Identifier
-
Mp00027:
Dyck paths
—to partition⟶
Integer partitions
St000517: Integer partitions ⟶ ℤ
Values
[1,0] => [] => 1
[1,0,1,0] => [1] => 1
[1,1,0,0] => [] => 1
[1,0,1,0,1,0] => [2,1] => 3
[1,0,1,1,0,0] => [1,1] => 1
[1,1,0,0,1,0] => [2] => 1
[1,1,0,1,0,0] => [1] => 1
[1,1,1,0,0,0] => [] => 1
[1,0,1,0,1,0,1,0] => [3,2,1] => 30
[1,0,1,0,1,1,0,0] => [2,2,1] => 10
[1,0,1,1,0,0,1,0] => [3,1,1] => 10
[1,0,1,1,0,1,0,0] => [2,1,1] => 6
[1,0,1,1,1,0,0,0] => [1,1,1] => 1
[1,1,0,0,1,0,1,0] => [3,2] => 5
[1,1,0,0,1,1,0,0] => [2,2] => 2
[1,1,0,1,0,0,1,0] => [3,1] => 4
[1,1,0,1,0,1,0,0] => [2,1] => 3
[1,1,0,1,1,0,0,0] => [1,1] => 1
[1,1,1,0,0,0,1,0] => [3] => 1
[1,1,1,0,0,1,0,0] => [2] => 1
[1,1,1,0,1,0,0,0] => [1] => 1
[1,1,1,1,0,0,0,0] => [] => 1
[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 720
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 252
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => 252
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 168
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 35
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 252
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 84
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => 168
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 105
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 30
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 35
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 20
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 10
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 72
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 28
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 28
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => 21
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 5
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => 56
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => 21
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => 42
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 30
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => 10
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => 15
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => 10
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => 6
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0] => [4,3] => 7
[1,1,1,0,0,0,1,1,0,0] => [3,3] => 3
[1,1,1,0,0,1,0,0,1,0] => [4,2] => 6
[1,1,1,0,0,1,0,1,0,0] => [3,2] => 5
[1,1,1,0,0,1,1,0,0,0] => [2,2] => 2
[1,1,1,0,1,0,0,0,1,0] => [4,1] => 5
[1,1,1,0,1,0,0,1,0,0] => [3,1] => 4
[1,1,1,0,1,0,1,0,0,0] => [2,1] => 3
[1,1,1,0,1,1,0,0,0,0] => [1,1] => 1
[1,1,1,1,0,0,0,0,1,0] => [4] => 1
[1,1,1,1,0,0,0,1,0,0] => [3] => 1
[1,1,1,1,0,0,1,0,0,0] => [2] => 1
[1,1,1,1,0,1,0,0,0,0] => [1] => 1
[1,1,1,1,1,0,0,0,0,0] => [] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 32760
[1,0,1,0,1,0,1,0,1,1,0,0] => [4,4,3,2,1] => 12012
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,3,3,2,1] => 12012
[1,0,1,0,1,0,1,1,0,1,0,0] => [4,3,3,2,1] => 8580
[1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 1980
[1,0,1,0,1,1,0,0,1,0,1,0] => [5,4,2,2,1] => 12012
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,4,2,2,1] => 4290
[1,0,1,0,1,1,0,1,0,0,1,0] => [5,3,2,2,1] => 8580
[1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 5940
[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => 1980
[1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => 1980
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 1320
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 840
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 126
[1,0,1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,1] => 12012
[1,0,1,1,0,0,1,0,1,1,0,0] => [4,4,3,1,1] => 4290
[1,0,1,1,0,0,1,1,0,0,1,0] => [5,3,3,1,1] => 4290
[1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => 2970
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => 660
[1,0,1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,1] => 8580
[1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => 2970
[1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => 5940
[1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 3960
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => 1260
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => 1980
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => 1260
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => 756
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => 140
[1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => 1980
[1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => 660
[1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => 1320
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 840
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => 252
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => 840
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 504
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 280
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 70
>>> Load all 1293 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 126
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 70
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 35
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 15
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [5,4,3,2] => 2184
[1,1,0,0,1,0,1,0,1,1,0,0] => [4,4,3,2] => 858
[1,1,0,0,1,0,1,1,0,0,1,0] => [5,3,3,2] => 858
[1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => 660
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => 165
[1,1,0,0,1,1,0,0,1,0,1,0] => [5,4,2,2] => 858
[1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 330
[1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => 660
[1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => 495
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => 180
[1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 165
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => 120
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => 84
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 14
[1,1,0,1,0,0,1,0,1,0,1,0] => [5,4,3,1] => 1716
[1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => 660
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => 660
[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => 495
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => 120
[1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => 1320
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => 495
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => 990
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 720
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => 252
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => 360
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => 252
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => 168
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => 35
[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => 495
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => 180
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => 360
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => 252
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => 84
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => 252
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => 168
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => 105
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => 30
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => 56
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => 35
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => 20
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => 10
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 132
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 55
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 55
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => 45
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 12
[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => 110
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => 45
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => 90
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 72
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => 28
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => 36
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => 28
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => 21
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => 5
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => 90
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => 36
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => 72
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 56
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => 21
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => 56
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 42
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 30
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 10
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => 21
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 15
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => 10
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 6
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 9
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => 8
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 7
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => 7
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => 6
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => 5
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 6
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 5
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => 4
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => 2441880
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2,1] => 930240
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2,1] => 930240
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,4,3,2,1] => 697680
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2,1] => 171360
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2,1] => 930240
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2,1] => 348840
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,3,2,1] => 514080
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2,1] => 171360
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,3,3,2,1] => 123760
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2,1] => 87360
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2,1] => 15015
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2,1] => 930240
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2,1] => 348840
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2,1] => 348840
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2,1] => 61880
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,2,1] => 371280
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2,1] => 171360
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2,1] => 61880
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,2,2,1] => 87360
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,2,2,1] => 60060
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,2,2,1] => 40040
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2,1] => 12870
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2,1] => 15015
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2,1] => 10010
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 3960
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 462
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,1] => 930240
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3,1,1] => 348840
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3,1,1] => 348840
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3,1,1] => 61880
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3,1,1] => 348840
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3,1,1] => 128520
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3,1,1] => 61880
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1,1] => 5005
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,1] => 262080
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 11880
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 7920
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 4620
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 630
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,1,1] => 171360
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [5,5,4,1,1,1] => 61880
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,4,1,1,1] => 61880
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1,1,1] => 10010
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1,1] => 60060
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 2640
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1,1] => 40040
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1,1] => 25740
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => 15840
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 4620
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 7920
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => 4620
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 2520
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 420
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,1,1,1] => 15015
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 5005
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1,1] => 6435
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 1980
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => 3960
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => 2310
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 630
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => 3960
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => 2310
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => 1260
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 630
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 140
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => 462
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 252
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => 126
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 56
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 21
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2] => 116280
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,5,4,3,2] => 46512
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [6,4,4,3,2] => 46512
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [4,4,4,3,2] => 9520
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,3,2] => 46512
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,5,3,3,2] => 18360
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [4,4,3,3,2] => 10920
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [6,3,3,3,2] => 9520
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [4,3,3,3,2] => 5460
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 1001
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,2] => 46512
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [5,5,4,2,2] => 18360
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [6,4,4,2,2] => 18360
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,4,4,2,2] => 3640
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,3,3,2,2] => 1430
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,2,2] => 9520
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [5,5,2,2,2] => 3640
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 990
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1001
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 495
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 330
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 42
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1] => 93024
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3,1] => 715
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => 32760
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2,1] => 12012
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2,1] => 12012
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2,1] => 8580
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 1980
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2,1] => 12012
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2,1] => 4290
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2,1] => 8580
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 5940
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 1980
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => 1980
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 1320
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 840
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 126
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,1] => 12012
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1,1] => 4290
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1,1] => 4290
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 2970
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 660
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,1] => 8580
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 2970
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => 5940
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => 3960
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 1260
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => 2970
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => 1980
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 1260
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 756
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 140
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => 1980
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 660
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => 1980
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => 1320
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => 840
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 252
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => 1320
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => 840
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => 504
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 280
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 70
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => 210
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => 126
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => 70
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => 35
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => 15
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3] => 4896
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [5,5,4,3] => 2040
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [6,4,4,3] => 2040
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [5,4,4,3] => 1680
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 455
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [6,5,3,3] => 2040
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [5,5,3,3] => 840
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [5,4,3,3] => 1365
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4,3,3] => 546
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [6,3,3,3] => 455
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [5,3,3,3] => 364
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,3,3,3] => 286
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 55
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,4,4,2] => 364
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2] => 2184
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [4,4,3,2] => 858
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [5,3,3,2] => 858
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 660
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 165
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [5,4,2,2] => 858
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 330
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => 660
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 495
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 180
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => 220
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => 165
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 120
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 84
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 14
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,4,4,1] => 286
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1] => 1716
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => 660
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => 660
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 495
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 120
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1] => 1716
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => 1320
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => 495
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => 1320
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => 990
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 720
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 252
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => 495
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 360
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => 252
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 168
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 35
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 330
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => 660
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 495
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 180
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => 495
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => 360
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => 252
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 84
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => 360
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 252
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 168
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 105
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 30
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => 84
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 56
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => 35
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 20
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 10
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [6,5,4] => 210
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 91
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [6,4,4] => 91
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,4,4] => 78
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 22
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,5,3] => 78
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 132
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => 55
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => 66
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => 55
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 45
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 12
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => 66
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => 132
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => 110
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => 45
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => 110
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => 90
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => 72
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => 28
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => 45
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => 36
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => 28
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 21
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => 5
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => 132
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => 55
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => 110
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 90
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => 36
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => 90
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => 72
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => 56
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => 21
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => 72
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 56
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => 42
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 30
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => 10
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => 28
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => 21
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => 15
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => 10
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => 6
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 11
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 5
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => 10
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 9
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 4
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => 9
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => 8
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => 7
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => 8
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 7
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => 6
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 7
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 6
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => 271252800
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2,1] => 106563600
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1] => 82882800
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1] => 21252000
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1] => 63756000
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1] => 16151520
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1] => 12113640
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1] => 2238390
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1] => 48454560
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1] => 12113640
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1] => 8953560
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1] => 1627920
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1] => 36340920
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1] => 8953560
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,2,1] => 6511680
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1] => 1162800
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1716
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,1] => 26860680
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 2772
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1,1] => 6511680
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,1,1] => 4651200
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 18480
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 2310
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1,1] => 813960
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 13860
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => 13860
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 6930
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 1050
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => 5544
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 1386
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1] => 5544
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => 2772
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => 1260
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 252
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => 924
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => 462
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 210
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => 84
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 28
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2] => 9687600
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2] => 6188
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2] => 10920
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2] => 10010
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2] => 5005
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 1287
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 132
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1] => 2441880
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1] => 930240
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2,1] => 930240
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1] => 697680
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,1] => 171360
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2,1] => 930240
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1] => 348840
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1] => 514080
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1] => 171360
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1] => 123760
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1] => 87360
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1] => 15015
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,1] => 930240
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1] => 348840
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,1] => 348840
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1] => 61880
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1] => 371280
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,1] => 171360
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1] => 61880
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1] => 87360
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1] => 60060
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1] => 40040
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1] => 12870
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1] => 15015
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1] => 10010
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => 3960
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 462
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1] => 930240
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1,1] => 348840
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1,1] => 348840
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1] => 61880
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1,1] => 348840
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1] => 128520
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1] => 61880
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1] => 5005
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1] => 262080
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 11880
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => 7920
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 4620
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 630
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1] => 171360
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1] => 61880
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1] => 61880
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1] => 10010
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1] => 60060
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 2640
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1] => 40040
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1] => 25740
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => 15840
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => 4620
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => 7920
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => 4620
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 2520
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 420
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1] => 15015
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 5005
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1] => 6435
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 1980
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => 3960
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => 2310
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 630
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => 3960
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => 2310
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => 1260
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => 630
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 140
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1] => 792
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => 462
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => 252
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => 126
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 56
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 21
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3] => 3876
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3] => 6120
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3] => 4760
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3] => 1820
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 273
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2] => 3060
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2] => 116280
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2] => 46512
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2] => 46512
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2] => 9520
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2] => 46512
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2] => 18360
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2] => 10920
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2] => 9520
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2] => 5460
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => 1001
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2] => 46512
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2] => 18360
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2] => 18360
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2] => 3640
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2] => 1430
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2] => 9520
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2] => 3640
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 990
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => 1001
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => 495
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => 330
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 42
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1] => 116280
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1] => 93024
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1] => 715
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => 32760
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1] => 12012
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1] => 12012
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1] => 8580
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => 1980
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1] => 12012
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1] => 4290
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1] => 8580
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 5940
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 1980
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => 1980
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => 1320
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => 840
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 126
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1] => 12012
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1] => 4290
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1] => 4290
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 2970
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 660
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1] => 8580
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => 2970
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => 5940
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => 3960
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 1260
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => 2970
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => 1980
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => 1260
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 756
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 140
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => 1980
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 660
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => 1980
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => 1320
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => 840
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 252
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1] => 1980
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => 1320
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => 840
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 504
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 280
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 70
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => 330
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => 210
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => 126
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => 70
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => 35
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => 15
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4] => 1224
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4] => 680
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 140
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3] => 4896
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3] => 2040
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3] => 2040
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3] => 1680
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => 455
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3] => 2040
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3] => 840
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3] => 1365
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3] => 546
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3] => 455
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3] => 364
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3] => 286
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 55
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2] => 364
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2] => 4080
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2] => 2184
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2] => 858
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2] => 858
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => 660
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => 165
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2] => 858
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 330
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => 660
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 495
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 180
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => 220
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => 165
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 120
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 84
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 14
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1] => 286
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1] => 3360
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1] => 1716
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => 660
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => 660
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => 495
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => 120
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1] => 1716
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => 1320
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => 495
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => 1320
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => 990
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 720
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => 252
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => 660
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => 495
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => 360
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => 252
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 168
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 35
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => 330
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => 660
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => 495
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 180
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1] => 660
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => 495
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => 360
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => 252
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 84
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => 495
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => 360
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => 252
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 168
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => 105
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 30
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => 120
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => 84
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => 56
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => 35
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => 20
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => 10
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 35
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,6,4] => 120
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4] => 210
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => 91
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [6,4,4] => 91
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,4] => 78
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 22
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,6,3] => 105
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [7,5,3] => 210
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,5,3] => 78
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,4,3] => 182
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => 132
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => 55
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => 66
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => 55
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 45
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 12
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,6,2] => 91
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [7,5,2] => 182
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => 66
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,2] => 156
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => 132
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => 110
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => 45
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => 132
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => 110
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => 90
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 72
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => 28
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => 55
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => 45
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => 36
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => 28
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 21
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => 5
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,6,1] => 78
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [7,5,1] => 156
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => 132
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => 55
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,4,1] => 132
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => 110
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => 90
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => 36
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,3,1] => 110
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => 90
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => 72
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 56
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => 21
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 90
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 72
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => 56
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => 42
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 30
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => 10
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => 36
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 28
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => 21
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => 15
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => 10
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => 6
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,6] => 13
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => 12
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 11
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => 11
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => 10
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 9
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => 10
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 9
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => 8
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 7
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 9
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 8
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => 7
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 6
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 5
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 8
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => 6
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 5
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 4
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => 9
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => 36
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => 10
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => 10
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => 45
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => 120
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1] => 420
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => 45
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [11] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => 11
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,2] => 11
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1] => 55
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,3] => 11
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1] => 110
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1] => 165
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1,1,1] => 330
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => 2310
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1,1] => 165
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1,1] => 2310
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1,1] => 660
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1,1] => 55
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1] => 12
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2] => 12
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,1] => 66
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [9,3] => 12
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1] => 132
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1] => 220
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,4] => 12
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1] => 132
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2] => 66
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1] => 660
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1] => 495
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1,1,1] => 792
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1,1,1,1,1] => 5544
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1,1,1,1] => 495
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1,1,1,1] => 2772
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1,1,1,1] => 16632
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1,1] => 3960
[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1,1,1] => 220
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1,1,1] => 6930
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1,1,1] => 4620
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1,1,1] => 990
[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1,1,1] => 66
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,5] => 13
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [9,5] => 14
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => 7
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 429
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,8] => 8
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3] => 240
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,2] => 1430
[] => [] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1] => 271252800
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,6,5,4,3,2,1] => 106563600
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,5,4,3,2,1] => 82882800
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,5,5,4,3,2,1] => 21252000
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,4,3,2,1] => 63756000
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,4,4,3,2,1] => 16151520
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,4,4,3,2,1] => 12113640
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4,3,2,1] => 2238390
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,3,2,1] => 48454560
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,3,3,2,1] => 12113640
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,2,1] => 36340920
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,2,2,1] => 8953560
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,2,2,2,1] => 1162800
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1716
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,1] => 26860680
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 2772
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,1,1] => 6511680
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1,1,1] => 4651200
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,1,1,1] => 813960
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1,1,1] => 6930
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 1050
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1,1] => 5544
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1,1,1] => 1386
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1,1,1] => 5544
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => 1260
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 252
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1,1] => 924
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1,1] => 210
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1] => 84
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 28
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2] => 9687600
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,2] => 6188
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2,2,2] => 5005
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2] => 1287
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => 132
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1] => 2441880
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3,2,1] => 930240
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3,2,1] => 930240
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,4,3,2,1] => 697680
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,2,1] => 171360
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,3,2,1] => 514080
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,2,1] => 15015
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,2,1] => 371280
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,2,2,1] => 171360
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,2,1] => 40040
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2,1] => 15015
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => 462
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,1] => 930240
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3,1,1] => 348840
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3,1,1] => 128520
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,1] => 262080
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1] => 630
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,1,1] => 171360
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4,1,1,1] => 10010
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,1,1] => 25740
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1,1] => 15840
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1,1,1] => 4620
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,2,1,1,1] => 7920
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1] => 420
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,1,1,1] => 15015
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,5,1,1,1,1] => 5005
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1,1] => 6435
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1,1] => 1980
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1] => 2310
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,1,1,1] => 3960
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => 630
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => 140
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1] => 792
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1] => 462
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1] => 252
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1] => 126
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => 56
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => 21
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4,3] => 3876
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,3] => 6120
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3,3] => 1820
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3] => 273
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2] => 116280
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3,2] => 46512
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,2] => 9520
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3,2] => 18360
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => [4,4,3,3,2] => 10920
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,3,3,2] => 9520
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2] => 1001
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2] => 495
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2] => 330
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => 42
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,1] => 116280
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1] => 93024
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,1] => 715
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1] => 32760
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2,1] => 12012
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,3,2,1] => 12012
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,3,2,1] => 8580
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1] => 1980
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,2,1] => 12012
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,2,1] => 8580
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,1] => 5940
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => 840
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => 126
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3,1,1] => 4290
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,1] => 8580
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1] => 3960
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => 756
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => 140
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1] => 1980
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1] => 660
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,1,1] => 1980
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => 840
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => 252
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,1,1] => 1980
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => 840
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => 280
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => 70
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1] => 330
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1] => 210
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => 126
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => 15
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4] => 140
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3] => 4896
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0] => [5,5,4,3] => 2040
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,4,3] => 2040
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3] => 455
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [5,5,3,3] => 840
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3] => 286
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2] => 2184
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [4,4,3,2] => 858
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [4,4,2,2] => 330
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => 180
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2] => 165
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1] => 3360
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1] => 1716
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => 495
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => 120
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1] => 1320
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2,1] => 495
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1] => 1320
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => 990
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 720
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => 252
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => 252
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => 168
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => 35
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => 252
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => 84
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => 168
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => 105
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => 30
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1] => 120
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => 84
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => 56
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => 35
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => 20
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => 10
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5] => 35
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [5,4,4] => 78
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4] => 22
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3] => 210
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => 132
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => 55
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3] => 66
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => 45
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => 12
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2] => 132
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2] => 110
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => 45
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => 90
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => 72
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => 28
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [7,2,2] => 55
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => 28
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => 21
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => 5
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [6,6,1] => 78
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1] => 132
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => 90
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => 36
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => 90
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => 72
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => 56
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => 21
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => 90
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => 72
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => 56
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => 42
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 30
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => 10
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => 36
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => 28
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => 15
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => 10
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => 6
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6] => 13
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,5] => 12
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => 5
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => 4
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => 10
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => 7
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => 3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => 9
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => 6
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => 5
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => 8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => 6
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => 5
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => 4
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 3
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,3,3,2,1] => 1710072000
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,2,2,1] => 1311055200
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,1,1] => 994593600
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3,2] => 38760
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3,3] => 1428
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,4,4,4,4] => 969
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,5,5,5] => 285
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,6,6] => 51
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,3,3,3] => 7752
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4,4,4] => 7084
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [4,4,3,2,1] => 12012
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2] => 2184
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,5,4,3,2,1] => 930240
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,5,4,3,2,1] => 930240
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2] => 116280
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2] => 116280
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => 1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => 10
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => 5
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => 9
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => 1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1] => 2441880
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3,3,3] => 67830
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,3,3,3,3] => 11628
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => 10
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1] => 110
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => 2310
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => 45
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1] => 271252800
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2] => 9687600
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => 2
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => 3
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => 12
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [4,4,4] => 22
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4] => 140
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,5,5,5] => 285
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,7,5,3,1] => 303600
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [11,9,7,5,3,1] => 45239040
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [] => 1
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,2,2] => 4862
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => 6
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => 36
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1] => 45
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => 120
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1] => 420
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,9] => 9
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1] => 32760
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => 72
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [6,6,6] => 51
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [6,6] => 6
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => 21
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1] => 56
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1] => 126
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,1,1,1,1] => 252
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => 3
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [6,6,5,4,3,2,1] => 106563600
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => 720
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 30
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [7,2,1] => 90
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => 1260
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0,0] => [8,2,1] => 110
[1,1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => 2310
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,4,4,3,2,1] => 171360
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,2,1] => 15015
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 1716
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [7,7] => 7
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4,4] => 969
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,3,3] => 1428
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 429
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1,1,1] => 330
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,1,1,1,1,1] => 462
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,1,1,1,1] => 462
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,1,1,1] => 330
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1] => 165
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,1] => 262080
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1] => 990
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,1] => 1320
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,1] => 1716
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,1] => 271252800
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => 4
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => 6
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [5,4,4,3,2,1] => 697680
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => 462
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,3,2,1] => 1320
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1,1] => 15840
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,1] => 262080
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [4,3,3,2,1] => 8580
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,2,1] => 5940
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,1] => 3960
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [5,5,4,3,2] => 46512
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1] => 2441880
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1] => 132
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => 90
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => 56
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => 5
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,1] => 93024
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [6,5,5,4,3,2,1] => 82882800
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [6,5,5,4,3,2,1] => 82882800
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => 132
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => 8
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => 7
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => 6
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => 5
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => 10
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1] => 15
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 28
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3] => 4896
[1,1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,1,1] => 930240
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1] => 6
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => 168
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => [7,5,3,1] => 3360
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [5,5,5,4,3,2,1] => 21252000
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [8,6,4,2] => 6840
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [10,8,6,4,2] => 657720
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => 10
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [5,5,5,4,3,2,1] => 21252000
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => 30
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => 105
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1] => 32760
[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,3,3,3,3,3] => 11628
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,2,1,1,1] => 18480
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,3,3,3,2,1] => 87360
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,2,2,1] => 40040
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [6,6,5,4,3,2,1] => 106563600
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [5,4,4,4,3,2,1] => 12113640
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => 3
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2] => 6840
[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,3,3,3,3,3,2] => 38760
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1] => 9
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => 8
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1,1,1,1] => 15015
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => 7
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => 6
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => 5
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => 5
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => 4
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => 72
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => 35
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => 28
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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:
4,0,1 6,1,1,1,1,1,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 4\ q + q^{3}$
$F_{4} = 6\ q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + 2\ q^{10} + q^{30}$
$F_{5} = 8\ q + q^{2} + 2\ q^{3} + q^{4} + 3\ q^{5} + 2\ q^{6} + q^{7} + 3\ q^{10} + q^{15} + q^{20} + 2\ q^{21} + 2\ q^{28} + 2\ q^{30} + 2\ q^{35} + q^{42} + q^{56} + q^{72} + q^{84} + q^{105} + 2\ q^{168} + 3\ q^{252} + q^{720}$
$F_{6} = 10\ q + q^{2} + 2\ q^{3} + 2\ q^{4} + 3\ q^{5} + 3\ q^{6} + 2\ q^{7} + q^{8} + q^{9} + 3\ q^{10} + q^{12} + q^{14} + 2\ q^{15} + q^{20} + 3\ q^{21} + 2\ q^{28} + 2\ q^{30} + 3\ q^{35} + 2\ q^{36} + q^{42} + 2\ q^{45} + 2\ q^{55} + 3\ q^{56} + 2\ q^{70} + 2\ q^{72} + 2\ q^{84} + 2\ q^{90} + q^{105} + q^{110} + 2\ q^{120} + 2\ q^{126} + q^{132} + q^{140} + 2\ q^{165} + 2\ q^{168} + 2\ q^{180} + 5\ q^{252} + q^{280} + q^{330} + 2\ q^{360} + 4\ q^{495} + q^{504} + 6\ q^{660} + q^{720} + q^{756} + 3\ q^{840} + 3\ q^{858} + q^{990} + 2\ q^{1260} + 3\ q^{1320} + q^{1716} + 5\ q^{1980} + q^{2184} + 2\ q^{2970} + q^{3960} + 3\ q^{4290} + 2\ q^{5940} + 3\ q^{8580} + 4\ q^{12012} + q^{32760}$
Description
The Kreweras number of an integer partition.
This is defined for $\lambda \vdash n$ with $k$ parts as
$$\frac{1}{n+1}\binom{n+1}{n+1-k,\mu_1(\lambda),\ldots,\mu_n(\lambda)}$$
where $\mu_j(\lambda)$ denotes the number of parts of $\lambda$ equal to $j$, see [1]. This formula indeed counts the number of noncrossing set partitions where the ordered block sizes are the partition $\lambda$.
These numbers refine the Narayana numbers $N(n,k) = \frac{1}{k}\binom{n-1}{k-1}\binom{n}{k-1}$ and thus sum up to the Catalan numbers $\frac{1}{n+1}\binom{2n}{n}$.
This is defined for $\lambda \vdash n$ with $k$ parts as
$$\frac{1}{n+1}\binom{n+1}{n+1-k,\mu_1(\lambda),\ldots,\mu_n(\lambda)}$$
where $\mu_j(\lambda)$ denotes the number of parts of $\lambda$ equal to $j$, see [1]. This formula indeed counts the number of noncrossing set partitions where the ordered block sizes are the partition $\lambda$.
These numbers refine the Narayana numbers $N(n,k) = \frac{1}{k}\binom{n-1}{k-1}\binom{n}{k-1}$ and thus sum up to the Catalan numbers $\frac{1}{n+1}\binom{2n}{n}$.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
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