Identifier
Values
[1,0] => [] => 1
[1,0,1,0] => [1] => 4
[1,1,0,0] => [] => 1
[1,0,1,0,1,0] => [2,1] => 20
[1,0,1,1,0,0] => [1,1] => 6
[1,1,0,0,1,0] => [2] => 10
[1,1,0,1,0,0] => [1] => 4
[1,1,1,0,0,0] => [] => 1
[1,0,1,0,1,0,1,0] => [3,2,1] => 64
[1,0,1,0,1,1,0,0] => [2,2,1] => 20
[1,0,1,1,0,0,1,0] => [3,1,1] => 36
[1,0,1,1,0,1,0,0] => [2,1,1] => 15
[1,0,1,1,1,0,0,0] => [1,1,1] => 4
[1,1,0,0,1,0,1,0] => [3,2] => 60
[1,1,0,0,1,1,0,0] => [2,2] => 20
[1,1,0,1,0,0,1,0] => [3,1] => 45
[1,1,0,1,0,1,0,0] => [2,1] => 20
[1,1,0,1,1,0,0,0] => [1,1] => 6
[1,1,1,0,0,0,1,0] => [3] => 20
[1,1,1,0,0,1,0,0] => [2] => 10
[1,1,1,0,1,0,0,0] => [1] => 4
[1,1,1,1,0,0,0,0] => [] => 1
[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 64
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 20
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => 36
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 15
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 4
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 60
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 20
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => 45
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 20
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 6
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 20
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 10
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 4
[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] => 140
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 45
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 84
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => 36
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 10
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => 175
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => 60
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => 140
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 64
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => 20
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => 70
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => 36
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => 15
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => 4
[1,1,1,0,0,0,1,0,1,0] => [4,3] => 140
[1,1,1,0,0,0,1,1,0,0] => [3,3] => 50
[1,1,1,0,0,1,0,0,1,0] => [4,2] => 126
[1,1,1,0,0,1,0,1,0,0] => [3,2] => 60
[1,1,1,0,0,1,1,0,0,0] => [2,2] => 20
[1,1,1,0,1,0,0,0,1,0] => [4,1] => 84
[1,1,1,0,1,0,0,1,0,0] => [3,1] => 45
[1,1,1,0,1,0,1,0,0,0] => [2,1] => 20
[1,1,1,0,1,1,0,0,0,0] => [1,1] => 6
[1,1,1,1,0,0,0,0,1,0] => [4] => 35
[1,1,1,1,0,0,0,1,0,0] => [3] => 20
[1,1,1,1,0,0,1,0,0,0] => [2] => 10
[1,1,1,1,0,1,0,0,0,0] => [1] => 4
[1,1,1,1,1,0,0,0,0,0] => [] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [4,3,2,2,1] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [3,3,2,2,1] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [5,2,2,2,1] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [4,3,3,1,1] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [4,4,2,1,1] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,1] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,1] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,2,2,1,1] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [5,4,1,1,1] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [5,3,1,1,1] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 0
[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [4,3,3,2] => 15
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => 4
[1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 20
[1,1,0,0,1,1,0,1,0,0,1,0] => [5,3,2,2] => 45
[1,1,0,0,1,1,0,1,0,1,0,0] => [4,3,2,2] => 20
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => 6
>>> Load all 875 entries. <<<
[1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 20
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => 10
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => 4
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [4,4,3,1] => 45
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,3,1] => 84
[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => 36
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => 10
[1,1,0,1,0,1,0,0,1,0,1,0] => [5,4,2,1] => 175
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,4,2,1] => 60
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,3,2,1] => 140
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 64
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => 20
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => 70
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => 36
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => 15
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => 4
[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => 140
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => 50
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => 126
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => 60
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => 20
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => 84
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => 45
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => 20
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => 6
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => 35
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => 20
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => 10
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => 4
[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] => 256
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 84
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 160
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => 70
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 20
[1,1,1,0,0,1,0,0,1,0,1,0] => [5,4,2] => 360
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => 126
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => 300
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 140
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => 45
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => 160
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => 84
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => 36
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => 10
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => 384
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => 140
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => 360
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 175
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => 60
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => 256
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 140
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 64
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 20
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => 120
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 70
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => 36
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 15
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => 4
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 280
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 105
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => 280
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 140
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => 50
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => 224
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => 126
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => 60
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => 20
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 140
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 84
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => 45
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 20
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => 6
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 56
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 35
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => 20
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 10
[1,1,1,1,1,0,1,0,0,0,0,0] => [1] => 4
[1,1,1,1,1,1,0,0,0,0,0,0] => [] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2,1] => 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1,1] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1,1] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1,1] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1,1] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1,1] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1,1] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1,1] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2,1] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2,1] => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2,1] => 0
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1,1] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1,1] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,1] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,1] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1,1] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1,1] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1,1] => 0
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1,1] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1,1] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [4,3,3,2] => 15
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 4
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 20
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [5,3,2,2] => 45
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,2] => 20
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 6
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => 35
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => 20
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 10
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,4,3,1] => 45
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [5,3,3,1] => 84
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 36
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 10
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1] => 175
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [4,4,2,1] => 60
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1] => 256
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1] => 140
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 64
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 20
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => 120
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 70
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => 36
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 15
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 4
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 105
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,4,1,1] => 280
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 140
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 50
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,3,1,1] => 224
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => 126
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => 60
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 20
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => 140
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 84
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 45
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 20
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 6
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => 56
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 35
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => 20
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 10
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 35
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 256
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => 84
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => 300
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => 160
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 70
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 20
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => 280
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,4,2] => 729
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,4,2] => 360
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => 126
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => 540
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => 300
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => 140
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => 45
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => 270
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => 160
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => 84
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 36
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => 10
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,5,1] => 735
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => 280
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,4,1] => 756
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 384
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => 140
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => 630
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => 360
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => 175
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => 60
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => 420
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 256
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => 140
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 64
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => 20
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => 189
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => 120
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => 70
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => 36
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => 15
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 504
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 196
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => 540
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 280
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 105
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => 480
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => 280
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => 140
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => 50
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => 360
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 224
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => 126
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 60
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => 20
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 216
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 140
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => 84
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 45
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 20
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 84
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 56
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 35
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 20
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 10
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [] => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 0
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1] => 0
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 0
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1] => 0
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1] => 0
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 0
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 0
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 0
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1] => 0
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1] => 0
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1] => 0
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1] => 0
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 0
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 0
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1] => 0
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1] => 0
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1] => 0
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 0
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 0
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1] => 0
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => 0
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => 0
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => 0
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => 0
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => 0
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => 0
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 0
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 0
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => 0
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => 0
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 0
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => 0
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1] => 0
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1] => 0
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => 0
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => 0
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 0
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1] => 0
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 0
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1] => 0
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1] => 0
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1] => 0
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => 0
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 0
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1] => 0
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1] => 0
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => 0
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => 0
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => 0
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2] => 15
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => 4
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 20
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2] => 45
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2] => 20
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 6
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => 35
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => 20
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 10
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 4
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1] => 45
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1] => 84
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => 36
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => 10
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1] => 175
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1] => 60
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1] => 256
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1] => 140
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 64
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => 20
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => 189
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => 120
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => 70
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => 36
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 15
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 4
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => 105
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1] => 280
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => 140
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 50
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1] => 360
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1] => 224
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => 126
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => 60
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 20
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => 216
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => 140
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => 84
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 45
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => 20
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 6
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => 84
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => 56
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => 35
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => 20
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => 10
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 35
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => 256
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => 84
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => 300
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => 160
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 70
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 20
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => 280
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [6,4,2] => 729
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,4,2] => 360
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => 126
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,3,2] => 875
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => 540
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => 300
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 140
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => 45
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => 420
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => 270
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => 160
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => 84
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 36
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => 10
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,1] => 735
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => 280
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,4,1] => 1280
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [6,4,1] => 756
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => 384
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => 140
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,3,1] => 1000
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => 630
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => 360
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 175
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => 60
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 640
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 420
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => 256
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => 140
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 64
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => 20
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => 280
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 189
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => 120
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => 70
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => 36
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => 15
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 336
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => 945
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 504
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => 196
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => 900
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => 540
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 280
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => 105
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => 750
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 480
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => 280
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 140
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => 50
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 540
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 360
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => 224
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 126
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 60
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 20
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 315
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 216
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => 140
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 84
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 45
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 20
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 120
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 84
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 56
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 35
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 20
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 10
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => 4
[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] => 165
[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] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 220
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => 440
[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] => 0
[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] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 286
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => 594
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => 770
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => 396
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 364
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => 780
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,2] => 1056
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1] => 540
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,3] => 1100
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1] => 924
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1] => 120
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 1001
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2] => 1404
[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] => 715
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [9,3] => 1540
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1] => 1280
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1] => 165
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,4] => 1375
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1] => 1485
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2] => 616
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1] => 315
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[] => [] => 1
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => 0
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => 0
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1] => 0
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1,1] => 0
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1,1,1] => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,2,1,1,1] => 0
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1] => 0
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 0
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2] => 0
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2] => 0
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => 0
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1] => 0
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,2,1] => 0
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => 0
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => 0
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,1] => 0
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => 0
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => 0
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,1,1] => 0
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1] => 0
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,1,1] => 0
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => 0
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => 0
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,1,1] => 0
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => 0
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => 0
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1] => 0
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => 0
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => 0
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => 0
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [4,4,2,2] => 20
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => 6
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2] => 20
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => 36
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => 10
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1] => 175
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2,1] => 60
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [6,3,2,1] => 256
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1] => 140
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 64
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => 20
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => 36
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => 15
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => 4
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => 60
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => 20
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => 45
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => 20
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => 6
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1] => 84
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => 56
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => 35
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => 20
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => 10
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => 4
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4] => 35
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => 256
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => 84
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3] => 300
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => 70
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => 20
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2] => 729
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2] => 360
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => 126
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => 300
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => 140
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => 45
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [7,2,2] => 420
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => 84
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => 36
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => 10
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1] => 735
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => 384
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => 140
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => 630
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => 360
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => 175
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => 60
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => 640
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => 420
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => 256
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => 140
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 64
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => 20
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => 280
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => 189
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => 70
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => 36
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => 15
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => 336
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,5] => 945
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => 196
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => 105
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => 750
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => 140
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => 50
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => 540
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => 126
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => 60
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => 20
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => 315
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => 216
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => 140
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => 84
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => 45
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 20
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 120
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => 84
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => 56
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => 35
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => 20
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 10
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => 4
[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] => 6
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => 10
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => 6
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => 20
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => 60
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => 10
[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] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 165
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => 220
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => 440
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => 4
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => 4
[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] => 0
[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] => 0
[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] => 0
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => 4
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => 120
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => 84
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => 56
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => 35
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => 20
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => 594
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1] => 924
[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] => 0
[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] => 0
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => 20
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => 50
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => 20
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [4,4,4] => 35
[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] => 15
[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] => 0
[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] => 0
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1] => 396
[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] => 0
[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] => 0
[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] => 0
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => 140
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => 45
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [6,6] => 336
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => 20
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => 20
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => 64
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 64
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => 20
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [7,2,1] => 640
[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] => 0
[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] => 924
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[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] => 0
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1] => 120
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [5,3,2,1] => 140
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,1] => 175
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => 45
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => 126
[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] => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,3,2,1] => 256
[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] => 0
[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] => 0
[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] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [6,5,1] => 735
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => 384
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => 175
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => 10
[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] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => 315
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => 216
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => 140
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => 84
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => 4
[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] => 0
[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] => 0
[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] => 15
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => 15
[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] => 4
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => 36
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => 6
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => 20
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => 20
[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] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => 50
[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] => 20
[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] => 6
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1] => 440
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => 315
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => 216
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => 140
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => 84
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => 196
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => 105
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => 360
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => 4
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => 45
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Description
The number of semistandard Young tableau of given shape, with entries at most 4.
This is also the dimension of the corresponding irreducible representation of $GL_4$.
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 $(n-1,\ldots,2,1)$.