Identifier
-
Mp00100:
Dyck paths
—touch composition⟶
Integer compositions
St000383: Integer compositions ⟶ ℤ
Values
[1,0] => [1] => 1
[1,0,1,0] => [1,1] => 1
[1,1,0,0] => [2] => 2
[1,0,1,0,1,0] => [1,1,1] => 1
[1,0,1,1,0,0] => [1,2] => 2
[1,1,0,0,1,0] => [2,1] => 1
[1,1,0,1,0,0] => [3] => 3
[1,1,1,0,0,0] => [3] => 3
[1,0,1,0,1,0,1,0] => [1,1,1,1] => 1
[1,0,1,0,1,1,0,0] => [1,1,2] => 2
[1,0,1,1,0,0,1,0] => [1,2,1] => 1
[1,0,1,1,0,1,0,0] => [1,3] => 3
[1,0,1,1,1,0,0,0] => [1,3] => 3
[1,1,0,0,1,0,1,0] => [2,1,1] => 1
[1,1,0,0,1,1,0,0] => [2,2] => 2
[1,1,0,1,0,0,1,0] => [3,1] => 1
[1,1,0,1,0,1,0,0] => [4] => 4
[1,1,0,1,1,0,0,0] => [4] => 4
[1,1,1,0,0,0,1,0] => [3,1] => 1
[1,1,1,0,0,1,0,0] => [4] => 4
[1,1,1,0,1,0,0,0] => [4] => 4
[1,1,1,1,0,0,0,0] => [4] => 4
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => 2
[1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,1,3] => 3
[1,0,1,0,1,1,1,0,0,0] => [1,1,3] => 3
[1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,2,2] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,3,1] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,4] => 4
[1,0,1,1,0,1,1,0,0,0] => [1,4] => 4
[1,0,1,1,1,0,0,0,1,0] => [1,3,1] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,4] => 4
[1,0,1,1,1,0,1,0,0,0] => [1,4] => 4
[1,0,1,1,1,1,0,0,0,0] => [1,4] => 4
[1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,2] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,2,1] => 1
[1,1,0,0,1,1,0,1,0,0] => [2,3] => 3
[1,1,0,0,1,1,1,0,0,0] => [2,3] => 3
[1,1,0,1,0,0,1,0,1,0] => [3,1,1] => 1
[1,1,0,1,0,0,1,1,0,0] => [3,2] => 2
[1,1,0,1,0,1,0,0,1,0] => [4,1] => 1
[1,1,0,1,0,1,0,1,0,0] => [5] => 5
[1,1,0,1,0,1,1,0,0,0] => [5] => 5
[1,1,0,1,1,0,0,0,1,0] => [4,1] => 1
[1,1,0,1,1,0,0,1,0,0] => [5] => 5
[1,1,0,1,1,0,1,0,0,0] => [5] => 5
[1,1,0,1,1,1,0,0,0,0] => [5] => 5
[1,1,1,0,0,0,1,0,1,0] => [3,1,1] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,2] => 2
[1,1,1,0,0,1,0,0,1,0] => [4,1] => 1
[1,1,1,0,0,1,0,1,0,0] => [5] => 5
[1,1,1,0,0,1,1,0,0,0] => [5] => 5
[1,1,1,0,1,0,0,0,1,0] => [4,1] => 1
[1,1,1,0,1,0,0,1,0,0] => [5] => 5
[1,1,1,0,1,0,1,0,0,0] => [5] => 5
[1,1,1,0,1,1,0,0,0,0] => [5] => 5
[1,1,1,1,0,0,0,0,1,0] => [4,1] => 1
[1,1,1,1,0,0,0,1,0,0] => [5] => 5
[1,1,1,1,0,0,1,0,0,0] => [5] => 5
[1,1,1,1,0,1,0,0,0,0] => [5] => 5
[1,1,1,1,1,0,0,0,0,0] => [5] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,3] => 3
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,3,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,4] => 4
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,4] => 4
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,4] => 4
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,4] => 4
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => 4
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,4,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,5] => 5
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,5] => 5
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,4,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,5] => 5
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,5] => 5
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,5] => 5
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,5] => 5
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,5] => 5
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5] => 5
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,5] => 5
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,5] => 5
>>> Load all 1885 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5] => 5
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5] => 5
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5] => 5
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,4] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,4] => 4
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4] => 4
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,4] => 4
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4] => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,2] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,3] => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [4,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,2] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [6] => 6
[1,1,0,1,0,1,0,1,1,0,0,0] => [6] => 6
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [6] => 6
[1,1,0,1,0,1,1,0,1,0,0,0] => [6] => 6
[1,1,0,1,0,1,1,1,0,0,0,0] => [6] => 6
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,2] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [6] => 6
[1,1,0,1,1,0,0,1,1,0,0,0] => [6] => 6
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [6] => 6
[1,1,0,1,1,0,1,0,1,0,0,0] => [6] => 6
[1,1,0,1,1,0,1,1,0,0,0,0] => [6] => 6
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [6] => 6
[1,1,0,1,1,1,0,0,1,0,0,0] => [6] => 6
[1,1,0,1,1,1,0,1,0,0,0,0] => [6] => 6
[1,1,0,1,1,1,1,0,0,0,0,0] => [6] => 6
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,3] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,2] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [6] => 6
[1,1,1,0,0,1,0,1,1,0,0,0] => [6] => 6
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [6] => 6
[1,1,1,0,0,1,1,0,1,0,0,0] => [6] => 6
[1,1,1,0,0,1,1,1,0,0,0,0] => [6] => 6
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [6] => 6
[1,1,1,0,1,0,0,1,1,0,0,0] => [6] => 6
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [6] => 6
[1,1,1,0,1,0,1,0,1,0,0,0] => [6] => 6
[1,1,1,0,1,0,1,1,0,0,0,0] => [6] => 6
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [6] => 6
[1,1,1,0,1,1,0,0,1,0,0,0] => [6] => 6
[1,1,1,0,1,1,0,1,0,0,0,0] => [6] => 6
[1,1,1,0,1,1,1,0,0,0,0,0] => [6] => 6
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,2] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [6] => 6
[1,1,1,1,0,0,0,1,1,0,0,0] => [6] => 6
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [6] => 6
[1,1,1,1,0,0,1,0,1,0,0,0] => [6] => 6
[1,1,1,1,0,0,1,1,0,0,0,0] => [6] => 6
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [6] => 6
[1,1,1,1,0,1,0,0,1,0,0,0] => [6] => 6
[1,1,1,1,0,1,0,1,0,0,0,0] => [6] => 6
[1,1,1,1,0,1,1,0,0,0,0,0] => [6] => 6
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [6] => 6
[1,1,1,1,1,0,0,0,1,0,0,0] => [6] => 6
[1,1,1,1,1,0,0,1,0,0,0,0] => [6] => 6
[1,1,1,1,1,0,1,0,0,0,0,0] => [6] => 6
[1,1,1,1,1,1,0,0,0,0,0,0] => [6] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,2] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,2,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,3] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,3] => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,2,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,3,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,4] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,4] => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,3,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,4] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,4] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,4] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,2,1,2] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,2,3] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,3] => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,3,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,3,2] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,4,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,5] => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,5] => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,4,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,5] => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,5] => 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,5] => 5
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,3,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,3,2] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,4,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,5] => 5
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,5] => 5
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,4,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,5] => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,5] => 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,5] => 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,4,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,5] => 5
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,5] => 5
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,5] => 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,2] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,3] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,3,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4] => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,3,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4] => 4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4] => 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4] => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,1,2] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,2,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,3] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,3] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,4,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,4,2] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,6] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,6] => 6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,6] => 6
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,6] => 6
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,6] => 6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,4,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,4,2] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,6] => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,6] => 6
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,6] => 6
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,6] => 6
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,6] => 6
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,6] => 6
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,6] => 6
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,6] => 6
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,6] => 6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,1,2] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,3] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,6] => 6
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,6] => 6
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,6] => 6
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,6] => 6
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,6] => 6
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,2] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,6] => 6
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,6] => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6] => 6
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,6] => 6
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,6] => 6
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6] => 6
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,6] => 6
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,6] => 6
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,6] => 6
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,4,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,6] => 6
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,6] => 6
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6] => 6
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,6] => 6
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,6] => 6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6] => 6
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,6] => 6
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,6] => 6
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,6] => 6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,5,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6] => 6
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6] => 6
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6] => 6
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,6] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,3] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,4] => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,4] => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,4] => 4
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4] => 4
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,1,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,3] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,3,2] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,4,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,5] => 5
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,5] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,5] => 5
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,5] => 5
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,5] => 5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,5] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,5] => 5
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,4,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,5] => 5
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,5] => 5
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,5] => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,5] => 5
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,5] => 5
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,5] => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,4] => 4
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,4] => 4
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,4] => 4
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,4] => 4
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [4,3] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,3] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,2] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [6,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7] => 7
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7] => 7
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7] => 7
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,2] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7] => 7
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7] => 7
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7] => 7
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [7] => 7
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [7] => 7
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7] => 7
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [7] => 7
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [7] => 7
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [7] => 7
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,3] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,2] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7] => 7
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7] => 7
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7] => 7
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [7] => 7
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [7] => 7
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,2] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7] => 7
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7] => 7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7] => 7
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [7] => 7
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [7] => 7
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7] => 7
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [7] => 7
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [7] => 7
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [7] => 7
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,2] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7] => 7
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [7] => 7
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7] => 7
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [7] => 7
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7] => 7
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [7] => 7
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [7] => 7
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7] => 7
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7] => 7
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7] => 7
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [7] => 7
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [7] => 7
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [7] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [7] => 7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4] => 4
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4] => 4
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4] => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [4,3] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,3] => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,2] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7] => 7
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [7] => 7
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7] => 7
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [7] => 7
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [7] => 7
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7] => 7
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7] => 7
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7] => 7
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [7] => 7
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [7] => 7
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7] => 7
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [7] => 7
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [7] => 7
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [7] => 7
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,3] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,3] => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7] => 7
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [7] => 7
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [7] => 7
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [7] => 7
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [7] => 7
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7] => 7
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [7] => 7
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7] => 7
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7] => 7
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7] => 7
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7] => 7
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7] => 7
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7] => 7
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [7] => 7
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [7] => 7
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7] => 7
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7] => 7
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7] => 7
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7] => 7
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7] => 7
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7] => 7
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7] => 7
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [7] => 7
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7] => 7
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7] => 7
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7] => 7
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7] => 7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7] => 7
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [7] => 7
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7] => 7
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [7] => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7] => 7
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,2] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7] => 7
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [7] => 7
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7] => 7
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7] => 7
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7] => 7
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7] => 7
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7] => 7
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7] => 7
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7] => 7
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,2] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7] => 7
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [7] => 7
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7] => 7
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7] => 7
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7] => 7
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7] => 7
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7] => 7
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7] => 7
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7] => 7
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [7] => 7
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7] => 7
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7] => 7
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7] => 7
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7] => 7
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,2] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7] => 7
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [7] => 7
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7] => 7
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7] => 7
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7] => 7
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7] => 7
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7] => 7
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7] => 7
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7] => 7
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7] => 7
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7] => 7
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7] => 7
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7] => 7
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7] => 7
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7] => 7
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7] => 7
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7] => 7
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,2,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,2,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,3,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,3,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,2,1,2] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,3,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,3,2] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,3,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,3,2] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,2,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,2,2,2] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,2,3,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,2,3,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,3,3] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,3,3] => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,3,3] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,3,3] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,3,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,4] => 4
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,4] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,1,4] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,4] => 4
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,3] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,3] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,2] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,2] => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,4,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,4,1] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,1,3] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,3,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,4,1,2] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,4,2,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,4,3] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,4,3] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,5,2] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,7] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,5,2] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,7] => 7
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,5,2] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,5,2] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2] => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,7] => 7
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,3,1,3] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,3,3,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,1,2] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,3] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,5,2] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,5,2] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,3] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,3] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,5,2] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2] => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,4,3] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,4,3] => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,5,2] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,2] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,5,2] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,6,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7] => 7
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7] => 7
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,7] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,3,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,3] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,3,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,2] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,1] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,1] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,1] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,2,1,3] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,3,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,2] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,2,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,3] => 3
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,3] => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,2] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,2] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,3] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,3] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,4,2] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,4,2] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,2] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,3,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,3] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,3,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,3,2] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,4,1] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,4,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,4,1] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,4,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [4,4] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4] => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [4,4] => 4
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,4] => 4
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => 4
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => 4
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => 4
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,3,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,3] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,3,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,3,2] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,4,1] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,4,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,4,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,4,1] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [4,4] => 4
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,4] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [4,4] => 4
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4] => 4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => 4
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => 4
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => 4
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => 4
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,8] => 8
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,9] => 9
[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
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,10] => 10
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,10] => 10
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [10,1] => 1
[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
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,10] => 10
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,10] => 10
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,10] => 10
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,10] => 10
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10] => 10
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10] => 10
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [8,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,7,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10] => 10
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [9,1] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,7,1] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10] => 10
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,8,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,1] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,7,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,8] => 8
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10] => 10
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,8] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,8] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,9] => 9
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,8] => 8
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,9] => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,10] => 10
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,8] => 8
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,9] => 9
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,8] => 8
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,8] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,8] => 8
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,8] => 8
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,8] => 8
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,8] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,8] => 8
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,9] => 9
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,9] => 9
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,4,1] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,6,1] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,5,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,4,1,3] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,6,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,6,2] => 2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,5,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,1,2,2] => 2
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,5,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,2,2,2,2] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,4,4] => 4
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,7,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [1,5,1,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,7,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,1,2] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,1,1,2,1,1] => 1
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,6,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,2,1,1,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,2,2,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,2,3,3] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,2,3] => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,3,2,2] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,1,4] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [4,4,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,5] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,8] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,8] => 8
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,4,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [9,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,9] => 9
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,9] => 9
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,9] => 9
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,9] => 9
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,9] => 9
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [1,9] => 9
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,9] => 9
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,9] => 9
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,9] => 9
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,9] => 9
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [5,5] => 5
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [5,5] => 5
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,5] => 5
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,5] => 5
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [9,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => [9,1] => 1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => [9,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => [9,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [9,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => [9,1] => 1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [9,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => [9,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => [9,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [9,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,8] => 8
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,4,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,8] => 8
[1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,8] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,6,2] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,7,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,7,1] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,10] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,4,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,6,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,7,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [9,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [9,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [9,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [9,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,1,3,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,10] => 10
[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,9] => 9
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,9] => 9
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,4,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,5,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,2,4,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,8] => 8
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,8] => 8
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,6,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,7,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,7,1] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,8] => 8
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,5,1,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,1] => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,7,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,5,1,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,9] => 9
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [9,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,5,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,6,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,6,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [8,1,1] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [1,9] => 9
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,4,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,8] => 8
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,8] => 8
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,1,0,0,0] => [5,5] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,1,0,0,0,0] => [5,5] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,9] => 9
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,8] => 8
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,8] => 8
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,9] => 9
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,8] => 8
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,6,1,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,8] => 8
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,8] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,8] => 8
[1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,6,2] => 2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,6,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,6,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,6,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,8,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,7,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,2,1,3,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,1,1,2,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,6,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,6] => 6
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,6] => 6
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,4] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,2,4,4] => 4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,6] => 6
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,6] => 6
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,8,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,8] => 8
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,8] => 8
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,7,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,4,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,9] => 9
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [1,6,1,2] => 2
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,9] => 9
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,9] => 9
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,9] => 9
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,9] => 9
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,9] => 9
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,9] => 9
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,6,1,2] => 2
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,9] => 9
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,8,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [5,5] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,8] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,9] => 9
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,8] => 8
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,9] => 9
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,10] => 10
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [1,7,1,1] => 1
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,7,1] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,8,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,8] => 8
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,8] => 8
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,10] => 10
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,8] => 8
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,8] => 8
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,10] => 10
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,6,2] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,1,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,8,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [8,1,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,8,1] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [8,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,8,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,8] => 8
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,9] => 9
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,9] => 9
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,9] => 9
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,9] => 9
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,9] => 9
[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10] => 10
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,4,4] => 4
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,2,2,4] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,6] => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [6,6] => 6
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,6] => 6
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [6,6] => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,6,2] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,7,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,5,2,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,6,2] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,6,2,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,8] => 8
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,4,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,6,2,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8] => 8
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8] => 8
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [10,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,1] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [10,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,1] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0] => [9,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,7,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,1,7,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,7,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [1,7,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [8,1,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,9] => 9
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,9] => 9
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0] => [9,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [8,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [1,6,2] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,9] => 9
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,8] => 8
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,8] => 8
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,9] => 9
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8] => 8
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,9] => 9
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,8] => 8
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,9] => 9
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,8] => 8
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,6,2] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => 2
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,9] => 9
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,6,2,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,8] => 8
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,8] => 8
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [4,4,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,5] => 5
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0,1,0] => [9,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => [9,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,2,1,4] => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,1,3,5] => 5
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [6,6] => 6
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [6,6] => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [7,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8] => 8
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,8] => 8
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,6,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,1,1] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0,1,0] => [8,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [7,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,1,2,4] => 4
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,8,1] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,7,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,8,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,5,3,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,6,2,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,5,5] => 5
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,3,5] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,5,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [8,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,7,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,9] => 9
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,4,1,3] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,8] => 8
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,8] => 8
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,2,3] => 3
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8] => 8
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,9] => 9
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,8] => 8
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Generating function
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Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 2,1,2 5,2,2,5 14,5,4,5,14 42,14,10,10,14,42 132,42,28,25,28,42,132
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = 2\ q + q^{2} + 2\ q^{3}$
$F_{4} = 5\ q + 2\ q^{2} + 2\ q^{3} + 5\ q^{4}$
$F_{5} = 14\ q + 5\ q^{2} + 4\ q^{3} + 5\ q^{4} + 14\ q^{5}$
$F_{6} = 42\ q + 14\ q^{2} + 10\ q^{3} + 10\ q^{4} + 14\ q^{5} + 42\ q^{6}$
$F_{7} = 132\ q + 42\ q^{2} + 28\ q^{3} + 25\ q^{4} + 28\ q^{5} + 42\ q^{6} + 132\ q^{7}$
Description
The last part of an integer composition.
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touch composition
Description
Sends a Dyck path to its touch composition given by the composition of lengths of its touch points.
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