,2,1,1] => 1306
[2,1,3,2,1,3] => [3,3,2,2,1,1] => 1306
[2,1,3,1,1,4] => [4,3,2,1,1,1] => 765
[2,1,4,5] => [5,4,2,1] => 82
[3,3,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1] => 4600
[3,3,1,1,2,2] => [3,3,2,2,1,1] => 1306
[3,3,2,2,1,1] => [3,3,2,2,1,1] => 1306
[3,3,2,1,1,2] => [3,3,2,2,1,1] => 1306
[3,3,3,3] => [3,3,3,3] => 214
[3,2,1,2,1,1,1,1] => [3,2,2,1,1,1,1,1] => 6508
[3,2,1,2,2,2] => [3,2,2,2,2,1] => 1824
[3,2,1,1,1,2,1,1] => [3,2,2,1,1,1,1,1] => 6508
[3,2,1,1,1,1,1,2] => [3,2,2,1,1,1,1,1] => 6508
[3,2,1,1,2,3] => [3,3,2,2,1,1] => 1306
[3,2,2,3,1,1] => [3,3,2,2,1,1] => 1306
[3,2,2,2,1,2] => [3,2,2,2,2,1] => 1824
[3,2,2,1,1,3] => [3,3,2,2,1,1] => 1306
[3,2,3,4] => [4,3,3,2] => 175
[3,1,1,3,1,1,1,1] => [3,3,1,1,1,1,1,1] => 4600
[3,1,1,3,2,2] => [3,3,2,2,1,1] => 1306
[3,1,1,2,1,2,1,1] => [3,2,2,1,1,1,1,1] => 6508
[3,1,1,2,1,1,1,2] => [3,2,2,1,1,1,1,1] => 6508
[3,1,1,2,2,3] => [3,3,2,2,1,1] => 1306
[3,1,1,1,1,3,1,1] => [3,3,1,1,1,1,1,1] => 4600
[3,1,1,1,1,2,1,2] => [3,2,2,1,1,1,1,1] => 6508
[3,1,1,1,1,1,1,3] => [3,3,1,1,1,1,1,1] => 4600
[3,1,1,1,2,4] => [4,3,2,1,1,1] => 765
[3,1,2,4,1,1] => [4,3,2,1,1,1] => 765
[3,1,2,3,1,2] => [3,3,2,2,1,1] => 1306
[3,1,2,2,1,3] => [3,3,2,2,1,1] => 1306
[3,1,2,1,1,4] => [4,3,2,1,1,1] => 765
[3,1,3,5] => [5,3,3,1] => 96
[4,4,1,1,1,1] => [4,4,1,1,1,1] => 470
[4,4,2,2] => [4,4,2,2] => 146
[4,3,1,2,1,1] => [4,3,2,1,1,1] => 765
[4,3,1,1,1,2] => [4,3,2,1,1,1] => 765
[4,3,2,3] => [4,3,3,2] => 175
[4,2,1,3,1,1] => [4,3,2,1,1,1] => 765
[4,2,1,2,1,2] => [4,2,2,2,1,1] => 1046
[4,2,1,1,1,3] => [4,3,2,1,1,1] => 765
[4,2,2,4] => [4,4,2,2] => 146
[4,1,1,4,1,1] => [4,4,1,1,1,1] => 470
[4,1,1,3,1,2] => [4,3,2,1,1,1] => 765
[4,1,1,2,1,3] => [4,3,2,1,1,1] => 765
[4,1,1,1,1,4] => [4,4,1,1,1,1] => 470
[4,1,2,5] => [5,4,2,1] => 82
[5,5,1,1] => [5,5,1,1] => 50
[5,4,1,2] => [5,4,2,1] => 82
[5,3,1,3] => [5,3,3,1] => 96
[5,2,1,4] => [5,4,2,1] => 82
[5,1,1,5] => [5,5,1,1] => 50
[6,6] => [6,6] => 7
[1,2,2,2,2,2,1] => [2,2,2,2,2,1,1] => 4876
[1,2,2,2,3,2] => [3,2,2,2,2,1] => 1824
[1,2,2,3,3,1] => [3,3,2,2,1,1] => 1306
[1,2,2,3,2,2] => [3,2,2,2,2,1] => 1824
[1,2,2,4,3] => [4,3,2,2,1] => 420
[1,2,3,3,2,1] => [3,3,2,2,1,1] => 1306
[1,2,3,4,2] => [4,3,2,2,1] => 420
[1,2,3,2,3,1] => [3,3,2,2,1,1] => 1306
[1,2,3,2,2,2] => [3,2,2,2,2,1] => 1824
[1,2,3,3,3] => [3,3,3,2,1] => 517
[1,2,4,4,1] => [4,4,2,1,1] => 259
[1,2,4,3,2] => [4,3,2,2,1] => 420
[1,2,4,2,3] => [4,3,2,2,1] => 420
[1,2,5,4] => [5,4,2,1] => 82
[1,3,3,2,2,1] => [3,3,2,2,1,1] => 1306
[1,3,3,3,2] => [3,3,3,2,1] => 517
[1,3,4,3,1] => [4,3,3,1,1] => 311
[1,3,4,2,2] => [4,3,2,2,1] => 420
[1,3,5,3] => [5,3,3,1] => 96
[1,3,2,3,2,1] => [3,3,2,2,1,1] => 1306
[1,3,2,4,2] => [4,3,2,2,1] => 420
[1,3,2,2,3,1] => [3,3,2,2,1,1] => 1306
[1,3,2,2,2,2] => [3,2,2,2,2,1] => 1824
[1,3,2,3,3] => [3,3,3,2,1] => 517
[1,3,3,4,1] => [4,3,3,1,1] => 311
[1,3,3,2,3] => [3,3,3,2,1] => 517
[1,3,4,4] => [4,4,3,1] => 110
[1,4,4,2,1] => [4,4,2,1,1] => 259
[1,4,5,2] => [5,4,2,1] => 82
[1,4,3,3,1] => [4,3,3,1,1] => 311
[1,4,3,2,2] => [4,3,2,2,1] => 420
[1,4,4,3] => [4,4,3,1] => 110
[1,4,2,4,1] => [4,4,2,1,1] => 259
[1,4,2,3,2] => [4,3,2,2,1] => 420
[1,4,2,2,3] => [4,3,2,2,1] => 420
[1,4,3,4] => [4,4,3,1] => 110
[1,5,5,1] => [5,5,1,1] => 50
[1,5,4,2] => [5,4,2,1] => 82
[1,5,3,3] => [5,3,3,1] => 96
[1,5,2,4] => [5,4,2,1] => 82
[1,6,5] => [6,5,1] => 17
[2,3,2,2,2,1] => [3,2,2,2,2,1] => 1824
[2,3,2,3,2] => [3,3,2,2,2] => 710
[2,3,3,3,1] => [3,3,3,2,1] => 517
[2,3,3,2,2] => [3,3,2,2,2] => 710
[2,3,4,3] => [4,3,3,2] => 175
[2,4,3,2,1] => [4,3,2,2,1] => 420
[2,4,4,2] => [4,4,2,2] => 146
[2,4,2,3,1] => [4,3,2,2,1] => 420
[2,4,2,2,2] => [4,2,2,2,2] => 572
[2,4,3,3] => [4,3,3,2] => 175
[2,5,4,1] => [5,4,2,1] => 82
[2,5,3,2] => [5,3,2,2] => 126
[2,5,2,3] => [5,3,2,2] => 126
[2,6,4] => [6,4,2] => 26
[2,2,3,2,2,1] => [3,2,2,2,2,1] => 1824
[2,2,3,3,2] => [3,3,2,2,2] => 710
[2,2,4,3,1] => [4,3,2,2,1] => 420
[2,2,4,2,2] => [4,2,2,2,2] => 572
[2,2,5,3] => [5,3,2,2] => 126
[2,2,2,3,2,1] => [3,2,2,2,2,1] => 1824
[2,2,2,4,2] => [4,2,2,2,2] => 572
[2,2,2,2,3,1] => [3,2,2,2,2,1] => 1824
[2,2,2,3,3] => [3,3,2,2,2] => 710
[2,2,3,4,1] => [4,3,2,2,1] => 420
[2,2,3,2,3] => [3,3,2,2,2] => 710
[2,3,4,2,1] => [4,3,2,2,1] => 420
[2,3,5,2] => [5,3,2,2] => 126
[2,3,2,4,1] => [4,3,2,2,1] => 420
[2,3,2,2,3] => [3,3,2,2,2] => 710
[2,3,3,4] => [4,3,3,2] => 175
[2,4,5,1] => [5,4,2,1] => 82
[2,4,2,4] => [4,4,2,2] => 146
[2,5,5] => [5,5,2] => 29
[3,4,2,2,1] => [4,3,2,2,1] => 420
[3,4,3,2] => [4,3,3,2] => 175
[3,5,3,1] => [5,3,3,1] => 96
[3,5,2,2] => [5,3,2,2] => 126
[3,6,3] => [6,3,3] => 30
[3,3,3,2,1] => [3,3,3,2,1] => 517
[3,3,4,2] => [4,3,3,2] => 175
[3,3,2,3,1] => [3,3,3,2,1] => 517
[3,3,2,2,2] => [3,3,2,2,2] => 710
[3,4,4,1] => [4,4,3,1] => 110
[3,4,2,3] => [4,3,3,2] => 175
[3,5,4] => [5,4,3] => 37
[3,2,4,2,1] => [4,3,2,2,1] => 420
[3,2,5,2] => [5,3,2,2] => 126
[3,2,3,3,1] => [3,3,3,2,1] => 517
[3,2,3,2,2] => [3,3,2,2,2] => 710
[3,2,4,3] => [4,3,3,2] => 175
[3,2,2,4,1] => [4,3,2,2,1] => 420
[3,2,2,3,2] => [3,3,2,2,2] => 710
[3,2,2,2,3] => [3,3,2,2,2] => 710
[3,3,5,1] => [5,3,3,1] => 96
[3,3,2,4] => [4,3,3,2] => 175
[3,4,5] => [5,4,3] => 37
[4,5,2,1] => [5,4,2,1] => 82
[4,6,2] => [6,4,2] => 26
[4,4,3,1] => [4,4,3,1] => 110
[4,5,3] => [5,4,3] => 37
[4,3,4,1] => [4,4,3,1] => 110
[4,3,3,2] => [4,3,3,2] => 175
[4,4,4] => [4,4,4] => 42
[4,2,5,1] => [5,4,2,1] => 82
[4,2,4,2] => [4,4,2,2] => 146
[4,2,3,3] => [4,3,3,2] => 175
[4,3,5] => [5,4,3] => 37
[5,6,1] => [6,5,1] => 17
[5,5,2] => [5,5,2] => 29
[5,4,3] => [5,4,3] => 37
[5,3,4] => [5,4,3] => 37
[5,2,5] => [5,5,2] => 29
[1,8,2] => [8,2,1] => 8
[1,7,1,2] => [7,2,1,1] => 24
[1,6,1,1,2] => [6,2,1,1,1] => 78
[1,5,1,1,1,2] => [5,2,1,1,1,1] => 270
[1,4,1,1,1,1,2] => [4,2,1,1,1,1,1] => 958
[1,3,1,1,1,1,1,2] => [3,2,1,1,1,1,1,1] => 3218
[1,2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1] => 9040
[1,1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1,1] => 17848
[1,11] => [11,1] => 2
[1,9,2] => [9,2,1] => 8
[1,7,3] => [7,3,1] => 11
[1,8,1,2] => [8,2,1,1] => 24
[1,6,2,2] => [6,2,2,1] => 44
[1,7,1,1,2] => [7,2,1,1,1] => 78
[1,5,2,1,2] => [5,2,2,1,1] => 149
[1,6,1,1,1,2] => [6,2,1,1,1,1] => 271
[1,4,2,1,1,2] => [4,2,2,1,1,1] => 516
[1,5,1,1,1,1,2] => [5,2,1,1,1,1,1] => 989
[1,3,2,1,1,1,2] => [3,2,2,1,1,1,1] => 1688
[1,4,1,1,1,1,1,2] => [4,2,1,1,1,1,1,1] => 3643
[1,2,2,1,1,1,1,2] => [2,2,2,1,1,1,1,1] => 4636
[1,3,1,1,1,1,1,1,2] => [3,2,1,1,1,1,1,1,1] => 12498
[1,1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1] => 9040
[1,2,1,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1,1,1] => 70076
[1,2,2,2,2,2] => [2,2,2,2,2,1] => 1268
[1,2,2,2,1,3] => [3,2,2,2,1,1] => 897
[1,2,2,1,3,2] => [3,2,2,2,1,1] => 897
[1,2,2,1,2,3] => [3,2,2,2,1,1] => 897
[1,2,2,1,1,4] => [4,2,2,1,1,1] => 516
[1,2,1,3,2,2] => [3,2,2,2,1,1] => 897
[1,2,1,3,1,3] => [3,3,2,1,1,1] => 644
[1,2,1,2,3,2] => [3,2,2,2,1,1] => 897
[1,2,1,2,2,3] => [3,2,2,2,1,1] => 897
[1,2,1,2,1,4] => [4,2,2,1,1,1] => 516
[1,2,1,1,4,2] => [4,2,2,1,1,1] => 516
[1,2,1,1,3,3] => [3,3,2,1,1,1] => 644
[1,2,1,1,2,4] => [4,2,2,1,1,1] => 516
[1,2,1,1,1,5] => [5,2,1,1,1,1] => 270
[1,1,3,2,2,2] => [3,2,2,2,1,1] => 897
[1,1,3,2,1,3] => [3,3,2,1,1,1] => 644
[1,1,3,1,3,2] => [3,3,2,1,1,1] => 644
[1,1,3,1,2,3] => [3,3,2,1,1,1] => 644
[1,1,3,1,1,4] => [4,3,1,1,1,1] => 381
[1,1,2,3,2,2] => [3,2,2,2,1,1] => 897
[1,1,2,3,1,3] => [3,3,2,1,1,1] => 644
[1,1,2,2,3,2] => [3,2,2,2,1,1] => 897
[1,1,2,2,2,3] => [3,2,2,2,1,1] => 897
[1,1,2,2,1,4] => [4,2,2,1,1,1] => 516
[1,1,2,1,4,2] => [4,2,2,1,1,1] => 516
[1,1,2,1,3,3] => [3,3,2,1,1,1] => 644
[1,1,2,1,2,4] => [4,2,2,1,1,1] => 516
[1,1,2,1,1,5] => [5,2,1,1,1,1] => 270
[1,1,1,4,2,2] => [4,2,2,1,1,1] => 516
[1,1,1,4,1,3] => [4,3,1,1,1,1] => 381
[1,1,1,3,3,2] => [3,3,2,1,1,1] => 644
[1,1,1,3,2,3] => [3,3,2,1,1,1] => 644
[1,1,1,3,1,4] => [4,3,1,1,1,1] => 381
[1,1,1,2,4,2] => [4,2,2,1,1,1] => 516
[1,1,1,2,3,3] => [3,3,2,1,1,1] => 644
[1,1,1,2,2,4] => [4,2,2,1,1,1] => 516
[1,1,1,2,1,5] => [5,2,1,1,1,1] => 270
[1,1,1,1,5,2] => [5,2,1,1,1,1] => 270
[1,1,1,1,4,3] => [4,3,1,1,1,1] => 381
[1,1,1,1,3,4] => [4,3,1,1,1,1] => 381
[1,1,1,1,2,5] => [5,2,1,1,1,1] => 270
[1,1,1,1,1,6] => [6,1,1,1,1,1] => 142
[12] => [12] => 1
[1,2,9] => [9,2,1] => 8
[3,2,7] => [7,3,2] => 20
[1,4,7] => [7,4,1] => 14
[1,1,2,1,7] => [7,2,1,1,1] => 78
[1,2,2,2,5] => [5,2,2,2,1] => 297
[1,1,2,3,5] => [5,3,2,1,1] => 223
[3,1,2,1,5] => [5,3,2,1,1] => 223
[1,3,2,1,5] => [5,3,2,1,1] => 223
[1,1,4,1,5] => [5,4,1,1,1] => 145
[1,1,1,2,1,1,5] => [5,2,1,1,1,1,1] => 989
[7,2,3] => [7,3,2] => 20
[1,1,2,1,2,2,3] => [3,2,2,2,1,1,1] => 3425
[1,8,3] => [8,3,1] => 11
[1,1,2,5,3] => [5,3,2,1,1] => 223
[3,1,2,3,3] => [3,3,3,2,1] => 517
[1,1,4,3,3] => [4,3,3,1,1] => 311
[1,1,1,2,1,3,3] => [3,3,2,1,1,1,1] => 2436
[5,1,2,1,3] => [5,3,2,1,1] => 223
[1,2,2,1,2,1,3] => [3,2,2,2,1,1,1] => 3425
[3,3,2,1,3] => [3,3,3,2,1] => 517
[1,5,2,1,3] => [5,3,2,1,1] => 223
[1,1,2,2,2,1,3] => [3,2,2,2,1,1,1] => 3425
[3,1,4,1,3] => [4,3,3,1,1] => 311
[1,3,4,1,3] => [4,3,3,1,1] => 311
[1,1,6,1,3] => [6,3,1,1,1] => 114
[1,1,1,2,3,1,3] => [3,3,2,1,1,1,1] => 2436
[3,1,1,2,1,1,3] => [3,3,2,1,1,1,1] => 2436
[1,3,1,2,1,1,3] => [3,3,2,1,1,1,1] => 2436
[1,1,3,2,1,1,3] => [3,3,2,1,1,1,1] => 2436
[1,1,1,4,1,1,3] => [4,3,1,1,1,1,1] => 1414
[1,1,1,1,2,1,1,1,3] => [3,2,1,1,1,1,1,1,1] => 12498
[9,2,1] => [9,2,1] => 8
[1,2,6,2,1] => [6,2,2,1,1] => 150
[1,1,2,1,4,2,1] => [4,2,2,1,1,1,1] => 1941
[5,2,2,2,1] => [5,2,2,2,1] => 297
[1,6,2,2,1] => [6,2,2,1,1] => 150
[1,1,2,3,2,2,1] => [3,2,2,2,1,1,1] => 3425
[3,1,2,1,2,2,1] => [3,2,2,2,1,1,1] => 3425
[1,3,2,1,2,2,1] => [3,2,2,2,1,1,1] => 3425
[1,1,4,1,2,2,1] => [4,2,2,1,1,1,1] => 1941
[1,1,1,2,1,1,2,2,1] => [2,2,2,1,1,1,1,1,1] => 18092
[7,4,1] => [7,4,1] => 14
[1,1,2,1,2,4,1] => [4,2,2,1,1,1,1] => 1941
[1,2,2,6,1] => [6,2,2,1,1] => 150
[3,8,1] => [8,3,1] => 11
[1,10,1] => [10,1,1] => 5
[1,1,2,7,1] => [7,2,1,1,1] => 78
[3,1,2,5,1] => [5,3,2,1,1] => 223
[1,3,2,5,1] => [5,3,2,1,1] => 223
[1,1,4,5,1] => [5,4,1,1,1] => 145
[1,1,1,2,1,5,1] => [5,2,1,1,1,1,1] => 989
[5,1,2,3,1] => [5,3,2,1,1] => 223
[1,2,2,1,2,3,1] => [3,2,2,2,1,1,1] => 3425
[1,5,2,3,1] => [5,3,2,1,1] => 223
[1,1,2,2,2,3,1] => [3,2,2,2,1,1,1] => 3425
[3,1,4,3,1] => [4,3,3,1,1] => 311
[1,1,6,3,1] => [6,3,1,1,1] => 114
[1,1,1,2,3,3,1] => [3,3,2,1,1,1,1] => 2436
[3,1,1,2,1,3,1] => [3,3,2,1,1,1,1] => 2436
[1,3,1,2,1,3,1] => [3,3,2,1,1,1,1] => 2436
[1,1,3,2,1,3,1] => [3,3,2,1,1,1,1] => 2436
[1,1,1,4,1,3,1] => [4,3,1,1,1,1,1] => 1414
[1,1,1,1,2,1,1,3,1] => [3,2,1,1,1,1,1,1,1] => 12498
[7,1,2,1,1] => [7,2,1,1,1] => 78
[1,2,4,1,2,1,1] => [4,2,2,1,1,1,1] => 1941
[3,2,2,1,2,1,1] => [3,2,2,2,1,1,1] => 3425
[1,4,2,1,2,1,1] => [4,2,2,1,1,1,1] => 1941
[1,1,2,1,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[5,3,2,1,1] => [5,3,2,1,1] => 223
[1,2,2,3,2,1,1] => [3,2,2,2,1,1,1] => 3425
[3,5,2,1,1] => [5,3,2,1,1] => 223
[1,7,2,1,1] => [7,2,1,1,1] => 78
[1,1,2,4,2,1,1] => [4,2,2,1,1,1,1] => 1941
[3,1,2,2,2,1,1] => [3,2,2,2,1,1,1] => 3425
[1,3,2,2,2,1,1] => [3,2,2,2,1,1,1] => 3425
[1,1,4,2,2,1,1] => [4,2,2,1,1,1,1] => 1941
[1,1,1,2,1,2,2,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[5,1,4,1,1] => [5,4,1,1,1] => 145
[1,2,2,1,4,1,1] => [4,2,2,1,1,1,1] => 1941
[3,3,4,1,1] => [4,3,3,1,1] => 311
[1,5,4,1,1] => [5,4,1,1,1] => 145
[1,1,2,2,4,1,1] => [4,2,2,1,1,1,1] => 1941
[3,1,6,1,1] => [6,3,1,1,1] => 114
[1,3,6,1,1] => [6,3,1,1,1] => 114
[1,1,8,1,1] => [8,1,1,1,1] => 43
[1,1,1,2,5,1,1] => [5,2,1,1,1,1,1] => 989
[3,1,1,2,3,1,1] => [3,3,2,1,1,1,1] => 2436
[1,3,1,2,3,1,1] => [3,3,2,1,1,1,1] => 2436
[1,1,3,2,3,1,1] => [3,3,2,1,1,1,1] => 2436
[1,1,1,4,3,1,1] => [4,3,1,1,1,1,1] => 1414
[1,1,1,1,2,1,3,1,1] => [3,2,1,1,1,1,1,1,1] => 12498
[5,1,1,2,1,1,1] => [5,2,1,1,1,1,1] => 989
[1,2,2,1,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[3,3,1,2,1,1,1] => [3,3,2,1,1,1,1] => 2436
[1,5,1,2,1,1,1] => [5,2,1,1,1,1,1] => 989
[1,1,2,2,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[3,1,3,2,1,1,1] => [3,3,2,1,1,1,1] => 2436
[1,3,3,2,1,1,1] => [3,3,2,1,1,1,1] => 2436
[1,1,5,2,1,1,1] => [5,2,1,1,1,1,1] => 989
[1,1,1,2,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[3,1,1,4,1,1,1] => [4,3,1,1,1,1,1] => 1414
[1,3,1,4,1,1,1] => [4,3,1,1,1,1,1] => 1414
[1,1,3,4,1,1,1] => [4,3,1,1,1,1,1] => 1414
[1,1,1,6,1,1,1] => [6,1,1,1,1,1,1] => 499
[1,1,1,1,2,3,1,1,1] => [3,2,1,1,1,1,1,1,1] => 12498
[3,1,1,1,2,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => 12498
[1,3,1,1,2,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => 12498
[1,1,3,1,2,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => 12498
[1,1,1,3,2,1,1,1,1] => [3,2,1,1,1,1,1,1,1] => 12498
[1,1,1,1,4,1,1,1,1] => [4,1,1,1,1,1,1,1,1] => 6904
[1,1,1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 70076
[2,2,2,2,1,2,1] => [2,2,2,2,2,1,1] => 4876
[2,2,2,1,2,1,2] => [2,2,2,2,2,1,1] => 4876
[2,2,2,1,2,2,1] => [2,2,2,2,2,1,1] => 4876
[2,2,2,1,1,2,2] => [2,2,2,2,2,1,1] => 4876
[2,2,1,2,1,2,2] => [2,2,2,2,2,1,1] => 4876
[2,2,1,2,1,1,2,1] => [2,2,2,2,1,1,1,1] => 9340
[2,2,1,2,2,1,2] => [2,2,2,2,2,1,1] => 4876
[2,2,1,2,2,2,1] => [2,2,2,2,2,1,1] => 4876
[2,2,1,1,2,2,2] => [2,2,2,2,2,1,1] => 4876
[2,2,1,1,2,1,2,1] => [2,2,2,2,1,1,1,1] => 9340
[2,2,1,1,1,2,2,1] => [2,2,2,2,1,1,1,1] => 9340
[2,1,2,1,2,2,2] => [2,2,2,2,2,1,1] => 4876
[2,1,2,1,2,1,2,1] => [2,2,2,2,1,1,1,1] => 9340
[2,1,2,1,1,2,2,1] => [2,2,2,2,1,1,1,1] => 9340
[2,1,2,1,1,1,2,2] => [2,2,2,2,1,1,1,1] => 9340
[2,1,2,2,1,2,2] => [2,2,2,2,2,1,1] => 4876
[2,1,2,2,1,1,2,1] => [2,2,2,2,1,1,1,1] => 9340
[2,1,2,2,2,1,2] => [2,2,2,2,2,1,1] => 4876
[2,1,2,2,2,2,1] => [2,2,2,2,2,1,1] => 4876
[2,1,1,2,2,2,2] => [2,2,2,2,2,1,1] => 4876
[2,1,1,2,2,1,2,1] => [2,2,2,2,1,1,1,1] => 9340
[2,1,1,2,1,2,1,2] => [2,2,2,2,1,1,1,1] => 9340
[2,1,1,2,1,2,2,1] => [2,2,2,2,1,1,1,1] => 9340
[2,1,1,1,2,2,2,1] => [2,2,2,2,1,1,1,1] => 9340
[2,1,1,1,2,1,2,2] => [2,2,2,2,1,1,1,1] => 9340
[1,2,1,2,2,2,2] => [2,2,2,2,2,1,1] => 4876
[1,2,1,2,2,1,2,1] => [2,2,2,2,1,1,1,1] => 9340
[1,2,1,2,1,2,1,2] => [2,2,2,2,1,1,1,1] => 9340
[1,2,1,2,1,2,2,1] => [2,2,2,2,1,1,1,1] => 9340
[1,2,1,2,1,1,2,2] => [2,2,2,2,1,1,1,1] => 9340
[1,2,1,1,2,1,2,2] => [2,2,2,2,1,1,1,1] => 9340
[1,2,1,1,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,2,1,1,2,2,1,2] => [2,2,2,2,1,1,1,1] => 9340
[1,2,1,1,2,2,2,1] => [2,2,2,2,1,1,1,1] => 9340
[1,2,1,1,1,2,2,2] => [2,2,2,2,1,1,1,1] => 9340
[1,2,1,1,1,2,1,2,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,2,1,1,1,1,2,2,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,2,2,1,2,2,2] => [2,2,2,2,2,1,1] => 4876
[1,2,2,1,2,1,2,1] => [2,2,2,2,1,1,1,1] => 9340
[1,2,2,1,1,2,1,2] => [2,2,2,2,1,1,1,1] => 9340
[1,2,2,1,1,2,2,1] => [2,2,2,2,1,1,1,1] => 9340
[1,2,2,1,1,1,2,2] => [2,2,2,2,1,1,1,1] => 9340
[1,2,2,2,1,2,2] => [2,2,2,2,2,1,1] => 4876
[1,2,2,2,1,1,2,1] => [2,2,2,2,1,1,1,1] => 9340
[1,2,2,2,2,1,2] => [2,2,2,2,2,1,1] => 4876
[1,1,2,2,2,2,2] => [2,2,2,2,2,1,1] => 4876
[1,1,2,2,2,1,2,1] => [2,2,2,2,1,1,1,1] => 9340
[1,1,2,2,1,2,1,2] => [2,2,2,2,1,1,1,1] => 9340
[1,1,2,2,1,2,2,1] => [2,2,2,2,1,1,1,1] => 9340
[1,1,2,1,2,1,2,2] => [2,2,2,2,1,1,1,1] => 9340
[1,1,2,1,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,2,1,2,2,2,1] => [2,2,2,2,1,1,1,1] => 9340
[1,1,2,1,1,2,1,2,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,2,1,1,1,2,2,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,1,2,2,1,2,2] => [2,2,2,2,1,1,1,1] => 9340
[1,1,1,2,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,1,2,2,2,1,2] => [2,2,2,2,1,1,1,1] => 9340
[1,1,1,2,2,2,2,1] => [2,2,2,2,1,1,1,1] => 9340
[1,1,1,2,1,2,2,2] => [2,2,2,2,1,1,1,1] => 9340
[1,1,1,2,1,2,1,2,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,1,1,2,2,1,2,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,1,1,2,1,2,2,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,1,1,1,2,2,2,1] => [2,2,2,1,1,1,1,1,1] => 18092
[2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1] => 17848
[3,2,2,2,2,1] => [3,2,2,2,2,1] => 1824
[4,3,2,2,1] => [4,3,2,2,1] => 420
[4,2,3,2,1] => [4,3,2,2,1] => 420
[4,2,2,3,1] => [4,3,2,2,1] => 420
[4,2,2,2,2] => [4,2,2,2,2] => 572
[5,4,2,1] => [5,4,2,1] => 82
[5,3,3,1] => [5,3,3,1] => 96
[5,3,2,2] => [5,3,2,2] => 126
[5,2,4,1] => [5,4,2,1] => 82
[5,2,3,2] => [5,3,2,2] => 126
[5,2,2,3] => [5,3,2,2] => 126
[6,5,1] => [6,5,1] => 17
[6,4,2] => [6,4,2] => 26
[6,3,3] => [6,3,3] => 30
[6,2,4] => [6,4,2] => 26
[7,5] => [7,5] => 6
[2,8,1] => [8,2,1] => 8
[2,1,7,1] => [7,2,1,1] => 24
[2,1,1,6,1] => [6,2,1,1,1] => 78
[2,1,1,1,5,1] => [5,2,1,1,1,1] => 270
[2,1,1,1,1,4,1] => [4,2,1,1,1,1,1] => 958
[2,1,1,1,1,1,3,1] => [3,2,1,1,1,1,1,1] => 3218
[2,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1] => 9040
[11,1] => [11,1] => 2
[2,9,1] => [9,2,1] => 8
[3,7,1] => [7,3,1] => 11
[2,1,8,1] => [8,2,1,1] => 24
[2,2,6,1] => [6,2,2,1] => 44
[2,1,1,7,1] => [7,2,1,1,1] => 78
[2,1,2,5,1] => [5,2,2,1,1] => 149
[2,1,1,1,6,1] => [6,2,1,1,1,1] => 271
[2,1,1,2,4,1] => [4,2,2,1,1,1] => 516
[2,1,1,1,1,5,1] => [5,2,1,1,1,1,1] => 989
[2,1,1,1,2,3,1] => [3,2,2,1,1,1,1] => 1688
[2,1,1,1,1,1,4,1] => [4,2,1,1,1,1,1,1] => 3643
[2,1,1,1,1,2,2,1] => [2,2,2,1,1,1,1,1] => 4636
[2,1,1,1,1,1,1,3,1] => [3,2,1,1,1,1,1,1,1] => 12498
[2,1,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1] => 9040
[2,1,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[2,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 70076
[2,2,2,2,2,1] => [2,2,2,2,2,1] => 1268
[3,1,2,2,2,1] => [3,2,2,2,1,1] => 897
[2,3,1,2,2,1] => [3,2,2,2,1,1] => 897
[3,2,1,2,2,1] => [3,2,2,2,1,1] => 897
[4,1,1,2,2,1] => [4,2,2,1,1,1] => 516
[2,2,3,1,2,1] => [3,2,2,2,1,1] => 897
[3,1,3,1,2,1] => [3,3,2,1,1,1] => 644
[2,3,2,1,2,1] => [3,2,2,2,1,1] => 897
[3,2,2,1,2,1] => [3,2,2,2,1,1] => 897
[4,1,2,1,2,1] => [4,2,2,1,1,1] => 516
[2,4,1,1,2,1] => [4,2,2,1,1,1] => 516
[3,3,1,1,2,1] => [3,3,2,1,1,1] => 644
[4,2,1,1,2,1] => [4,2,2,1,1,1] => 516
[5,1,1,1,2,1] => [5,2,1,1,1,1] => 270
[2,2,2,3,1,1] => [3,2,2,2,1,1] => 897
[3,1,2,3,1,1] => [3,3,2,1,1,1] => 644
[2,3,1,3,1,1] => [3,3,2,1,1,1] => 644
[3,2,1,3,1,1] => [3,3,2,1,1,1] => 644
[4,1,1,3,1,1] => [4,3,1,1,1,1] => 381
[2,2,3,2,1,1] => [3,2,2,2,1,1] => 897
[3,1,3,2,1,1] => [3,3,2,1,1,1] => 644
[2,3,2,2,1,1] => [3,2,2,2,1,1] => 897
[3,2,2,2,1,1] => [3,2,2,2,1,1] => 897
[4,1,2,2,1,1] => [4,2,2,1,1,1] => 516
[2,4,1,2,1,1] => [4,2,2,1,1,1] => 516
[3,3,1,2,1,1] => [3,3,2,1,1,1] => 644
[4,2,1,2,1,1] => [4,2,2,1,1,1] => 516
[5,1,1,2,1,1] => [5,2,1,1,1,1] => 270
[2,2,4,1,1,1] => [4,2,2,1,1,1] => 516
[3,1,4,1,1,1] => [4,3,1,1,1,1] => 381
[2,3,3,1,1,1] => [3,3,2,1,1,1] => 644
[3,2,3,1,1,1] => [3,3,2,1,1,1] => 644
[4,1,3,1,1,1] => [4,3,1,1,1,1] => 381
[2,4,2,1,1,1] => [4,2,2,1,1,1] => 516
[3,3,2,1,1,1] => [3,3,2,1,1,1] => 644
[4,2,2,1,1,1] => [4,2,2,1,1,1] => 516
[5,1,2,1,1,1] => [5,2,1,1,1,1] => 270
[2,5,1,1,1,1] => [5,2,1,1,1,1] => 270
[3,4,1,1,1,1] => [4,3,1,1,1,1] => 381
[4,3,1,1,1,1] => [4,3,1,1,1,1] => 381
[5,2,1,1,1,1] => [5,2,1,1,1,1] => 270
[6,1,1,1,1,1] => [6,1,1,1,1,1] => 142
[2,2,1,2,1,2,1,1] => [2,2,2,2,1,1,1,1] => 9340
[2,2,1,1,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[2,1,2,1,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[2,1,2,1,2,1,1,2] => [2,2,2,2,1,1,1,1] => 9340
[2,1,2,1,2,2,1,1] => [2,2,2,2,1,1,1,1] => 9340
[2,1,2,1,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[2,1,1,2,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 18092
[2,1,1,2,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[2,1,1,2,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[2,1,1,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1] => 18092
[2,1,1,1,2,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 18092
[2,1,1,1,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[2,1,1,1,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,2,1,2,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,2,1,1,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,2,1,1,1,2,1,1,2] => [2,2,2,1,1,1,1,1,1] => 18092
[1,2,1,1,1,2,2,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,2,1,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,2,2,1,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,2,2,2,1,2,1,1] => [2,2,2,2,1,1,1,1] => 9340
[1,2,2,1,2,1,1,2] => [2,2,2,2,1,1,1,1] => 9340
[1,2,2,1,2,2,1,1] => [2,2,2,2,1,1,1,1] => 9340
[1,2,1,2,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,2,1,2,2,1,1,2] => [2,2,2,2,1,1,1,1] => 9340
[1,2,1,2,2,2,1,1] => [2,2,2,2,1,1,1,1] => 9340
[1,2,1,2,1,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,2,1,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1] => 18092
[1,2,1,1,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,2,1,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,2,1,1,1,2,1,2] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,2,1,1,2,1,1,2] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,2,1,1,2,2,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,2,2,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,2,2,1,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,2,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,2,1,2,2,1,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,1,2,1,1,1,2,2] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,1,2,1,1,2,1,2] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,1,2,1,2,1,1,2] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,1,2,2,1,1,1,2] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,1,2,2,1,2,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[2,1,1,1,1,1,1,3] => [3,2,1,1,1,1,1,1] => 3218
[2,1,1,1,1,1,2,2] => [2,2,2,1,1,1,1,1] => 4636
[2,1,1,1,1,2,1,2] => [2,2,2,1,1,1,1,1] => 4636
[2,1,1,1,2,1,1,2] => [2,2,2,1,1,1,1,1] => 4636
[2,1,1,2,1,1,1,2] => [2,2,2,1,1,1,1,1] => 4636
[2,1,2,1,1,1,1,2] => [2,2,2,1,1,1,1,1] => 4636
[2,2,1,1,1,1,1,2] => [2,2,2,1,1,1,1,1] => 4636
[3,1,1,1,1,1,1,2] => [3,2,1,1,1,1,1,1] => 3218
[1,2,2,4,2,1] => [4,2,2,2,1,1] => 1046
[1,2,4,2,2,1] => [4,2,2,2,1,1] => 1046
[1,2,5,2,2] => [5,2,2,2,1] => 297
[1,3,5,2,1] => [5,3,2,1,1] => 223
[1,4,2,2,2,1] => [4,2,2,2,1,1] => 1046
[1,5,2,2,2] => [5,2,2,2,1] => 297
[1,5,3,2,1] => [5,3,2,1,1] => 223
[2,5,2,2,1] => [5,2,2,2,1] => 297
[2,6,2,2] => [6,2,2,2] => 85
[2,2,5,2,1] => [5,2,2,2,1] => 297
[6,2,2,2] => [6,2,2,2] => 85
[2,2,2,2,2,1,1] => [2,2,2,2,2,1,1] => 4876
[1,2,2,2,2,1,1,1] => [2,2,2,2,1,1,1,1] => 9340
[1,2,2,1,2,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,2,1,2,2,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,2,1,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 70076
[9,2] => [9,2] => 3
[1,9,1] => [9,1,1] => 5
[10,2] => [10,2] => 3
[1,1,1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,2,2,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,2,1,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,2,2,2,3,1,1] => [3,2,2,2,1,1,1] => 3425
[1,2,2,3,1,2,1] => [3,2,2,2,1,1,1] => 3425
[1,2,2,4,1,1,1] => [4,2,2,1,1,1,1] => 1941
[1,2,3,1,2,2,1] => [3,2,2,2,1,1,1] => 3425
[1,2,3,1,3,1,1] => [3,3,2,1,1,1,1] => 2436
[1,2,3,2,1,2,1] => [3,2,2,2,1,1,1] => 3425
[1,2,4,1,1,2,1] => [4,2,2,1,1,1,1] => 1941
[1,2,3,2,2,1,1] => [3,2,2,2,1,1,1] => 3425
[1,2,3,3,1,1,1] => [3,3,2,1,1,1,1] => 2436
[1,2,4,2,1,1,1] => [4,2,2,1,1,1,1] => 1941
[1,2,5,1,1,1,1] => [5,2,1,1,1,1,1] => 989
[1,3,1,2,2,2,1] => [3,2,2,2,1,1,1] => 3425
[1,3,1,3,1,2,1] => [3,3,2,1,1,1,1] => 2436
[1,3,1,3,2,1,1] => [3,3,2,1,1,1,1] => 2436
[1,3,2,1,3,1,1] => [3,3,2,1,1,1,1] => 2436
[1,4,1,1,2,2,1] => [4,2,2,1,1,1,1] => 1941
[1,4,1,1,3,1,1] => [4,3,1,1,1,1,1] => 1414
[1,3,2,2,1,2,1] => [3,2,2,2,1,1,1] => 3425
[1,3,3,1,1,2,1] => [3,3,2,1,1,1,1] => 2436
[1,4,1,2,1,2,1] => [4,2,2,1,1,1,1] => 1941
[1,4,2,1,1,2,1] => [4,2,2,1,1,1,1] => 1941
[1,5,1,1,1,2,1] => [5,2,1,1,1,1,1] => 989
[1,3,2,3,1,1,1] => [3,3,2,1,1,1,1] => 2436
[1,3,3,1,2,1,1] => [3,3,2,1,1,1,1] => 2436
[1,3,4,1,1,1,1] => [4,3,1,1,1,1,1] => 1414
[1,4,1,2,2,1,1] => [4,2,2,1,1,1,1] => 1941
[1,4,1,3,1,1,1] => [4,3,1,1,1,1,1] => 1414
[1,5,1,1,2,1,1] => [5,2,1,1,1,1,1] => 989
[1,4,2,2,1,1,1] => [4,2,2,1,1,1,1] => 1941
[1,4,3,1,1,1,1] => [4,3,1,1,1,1,1] => 1414
[1,5,2,1,1,1,1] => [5,2,1,1,1,1,1] => 989
[1,6,1,1,1,1,1] => [6,1,1,1,1,1,1] => 499
[2,1,2,2,3,1,1] => [3,2,2,2,1,1,1] => 3425
[2,1,2,3,1,2,1] => [3,2,2,2,1,1,1] => 3425
[2,1,2,3,2,1,1] => [3,2,2,2,1,1,1] => 3425
[2,1,2,4,1,1,1] => [4,2,2,1,1,1,1] => 1941
[2,1,3,1,2,2,1] => [3,2,2,2,1,1,1] => 3425
[2,1,3,1,3,1,1] => [3,3,2,1,1,1,1] => 2436
[2,1,3,2,1,2,1] => [3,2,2,2,1,1,1] => 3425
[2,1,4,1,1,2,1] => [4,2,2,1,1,1,1] => 1941
[2,1,3,2,2,1,1] => [3,2,2,2,1,1,1] => 3425
[2,1,3,3,1,1,1] => [3,3,2,1,1,1,1] => 2436
[2,1,4,1,2,1,1] => [4,2,2,1,1,1,1] => 1941
[2,1,4,2,1,1,1] => [4,2,2,1,1,1,1] => 1941
[2,1,5,1,1,1,1] => [5,2,1,1,1,1,1] => 989
[2,2,1,2,3,1,1] => [3,2,2,2,1,1,1] => 3425
[2,2,1,3,1,2,1] => [3,2,2,2,1,1,1] => 3425
[2,2,1,3,2,1,1] => [3,2,2,2,1,1,1] => 3425
[2,2,1,4,1,1,1] => [4,2,2,1,1,1,1] => 1941
[3,1,1,2,2,2,1] => [3,2,2,2,1,1,1] => 3425
[3,1,1,3,1,2,1] => [3,3,2,1,1,1,1] => 2436
[3,1,1,3,2,1,1] => [3,3,2,1,1,1,1] => 2436
[2,2,2,1,3,1,1] => [3,2,2,2,1,1,1] => 3425
[2,3,1,1,2,2,1] => [3,2,2,2,1,1,1] => 3425
[2,3,1,1,3,1,1] => [3,3,2,1,1,1,1] => 2436
[3,1,2,1,3,1,1] => [3,3,2,1,1,1,1] => 2436
[3,2,1,1,2,2,1] => [3,2,2,2,1,1,1] => 3425
[3,2,1,1,3,1,1] => [3,3,2,1,1,1,1] => 2436
[4,1,1,1,2,2,1] => [4,2,2,1,1,1,1] => 1941
[4,1,1,1,3,1,1] => [4,3,1,1,1,1,1] => 1414
[2,2,3,1,1,2,1] => [3,2,2,2,1,1,1] => 3425
[2,3,1,2,1,2,1] => [3,2,2,2,1,1,1] => 3425
[2,3,2,1,1,2,1] => [3,2,2,2,1,1,1] => 3425
[2,4,1,1,1,2,1] => [4,2,2,1,1,1,1] => 1941
[3,1,2,2,1,2,1] => [3,2,2,2,1,1,1] => 3425
[3,1,3,1,1,2,1] => [3,3,2,1,1,1,1] => 2436
[3,2,1,2,1,2,1] => [3,2,2,2,1,1,1] => 3425
[4,1,1,2,1,2,1] => [4,2,2,1,1,1,1] => 1941
[3,2,2,1,1,2,1] => [3,2,2,2,1,1,1] => 3425
[3,3,1,1,1,2,1] => [3,3,2,1,1,1,1] => 2436
[4,1,2,1,1,2,1] => [4,2,2,1,1,1,1] => 1941
[4,2,1,1,1,2,1] => [4,2,2,1,1,1,1] => 1941
[5,1,1,1,1,2,1] => [5,2,1,1,1,1,1] => 989
[2,2,2,3,1,1,1] => [3,2,2,2,1,1,1] => 3425
[2,2,3,1,2,1,1] => [3,2,2,2,1,1,1] => 3425
[2,2,3,2,1,1,1] => [3,2,2,2,1,1,1] => 3425
[2,2,4,1,1,1,1] => [4,2,2,1,1,1,1] => 1941
[2,3,1,2,2,1,1] => [3,2,2,2,1,1,1] => 3425
[2,3,1,3,1,1,1] => [3,3,2,1,1,1,1] => 2436
[2,3,2,1,2,1,1] => [3,2,2,2,1,1,1] => 3425
[2,4,1,1,2,1,1] => [4,2,2,1,1,1,1] => 1941
[2,3,2,2,1,1,1] => [3,2,2,2,1,1,1] => 3425
[2,3,3,1,1,1,1] => [3,3,2,1,1,1,1] => 2436
[2,4,1,2,1,1,1] => [4,2,2,1,1,1,1] => 1941
[2,4,2,1,1,1,1] => [4,2,2,1,1,1,1] => 1941
[2,5,1,1,1,1,1] => [5,2,1,1,1,1,1] => 989
[3,1,2,3,1,1,1] => [3,3,2,1,1,1,1] => 2436
[3,1,3,1,2,1,1] => [3,3,2,1,1,1,1] => 2436
[3,1,4,1,1,1,1] => [4,3,1,1,1,1,1] => 1414
[3,2,1,2,2,1,1] => [3,2,2,2,1,1,1] => 3425
[3,2,1,3,1,1,1] => [3,3,2,1,1,1,1] => 2436
[4,1,1,2,2,1,1] => [4,2,2,1,1,1,1] => 1941
[4,1,1,3,1,1,1] => [4,3,1,1,1,1,1] => 1414
[3,3,1,1,2,1,1] => [3,3,2,1,1,1,1] => 2436
[4,1,2,1,2,1,1] => [4,2,2,1,1,1,1] => 1941
[4,2,1,1,2,1,1] => [4,2,2,1,1,1,1] => 1941
[5,1,1,1,2,1,1] => [5,2,1,1,1,1,1] => 989
[3,2,2,2,1,1,1] => [3,2,2,2,1,1,1] => 3425
[3,2,3,1,1,1,1] => [3,3,2,1,1,1,1] => 2436
[3,3,2,1,1,1,1] => [3,3,2,1,1,1,1] => 2436
[3,4,1,1,1,1,1] => [4,3,1,1,1,1,1] => 1414
[4,1,2,2,1,1,1] => [4,2,2,1,1,1,1] => 1941
[4,1,3,1,1,1,1] => [4,3,1,1,1,1,1] => 1414
[4,2,1,2,1,1,1] => [4,2,2,1,1,1,1] => 1941
[4,2,2,1,1,1,1] => [4,2,2,1,1,1,1] => 1941
[4,3,1,1,1,1,1] => [4,3,1,1,1,1,1] => 1414
[5,1,2,1,1,1,1] => [5,2,1,1,1,1,1] => 989
[5,2,1,1,1,1,1] => [5,2,1,1,1,1,1] => 989
[6,1,1,1,1,1,1] => [6,1,1,1,1,1,1] => 499
[11] => [11] => 1
[2,9] => [9,2] => 3
[1,1,2,2,4,1] => [4,2,2,1,1,1] => 516
[1,2,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 70076
[1,2,2,2,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,2,2,1,1,1,1,2,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 70076
[1,1,1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 70076
[1,1,1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1,1,1] => 70076
[1,1,2,3,2,3] => [3,3,2,2,1,1] => 1306
[1,2,2,2,2,3] => [3,2,2,2,2,1] => 1824
[5,1,1,1,1,2] => [5,2,1,1,1,1] => 270
[1,1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1,1] => 17848
[1,2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1] => 9040
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1] => 35696
[1,1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1,1] => 6204
[1,1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1,1] => 6204
[1,1,1,1,1,5,1] => [5,1,1,1,1,1,1] => 498
[1,1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1,1] => 9040
[1,1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => 6204
[1,1,1,3,1,3,1] => [3,3,1,1,1,1,1] => 1204
[1,1,1,5,1,1,1] => [5,1,1,1,1,1,1] => 498
[1,1,1,7,1] => [7,1,1,1,1] => 43
[1,1,1,4,1,2,1] => [4,2,1,1,1,1,1] => 958
[1,1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1] => 9040
[1,1,1,2,1,4,1] => [4,2,1,1,1,1,1] => 958
[1,1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1] => 9040
[1,1,1,2,3,2,1] => [3,2,2,1,1,1,1] => 1688
[1,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1] => 6204
[1,3,1,1,1,3,1] => [3,3,1,1,1,1,1] => 1204
[1,3,1,3,1,1,1] => [3,3,1,1,1,1,1] => 1204
[1,3,1,5,1] => [5,3,1,1,1] => 113
[1,3,1,2,1,2,1] => [3,2,2,1,1,1,1] => 1688
[1,5,1,1,1,1,1] => [5,1,1,1,1,1,1] => 498
[1,5,1,3,1] => [5,3,1,1,1] => 113
[1,7,1,1,1] => [7,1,1,1,1] => 43
[1,6,1,2,1] => [6,2,1,1,1] => 78
[1,4,1,2,1,1,1] => [4,2,1,1,1,1,1] => 958
[1,4,1,4,1] => [4,4,1,1,1] => 132
[1,4,1,1,1,2,1] => [4,2,1,1,1,1,1] => 958
[1,4,3,2,1] => [4,3,2,1,1] => 209
[1,2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 9040
[1,2,1,2,1,3,1] => [3,2,2,1,1,1,1] => 1688
[1,2,1,4,1,1,1] => [4,2,1,1,1,1,1] => 958
[1,2,1,6,1] => [6,2,1,1,1] => 78
[1,2,1,3,1,2,1] => [3,2,2,1,1,1,1] => 1688
[1,2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1,1] => 9040
[1,2,1,1,1,4,1] => [4,2,1,1,1,1,1] => 958
[1,2,1,1,3,2,1] => [3,2,2,1,1,1,1] => 1688
[1,2,3,2,1,1,1] => [3,2,2,1,1,1,1] => 1688
[1,2,3,4,1] => [4,3,2,1,1] => 209
[1,2,3,1,1,2,1] => [3,2,2,1,1,1,1] => 1688
[1,2,5,2,1] => [5,2,2,1,1] => 149
[1,2,2,1,2,2,1] => [2,2,2,2,1,1,1] => 2408
[1,1,9] => [9,1,1] => 5
[1,1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1,1] => 6204
[1,1,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 70076
[1,1,2,2,1,2,3] => [3,2,2,2,1,1,1] => 3425
[1,1,1,1,2,2,2,1,1] => [2,2,2,1,1,1,1,1,1] => 18092
[1,1,1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 70076
[1,1,1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1,1,1] => 70076
[1,1,1,2,2,2,3] => [3,2,2,2,1,1,1] => 3425
[1,6,4] => [6,4,1] => 14
[1,5,5] => [5,5,1] => 16
[1,4,6] => [6,4,1] => 14
[1,3,7] => [7,3,1] => 11
[1,2,8] => [8,2,1] => 8
[1,2,1,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,2,1,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,1,1,1,2,1,2,1,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1,1,1] => 35420
[1,1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1,1] => 9040
[1,1,2,2,2,2,1] => [2,2,2,2,1,1,1] => 2408
[1,1,2,2,2,1,1,1] => [2,2,2,1,1,1,1,1] => 4636
[1,1,2,2,3,1,1] => [3,2,2,1,1,1,1] => 1688
[1,1,2,2,1,2,1,1] => [2,2,2,1,1,1,1,1] => 4636
[1,1,2,3,2,1,1] => [3,2,2,1,1,1,1] => 1688
[1,1,2,1,2,2,1,1] => [2,2,2,1,1,1,1,1] => 4636
[1,1,3,2,2,1,1] => [3,2,2,1,1,1,1] => 1688
[1,1,1,2,2,2,1,1] => [2,2,2,1,1,1,1,1] => 4636
[1,2,2,2,2,1,1] => [2,2,2,2,1,1,1] => 2408
[1,1,2,2,2,4] => [4,2,2,2,1,1] => 1046
[1,1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1] => 9040
[1,1,2,5,1,1] => [5,2,1,1,1,1] => 270
[1,1,5,2,1,1] => [5,2,1,1,1,1] => 270
[1,1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1,1] => 9040
[1,4,2,2,1,1] => [4,2,2,1,1,1] => 516
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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:
1,1 1,2,0,1 1,2,1,0,3,0,0,0,0,1 1,2,2,0,3,0,3,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = q + 2\ q^{2} + q^{4}$
$F_{4} = q + 2\ q^{2} + q^{3} + 3\ q^{5} + q^{10}$
$F_{5} = q + 2\ q^{2} + 2\ q^{3} + 3\ q^{5} + 3\ q^{7} + 4\ q^{13} + q^{26}$
$F_{6} = q + 2\ q^{2} + 2\ q^{3} + q^{4} + 3\ q^{5} + 6\ q^{8} + q^{11} + 4\ q^{14} + 6\ q^{20} + 5\ q^{38} + q^{76}$
$F_{7} = q + 2\ q^{2} + 2\ q^{3} + 2\ q^{4} + 3\ q^{5} + 6\ q^{8} + 3\ q^{10} + 3\ q^{13} + 4\ q^{14} + 12\ q^{23} + 4\ q^{32} + 5\ q^{42} + 10\ q^{60} + 6\ q^{116} + q^{232}$
$F_{8} = q + 2\ q^{2} + 2\ q^{3} + 2\ q^{4} + 4\ q^{5} + 6\ q^{8} + 6\ q^{11} + 7\ q^{14} + 3\ q^{17} + 12\ q^{24} + 6\ q^{30} + 12\ q^{40} + 5\ q^{43} + q^{56} + 20\ q^{73} + 10\ q^{103} + 6\ q^{136} + 15\ q^{196} + 7\ q^{382} + q^{764}$
$F_{9} = q + 2\ q^{2} + 2\ q^{3} + 2\ q^{4} + 5\ q^{5} + 6\ q^{8} + 6\ q^{11} + 3\ q^{13} + 7\ q^{14} + 6\ q^{19} + q^{23} + 12\ q^{24} + 12\ q^{33} + 17\ q^{43} + 12\ q^{53} + 4\ q^{72} + 20\ q^{77} + 10\ q^{96} + 30\ q^{131} + 6\ q^{141} + 5\ q^{184} + 30\ q^{244} + 20\ q^{347} + 7\ q^{462} + 21\ q^{668} + 8\ q^{1310} + q^{2620}$
$F_{10} = q + 2\ q^{2} + 2\ q^{3} + 2\ q^{4} + 5\ q^{5} + q^{6} + 6\ q^{8} + 6\ q^{11} + 13\ q^{14} + 6\ q^{20} + 3\ q^{23} + 12\ q^{24} + 3\ q^{27} + 12\ q^{34} + 6\ q^{40} + 5\ q^{43} + 12\ q^{44} + 24\ q^{61} + 4\ q^{74} + 20\ q^{78} + 4\ q^{81} + 6\ q^{100} + 20\ q^{109} + 6\ q^{142} + 30\ q^{145} + 30\ q^{180} + 20\ q^{248} + 30\ q^{265} + 15\ q^{332} + q^{348} + 60\ q^{460} + 7\ q^{492} + 15\ q^{652} + 42\ q^{868} + 35\ q^{1244} + 8\ q^{1660} + 28\ q^{2412} + 9\ q^{4748} + q^{9496}$
Description
The sum of the entries in the column specified by the partition of the change of basis matrix from elementary symmetric functions to Schur symmetric functions.
For example, $e_{22} = s_{1111} + s_{211} + s_{22}$, so the statistic on the partition $22$ is $3$.
For example, $e_{22} = s_{1111} + s_{211} + s_{22}$, so the statistic on the partition $22$ is $3$.
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Description
Sends a composition to the partition obtained by sorting the entries.
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