Identifier
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] => 60
[1,0,1,0,1,1,0,0] => [2,2,1] => 15
[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] => 10
[1,1,0,0,1,1,0,0] => [2,2] => 3
[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] => 12600
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 2520
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => 1890
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 840
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 105
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 1260
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 280
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => 420
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 210
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 45
[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] => 1260
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 280
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 210
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => 105
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 15
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => 280
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => 70
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => 105
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 60
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => 15
[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] => 35
[1,1,1,0,0,0,1,1,0,0] => [3,3] => 10
[1,1,1,0,0,1,0,0,1,0] => [4,2] => 15
[1,1,1,0,0,1,0,1,0,0] => [3,2] => 10
[1,1,1,0,0,1,1,0,0,0] => [2,2] => 3
[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
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 12600
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 945
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => 12600
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => 9450
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => 3780
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => 420
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 4200
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => 840
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => 2520
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 1260
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 560
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 105
[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
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => 6300
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => 3150
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => 1260
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 105
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => 2800
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 12600
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => 2520
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => 3780
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => 1890
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => 840
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => 105
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => 1575
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => 2520
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => 1260
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => 280
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => 756
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => 420
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => 210
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => 45
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => 56
>>> Load all 581 entries. <<<
[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
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => 2100
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 280
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => 1575
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => 2520
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 1260
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => 280
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => 378
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => 210
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => 105
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => 15
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => 1260
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => 315
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => 504
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 280
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => 70
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => 168
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 105
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 60
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 15
[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] => 126
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 35
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => 56
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 35
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => 10
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => 21
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => 15
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => 10
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => 3
[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
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 4725
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 12600
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 1260
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 2100
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => 3150
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 1260
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 210
[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
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 945
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 12600
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 945
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 12600
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 9450
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 3780
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 420
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => 4200
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 840
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => 2520
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => 1260
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 560
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 105
[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
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 6300
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 3150
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 1260
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 105
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 2800
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 12600
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 2520
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 3780
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => 1890
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 840
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 105
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 1575
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => 2520
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => 1260
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 280
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => 1260
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 756
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 420
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 210
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 45
[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
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 2100
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 280
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => 1575
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => 2520
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => 1260
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => 280
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => 630
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => 378
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => 210
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 105
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => 15
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 1260
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => 315
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => 840
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => 504
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => 280
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => 70
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => 252
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 168
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => 105
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 60
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => 15
[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
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 126
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => 210
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 126
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 35
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => 84
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => 56
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => 35
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => 10
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => 28
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 21
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => 15
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 10
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => 3
[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
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 3150
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => 2520
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 378
[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
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 4725
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 12600
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 1260
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 2100
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => 3150
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => 1260
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 210
[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
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 945
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => 12600
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 945
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 12600
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => 9450
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 3780
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 420
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => 4200
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 840
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => 2520
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 1260
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 560
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 105
[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
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 6300
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 3150
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 1260
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 105
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => 2800
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 12600
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => 2520
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => 3780
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => 1890
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 840
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 105
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 1575
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => 2520
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => 1260
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 280
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => 1260
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => 756
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 420
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => 210
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 45
[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
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 2100
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 280
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => 1575
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => 2520
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 1260
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => 280
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => 630
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => 378
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => 210
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 105
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => 15
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => 1260
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => 315
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => 840
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => 504
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 280
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => 70
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 360
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 252
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => 168
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => 105
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 60
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => 15
[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
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => 126
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => 210
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 126
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => 35
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => 120
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 84
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => 56
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 35
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => 10
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 36
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 28
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => 21
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 15
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 10
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 3
[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] => 45
[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] => 630
[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
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 3150
[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] => 2520
[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] => 378
[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
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1] => 4725
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1] => 1260
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => 1260
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => 210
[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
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => 945
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => 12600
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => 945
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => 3780
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => 420
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => 4200
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => 840
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => 2520
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => 560
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => 105
[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
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => 6300
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => 2800
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 12600
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => 2520
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => 1890
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => 840
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => 105
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => 1260
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => 280
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => 420
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => 210
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => 45
[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
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => 2100
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => 280
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => 1575
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => 2520
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => 1260
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => 280
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => 210
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => 105
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => 15
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => 1260
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => 315
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => 840
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => 504
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => 280
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => 70
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => 360
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => 252
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => 168
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => 105
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 60
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => 15
[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
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => 126
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => 35
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => 120
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => 35
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => 10
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => 36
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => 15
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => 10
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => 3
[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
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [] => 1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [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] => 15
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => 10
[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
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [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
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [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
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => 45
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => 3
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => 10
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => 280
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [] => 1
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [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] => 630
[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
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => 1260
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => 4
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [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
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => 12600
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 60
[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] => 360
[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] => 2520
[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] => 15
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => 1260
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => 280
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => 15
[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
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [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] => 840
[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
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => 10
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => 45
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => 210
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => 3
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => 10
[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
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [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
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [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] => 126
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => 35
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => 504
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => 105
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => 280
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Description
The number of set partitions whose sorted block sizes correspond to the partition.
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 $(n-1,\ldots,2,1)$.