Identifier
-
Mp00102:
Dyck paths
—rise composition⟶
Integer compositions
St000657: 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] => 1
[1,1,0,0,1,0] => [2,1] => 1
[1,1,0,1,0,0] => [2,1] => 1
[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] => 1
[1,0,1,1,0,0,1,0] => [1,2,1] => 1
[1,0,1,1,0,1,0,0] => [1,2,1] => 1
[1,0,1,1,1,0,0,0] => [1,3] => 1
[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] => [2,1,1] => 1
[1,1,0,1,0,1,0,0] => [2,1,1] => 1
[1,1,0,1,1,0,0,0] => [2,2] => 2
[1,1,1,0,0,0,1,0] => [3,1] => 1
[1,1,1,0,0,1,0,0] => [3,1] => 1
[1,1,1,0,1,0,0,0] => [3,1] => 1
[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] => 1
[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] => [1,1,2,1] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,1,3] => 1
[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] => 1
[1,0,1,1,0,1,0,0,1,0] => [1,2,1,1] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,0] => [1,2,2] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,3,1] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,3,1] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,3,1] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,4] => 1
[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] => 1
[1,1,0,0,1,1,0,0,1,0] => [2,2,1] => 1
[1,1,0,0,1,1,0,1,0,0] => [2,2,1] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,3] => 2
[1,1,0,1,0,0,1,0,1,0] => [2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0] => [2,1,2] => 1
[1,1,0,1,0,1,0,0,1,0] => [2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0] => [2,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0] => [2,1,2] => 1
[1,1,0,1,1,0,0,0,1,0] => [2,2,1] => 1
[1,1,0,1,1,0,0,1,0,0] => [2,2,1] => 1
[1,1,0,1,1,0,1,0,0,0] => [2,2,1] => 1
[1,1,0,1,1,1,0,0,0,0] => [2,3] => 2
[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] => [3,1,1] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,1,1] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,2] => 2
[1,1,1,0,1,0,0,0,1,0] => [3,1,1] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,1,1] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,1,1] => 1
[1,1,1,0,1,1,0,0,0,0] => [3,2] => 2
[1,1,1,1,0,0,0,0,1,0] => [4,1] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,1] => 1
[1,1,1,1,0,0,1,0,0,0] => [4,1] => 1
[1,1,1,1,0,1,0,0,0,0] => [4,1] => 1
[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] => 1
[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] => [1,1,1,2,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => 1
[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] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,2,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,2,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,2,2] => 1
[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] => [1,1,3,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,3,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => 1
[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] => 1
[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] => [1,2,2,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,1,2] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,1,2] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,2,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,2,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3] => 1
[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] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,3,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,3,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,3,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2] => 1
>>> Load all 3514 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] => [1,4,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,4,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,4,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => 1
[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] => 1
[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] => [2,1,2,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => 1
[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] => [2,2,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2] => 2
[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] => [2,3,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,2] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,2,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,3] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,2] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,2] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,2,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,2,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,2,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,3] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,2,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,2,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,2,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,3,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,4] => 2
[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] => 1
[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] => [3,2,1] => 1
[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] => [3,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,2] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,2] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,3] => 3
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,1,2] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,1,2] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,1,2] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,2,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,2,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,2,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,3] => 3
[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] => [4,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,2] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,2] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,2] => 2
[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] => [5,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,1] => 1
[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] => 1
[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] => [1,1,1,1,2,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,3] => 1
[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] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,2,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,2,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,2,2] => 1
[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] => [1,1,1,3,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,3,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,4] => 1
[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] => 1
[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] => [1,1,2,2,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,3] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,2,1,2] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,2,1,2] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,2,2,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,2,2,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,2,2,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,2,3] => 1
[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] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,3,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,3,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,3,2] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,3,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,3,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,3,1,1] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,3,2] => 1
[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] => [1,1,4,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,4,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,4,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5] => 1
[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] => 1
[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] => [1,2,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => 1
[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] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,2,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,2,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,2,2] => 1
[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] => [1,2,3,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,3,1] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,2] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,1,2,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,2,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,3] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,2] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,2] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,2,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,2,1] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,2,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,3] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,2,2] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,2,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,2,2] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,2,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,2,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,2,1,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,2,2] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,3,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,3,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,3,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,3,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4] => 1
[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] => 1
[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] => [1,3,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,3,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,1,2] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,3,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,3,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,3,1,2] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,3,2,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,1] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,3,2,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,3] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,3,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,3,1,2] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,3,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,3,1,2] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,3,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,3,1,2] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,3,2,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,3,2,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,3,2,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,3,3] => 1
[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] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,4,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,4,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,4,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,4,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,4,1,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,4,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,4,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,4,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,4,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,4,2] => 1
[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] => [1,5,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,5,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,5,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,5,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,6] => 1
[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] => 1
[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] => [2,1,1,2,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => 1
[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] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => 1
[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] => [2,1,3,1] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => 1
[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] => 1
[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] => [2,2,2,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,2,1,2] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,2,1,2] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,2,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,2,2,1] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,2,2,1] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,2,3] => 2
[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] => [2,3,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,2] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,1] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,2] => 2
[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] => [2,4,1] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,4,1] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,4,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,2] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,2,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,2,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,3] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,2] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,2] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,2,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,2,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,2,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,3] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,2,2] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,2,2] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,2,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,2,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,2,1,1] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,2,2] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,3,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,3,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,3,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,2,1,2] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,2,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,2,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,2,3] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,2,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,2,1,2] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,2,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,2,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,2,1,2] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,2,3] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,2,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,2,1,2] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,2,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,2,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,2,1,2] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,2,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1,2] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,2,2,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,2,2,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,2,2,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,2,2,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,3] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,2] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,3,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,3,2] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,1,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,2] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,1,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,2] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,4,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,4,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,4,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,5] => 2
[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] => 1
[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] => [3,1,2,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => 1
[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] => [3,2,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,2] => 2
[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] => [3,3,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,3,1] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,1,2] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,2,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,2,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,3] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,1,2] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,1,2] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,2,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,2,1] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,2,1] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,3] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,2] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,3,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,3,1] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,3,1] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,3,1] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4] => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,2] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,3] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,2] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,1,1,2] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,2,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,1,2,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,1,2,1] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,3] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,2] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,1,1,2] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,2] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,2,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,2,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,2,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,2,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,3] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,2,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,2,2] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,2,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,2,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,2,2] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,2,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,2,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,2,1,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,2,2] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,2,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,2,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,2,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,2,2] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,3,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,3,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,3,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,3,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,3,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4] => 3
[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] => 1
[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] => [4,2,1] => 1
[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] => [4,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,2,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,2,1] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,2,1] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,2] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,2] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,2] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,2,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,2,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,1] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,2,1] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,1,2] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,1,2] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,1,2] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,1,2] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,2,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,2,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,2,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,2,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,3] => 3
[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] => [5,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,2] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,1] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,2] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,1] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,2] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,2] => 2
[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] => [6,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,1] => 1
[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
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,2] => 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
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,3] => 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] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,2,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,2,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,2,2] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,3,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,3,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,3,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,4] => 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] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,2,2,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,2,3] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,2,1,2] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,2,1,2] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,2,2,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,2,2,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,2,2,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,2,3] => 1
[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] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,3,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,3,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,3,2] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,3,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,3,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,3,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,3,2] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,4,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,4,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,4,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,4,1] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,5] => 1
[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] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,2,1,2,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,2,1,3] => 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] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,2,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,2,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,2,2,2] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,2,3,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,3,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,2,3,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,2,4] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,2,1,2,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,2,1,3] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,2,1,1,2] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,2,1,1,2] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,2,1,2,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,2,1,2,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,2,1,2,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,2,1,3] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,2,2,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,2,2,2] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,2,2,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,2,2,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,2,2,2] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,2,2,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,2,2,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,2,2,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,2,2,2] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,2,3,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,2,3,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,2,3,1] => 1
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,2,3,1] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,2,4] => 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] => 1
[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] => [1,1,3,2,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,3,3] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,3,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,3,1,2] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,3,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,3,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,3,1,2] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,3,2,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,3,2,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,3,2,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,3,3] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,3,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,3,1,2] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,3,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,3,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,3,1,2] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,3,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,3,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,3,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,3,1,2] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,3,2,1] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,3,2,1] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,3,2,1] => 1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,3,2,1] => 1
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,3,3] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,4,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,4,2] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,4,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,4,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,4,2] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,4,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,4,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,4,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,4,2] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,4,1,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,4,1,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,4,1,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,4,1,1] => 1
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,4,2] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,5,1] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,6] => 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] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => 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] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,2,2] => 1
[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] => [1,2,1,3,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,3,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => 1
[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] => 1
[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] => [1,2,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,3] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,2,1,2] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,2,2,1,2] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,2,3] => 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] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,2] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,2] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,1] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,4,1] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,4,1] => 1
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,4,1] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,5] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,2,1,2,2] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,2,1,3,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,2,1,3,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,1,3] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,1,2] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,1,2] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,1,2,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,1,2,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,1,2,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,1,3] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,2,1,2,2] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,2,1,2,2] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,2,1,2,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,2,1,2,2] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,2,1,3,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,2,1,3,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,2,1,3,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,2,1,3,1] => 1
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,2,1,4] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,2,2,2,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,2,2,3] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,2,2,1,2] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,2,2,1,2] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,2,2,2,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,2,2,2,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,2,2,2,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,2,2,3] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,2,2,1,2] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,2,2,1,2] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,2,2,1,2] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,2,2,2,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,2,2,2,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,2,2,2,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,2,2,2,1] => 1
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,2,2,3] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,2] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,2,3,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,2,3,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,2,3,2] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,2,3,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,2,3,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,2,3,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,2,3,2] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,2,3,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,2,3,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,2,3,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,2] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,2,4,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,2,4,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,2,4,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,2,4,1] => 1
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,2,4,1] => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,5] => 1
[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] => 1
[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] => [1,3,1,2,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => 1
[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] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,3,2,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,3,2,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,3,2,2] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,3,3,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,3,3,1] => 1
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,3,1,1,2] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,3,1,2,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,3,1,2,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,3,1,3] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,3,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,3,1,1,2] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,3,1,1,2] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,3,1,2,1] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,3,1,2,1] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,3,1,2,1] => 1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,3,1,3] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,3,2,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,3,2,2] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,3,2,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,3,2,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,3,2,2] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,3,2,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,3,2,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,3,2,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,3,2,2] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,3,3,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,3,3,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,3,3,1] => 1
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,3,3,1] => 1
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,3,4] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,3,1,1,2] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,3,1,2,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,3,1,2,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,3,1,3] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,3,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,3,1,1,2] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,3,1,1,2] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,3,1,2,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,3,1,2,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,3,1,2,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,3,1,3] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,3,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,3,1,1,2] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,3,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,3,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,3,1,1,2] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,3,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,3,1,1,2] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,3,1,2,1] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,3,1,2,1] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,3,1,2,1] => 1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,3,1,2,1] => 1
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,3,1,3] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,3,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,3,2,2] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,3,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,3,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,3,2,2] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,3,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,3,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,3,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,3,2,2] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,3,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,3,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,3,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,3,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,2,2] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,3,3,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,3,3,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,3,3,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,3,3,1] => 1
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,3,3,1] => 1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,3,4] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => 1
[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] => [1,4,2,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,4,3] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,4,1,2] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,4,1,2] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,4,2,1] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,4,2,1] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,4,2,1] => 1
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,4,3] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,4,1,2] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,4,1,2] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,4,1,2] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,4,2,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,4,2,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,4,2,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,4,2,1] => 1
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,4,3] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,4,1,2] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,4,1,2] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,4,1,2] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,4,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,4,1,2] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,4,2,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,4,2,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,4,2,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,4,2,1] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,4,2,1] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,4,3] => 1
[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] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,5,2] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,5,2] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,5,2] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,5,1,1] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,5,2] => 1
[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] => [1,6,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,6,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,6,1] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,6,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,6,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,7] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => 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] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => 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] => 1
[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] => [2,1,2,2,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => 1
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,2,3] => 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] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,2] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,2] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,1] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,1] => 1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,1] => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => 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] => 1
[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] => [2,2,1,2,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => 1
[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] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,3,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,2,3,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,2,1,3] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => 1
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,1,3] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,2,2,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,2,3,1] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,2,3,1] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,2,3,1] => 1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,2,3,1] => 1
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,4] => 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] => 1
[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] => [2,3,2,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,3] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,3,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,2] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,3,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,1,2] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,3,2,1] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,2,1] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,2,1] => 1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,3] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,3,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,3,1,2] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,3,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,3,1,2] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,3,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1] => 1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,1,2] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,3,2,1] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,2,1] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,2,1] => 1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,2,1] => 1
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,3] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,2] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,4,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,4,2] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,4,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,4,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,4,2] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,4,1,1] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,4,1,1] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,4,1,1] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,4,1,1] => 1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,4,2] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,5,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,5,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,5,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,5,1] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,5,1] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,6] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,2,3] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,2] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,2] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,1] => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,1,3] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,1,2] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,1,2] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,1,2,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,1,2,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,1,2,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,1,3] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,1,2,2] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,1,2,2] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,1,2,2] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,1,3,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,1,3,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,1,3,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,3,1] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,1,4] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,1,2,3] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,1,2,3] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,1,2,1,2] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,1,2,1,2] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,1,2,1,2] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,1,2,2,1] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,1,2,2,1] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,1,2,2,1] => 1
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,1,2,2,1] => 1
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,1,2,3] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,2] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,2] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,3,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,1,3,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,1,3,2] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,1,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,1,3,1,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,1,3,1,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,1,3,1,1] => 1
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,1,3,2] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,1,4,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,1,4,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,1,4,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,1,4,1] => 1
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,4,1] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,1,5] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,2,1,2,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,2,3,1] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,2,3,1] => 1
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,2,1,3] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,2,1,3] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2] => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,2,3,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,2,3,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,2,3,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,2,3,1] => 1
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,4] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,2,1,3] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => 1
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,2,1,3] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,2,1,1,2] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,2,1,1,2] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,2,1,1,2] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [2,2,1,2,1] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,2,1,2,1] => 1
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,2,1,2,1] => 1
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,2,1,2,1] => 1
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,1,3] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2] => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,2,2,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,2,3,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,2,3,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,2,3,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,2,3,1] => 1
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,2,3,1] => 1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,4] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,3,2,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,3] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,3,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,3,1,2] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,3,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,1,2] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,3,2,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,2,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,3,2,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,3] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,3,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,3,1,2] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,3,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,3,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,3,1,2] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,3,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,3,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,3,1,2] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,3,2,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,3,2,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,3,2,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,3,2,1] => 1
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,3,3] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,3,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,3,1,2] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,3,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,3,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,3,1,2] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,3,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,3,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,3,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,3,1,2] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,3,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,3,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,3,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,3,1,2] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,3,2,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,3,2,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,3,2,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,3,2,1] => 1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,3,2,1] => 1
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,3] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,4,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,4,2] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,4,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,4,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,4,2] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,4,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,4,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,4,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,4,2] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,4,1,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,4,1,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,4,1,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,4,1,1] => 1
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,4,2] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,4,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,4,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,4,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,4,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,4,1,1] => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,4,2] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,5,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,5,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,5,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,5,1] => 1
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,5,1] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,5,1] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,6] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => 1
[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] => [3,2,2,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,2,1,2] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,2] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,2,1] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,2,1] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => 1
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,3] => 2
[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] => [3,3,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,3,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,3,2] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,3,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,3,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,3,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,4,1] => 1
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,1] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,1,1,3] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => 1
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [3,1,1,3] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,2] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [3,1,2,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,1,2,2] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,1,2,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,2,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,1,2,2] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,3,1] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,1,3,1] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [3,1,3,1] => 1
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,1,3,1] => 1
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,1,4] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,2] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,2,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,2,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,3] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,1,2] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,1,2] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,2,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,2,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [3,2,3] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [3,2,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,1,2] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [3,2,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [3,2,1,2] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [3,2,1,2] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,2,1] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,2,1] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,2,1] => 1
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 1
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [3,2,3] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [3,3,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,3,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,3,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [3,3,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,3,2] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,3,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,3,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,3,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,2] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,3,1,1] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,3,1,1] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,3,1,1] => 1
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [3,3,1,1] => 1
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,4,1] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,4,1] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [3,4,1] => 1
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,4,1] => 1
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,4,1] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,5] => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,4] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,1,3] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,1,3] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,2,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,2,2] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,2,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,2,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,2,2] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,2,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,2,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,2,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,2,2] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,3,1] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,3,1] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,3,1] => 1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,3,1] => 1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,4] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,1,3] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,1,3] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,1,2] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,1,1,1,2] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,1,2] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,1,2,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,1,2,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,1,2,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,1,2,1] => 1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,1,3] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [3,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,1,2,2] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [3,1,2,2] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [3,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [3,1,2,2] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [3,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,1,2,1,1] => 1
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,1,2,2] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,1,3,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,1,3,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,1,3,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,3,1] => 1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,1,3,1] => 1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,1,4] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,2,1,2] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,2,2,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,2,2,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,2,3] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,2,1,2] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [3,2,1,2] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,2,2,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,2,2,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,2,2,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [3,2,3] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [3,2,1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,2,1,2] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,2,1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,2,1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [3,2,1,2] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [3,2,1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,2,1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [3,2,1,2] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,2,2,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,2,2,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,2,2,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 1
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,2,3] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [3,2,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,2,1,2] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,2,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,2,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,2,1,2] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,2,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,2,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,2,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [3,2,1,2] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,2,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,2,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,2,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,2,1,2] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,2,2,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,2,2,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,2,2,1] => 1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,2,2,1] => 1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,2,3] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,3,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,3,2] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,3,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,3,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,3,2] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,3,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,3,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,3,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3,2] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [3,3,1,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [3,3,1,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [3,3,1,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,3,1,1] => 1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,2] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [3,3,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [3,3,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,3,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [3,3,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,3,1,1] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,4,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,4,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,4,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,4,1] => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,4,1] => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,4,1] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,5] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,2,2] => 2
[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] => [4,3,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,1] => 1
[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] => [4,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,1,2,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,1,2,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,1,3] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,1] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,1,2,1] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,1,2,1] => 1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,1,3] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,2,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,2,2] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,2,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,2,2] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,2,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,2,2] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,3,1] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,1] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [4,3,1] => 1
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,1] => 1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4] => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,1,3] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,2,1] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [4,1,2,1] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,1,3] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [4,1,2,1] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,1,2,1] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,1,2,1] => 1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [4,1,3] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,2,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,2,2] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [4,2,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,2,2] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,2,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,2,2] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [4,2,1,1] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,2,2] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,1] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,1] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,3,1] => 1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,3,1] => 1
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,1] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,4] => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,1,3] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,1,3] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,1,2,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,1,2,1] => 1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,1,2,1] => 1
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,1,3] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,1,1,2] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,1,2,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,1,2,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [4,1,2,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,1,2,1] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,1,2,1] => 1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,1,3] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [4,2,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,2,2] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [4,2,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,2,2] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [4,2,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,2,2] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,2,1,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,2,2] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,2,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,2,2] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,3,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,3,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,3,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,3,1] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,3,1] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,3,1] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,4] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,2,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,3] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,1,2] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,1,2] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,2,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,2,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,2,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,3] => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,1,2] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,1,2] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,1,2] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,2,1] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,2,1] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,2,1] => 1
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,2,1] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,3] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,1,2] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,1,2] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [5,1,2] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [5,1,2] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,2,1] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [5,2,1] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,1] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,2,1] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,2,1] => 1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [5,3] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,1,2] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,1,2] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,1,2] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,1,2] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,1,2] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,2,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,2,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,2,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,1] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,2,1] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,2,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,3] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,2] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,2] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,2] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,2] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,2] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,2] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,1] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8] => 8
[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] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,7,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,2,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,7,1] => 1
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,6,2] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,1,1,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [5,3,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,7,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,6,1,1] => 1
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,5,3] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [6,2,1] => 1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [5,2,1,1] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [4,4,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,7,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,6,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,6,2] => 1
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,5,2,1] => 1
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,4,4] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [6,1,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [5,2,1,1] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [5,1,2,1] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [4,3,1,1] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,5,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,7,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,6,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,6,1,1] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,5,2,1] => 1
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,5,1,2] => 1
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,4,3,1] => 1
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,5] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [6,2,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [4,2,2,1] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,6,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,2] => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,7,1] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,6,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,6,2] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,5,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,4,2,2] => 1
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,3,4,1] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,7] => 2
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,6] => 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] => [6,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0] => [4,3,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0] => [5,1,2,1] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [5,2,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0] => [4,2,1,1,1] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,7,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [6,1,2] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,6,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,6,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,6,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,5,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,4,3,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,5,1,2] => 1
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,5,2,1] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,4,2,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,4,1,3] => 1
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,6,1] => 1
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,5,1] => 1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,7] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0] => [6,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [3,3,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [2,4,2,1] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,6,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [6,1,2] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [5,2,2] => 2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,5,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,4,2,2] => 1
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,3,3,1,1] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,6,1] => 1
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,5,1] => 1
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,5,2] => 2
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,6,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [6,1,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [5,2,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [6,1,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [3,4,1,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0] => [5,3,1] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,1,1,2,1] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,6,1,1] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,5,2,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0] => [6,1,2] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => [5,1,1,2] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0] => [4,3,2] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,6,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [1,4,2,1,1] => 1
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,3,4,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,5,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,4,2,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,5,3] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,4,1,1,2] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,5,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,2,4,1,1] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,6,1] => 1
[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,3,1,4] => 1
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,4,3] => 2
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,5,2] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,1,1,2] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,1,1,2,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,1,1,2,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,1,1,3] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,1,1,2,2] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,1,1,2,2] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,1,1,3,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,1,1,3,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1,3,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,1,1,4] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,1,1,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,1,1,2,1,2] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,1,1,2,3] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,1,1,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,1,1,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,1,1,2,1,2] => 1
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,1,1,2,3] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,1,1,3,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,1,1,3,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,1,1,3,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,1,1,3,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,1,1,3,1,1] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,1,1,4,1] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,1,1,4,1] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,4,1] => 1
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,1,1,5] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,1,2,1,1,2] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,1,2,1,2,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,1,2,1,2,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,1,2,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,1,2,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,1,2,2,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,1,2,4] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,1,2,1,3] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,1,2,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,1,2,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,1,2,1,1,2] => 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,1,2,2,1,1] => 1
[1,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,1,2,2,1,1] => 1
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,1,2,4] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,1,3,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,1,3,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,1,3,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,1,3,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,1,3,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,1,3,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,1,3,1,1,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,1,4,2] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,1,4,1,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,1,4,2] => 1
[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,1,4,1,1] => 1
[1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1,4,1,1] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,1,5,1] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,5,1] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,5,1] => 1
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,5,1] => 1
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,6] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,1,2] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [2,2,1,1,2,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [2,2,1,2,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [2,2,1,2,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [2,2,1,2,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [2,2,1,3,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [2,2,2,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [2,2,2,1,2] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [2,2,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [2,2,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2,3] => 2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [2,2,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [2,2,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [2,2,3,1,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [2,2,3,1,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,3,2] => 2
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,5] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,1,2] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [2,2,1,1,2,1] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [2,2,1,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [2,2,1,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,1,4] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [2,2,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [2,2,1,1,1,2] => 1
[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [2,2,1,1,2,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,1,1,3] => 1
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [2,2,1,3,1] => 1
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,1,4] => 1
[1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [2,2,2,1,2] => 1
[1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [2,2,2,1,1,1] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [2,2,2,2,1] => 1
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [2,2,2,2,1] => 1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [2,2,3,1,1] => 1
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,5] => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [2,3,1,1,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [2,3,1,2,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [2,3,2,1,1] => 1
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [2,3,3,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [2,3,1,2,1] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [2,3,1,3] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [2,3,1,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [2,3,1,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [2,3,1,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [2,3,1,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [2,3,1,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [2,3,1,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [2,4,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [2,4,3] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [2,4,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [2,4,3] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [2,4,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [2,4,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [2,4,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [2,4,1,2] => 1
[1,1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [2,4,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [2,4,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [2,4,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,4,2,1] => 1
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,4,3] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [2,5,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [2,5,2] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [2,5,2] => 2
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [2,5,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [2,5,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [2,5,2] => 2
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [2,5,1,1] => 1
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,5,2] => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [2,5,1,1] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [2,5,1,1] => 1
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [2,5,1,1] => 1
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,5,1,1] => 1
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,5,2] => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,6,1] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,6,1] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [2,6,1] => 1
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,6,1] => 1
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,6,1] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,7] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,1,2] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,1,1,2,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,1,1,2,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,1,1,1,3] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,1,1,2,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,1,2,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,1,2,1,1,1] => 1
[1,1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,1,3,1,1] => 1
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,1,3,2] => 1
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,1,4,1] => 1
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,5] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,2,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,2,2] => 2
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,2,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,2,2] => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,2,1,1,2] => 1
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,2,1,3] => 1
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,2,2,2] => 2
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,2,4] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [3,3,1,1,1] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [3,3,1,1,1] => 1
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,3,1,1,1] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [3,4,1,1] => 1
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,4,1,1] => 1
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2] => 2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [3,5,1] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [3,5,1] => 1
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,5,1] => 1
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,6] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,1,2] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,1,1,2,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,1,2,1,1] => 1
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,1,1,4] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,3,1,1] => 1
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,1,4,1] => 1
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,5] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,1,2] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,1,1,2,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,1,1,3] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,1,2,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,1,4] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [3,1,1,1,1,2] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,1,1,3] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,1,1,1,1,2] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,1,1,2] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,1,1,2,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,1,1,2,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,1,1,2,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,1,1,3] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,1,1,2,1,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,1,1,2,1,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,1,1,2,1,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,1,1,2,1,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,1,1,2,2] => 1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,1,1,3,1] => 1
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,1,1,3,1] => 1
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,1,1,4] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,1,2,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,1,2,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,1,2,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,1,2,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,1,2,2,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,1,3,1,1] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,1,3,1,1] => 1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,1,3,1,1] => 1
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,1,3,1,1] => 1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,1,4,1] => 1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,1,4,1] => 1
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,5] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [3,2,1,2,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [3,2,2,1,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [3,2,2,2] => 2
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,2,2,2] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [3,2,1,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [3,2,1,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [3,2,1,1,2] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [3,2,1,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [3,2,1,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,2,1,1,2] => 1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [3,2,2,1,1] => 1
[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [3,2,3,1] => 1
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [3,2,4] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [3,3,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [3,3,1,2] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [3,3,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [3,3,2,1] => 1
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [3,3,1,2] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [3,3,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [3,3,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [3,3,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [3,3,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,3,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,1,2] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [3,3,2,1] => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [3,3,2,1] => 1
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [3,4,2] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [3,4,1,1] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [3,4,2] => 2
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,4,2] => 2
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [3,4,1,1] => 1
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,4,1,1] => 1
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2] => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [3,5,1] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [3,5,1] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [3,5,1] => 1
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3,5,1] => 1
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,5,1] => 1
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,5,1] => 1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,6] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0] => [4,1,1,1,2] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0] => [4,1,1,2,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,1,1,3] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0,0] => [4,1,2,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,1,3,1] => 1
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,1,4] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0] => [4,2,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0] => [4,2,3] => 2
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0] => [4,2,3] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2] => 2
[1,1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,1,1] => 1
[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0] => [4,3,2] => 2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0] => [4,4,1] => 1
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,4,1] => 1
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,5] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,1,2,2] => 1
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,1,4] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0,0] => [4,1,1,1,2] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0] => [4,1,1,1,2] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,1,1,2,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,1,1,3] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,1,2,2] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0] => [4,1,2,1,1] => 1
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => [4,1,2,2] => 1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,3,1] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0] => [4,2,1,1,1] => 1
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [4,2,1,1,1] => 1
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [4,4,1] => 1
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,4,1] => 1
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [4,4,1] => 1
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5] => 4
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,1,3,1] => 1
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,1,4] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,1,2,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,1,1,2,1] => 1
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,1,4] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,1,1,1,2] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,1,1,2,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,1,1,3] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,1,1,1,2] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,1,1,3] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,1,1,1,2] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,1,1,1,2] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,1,1,1,2] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,1,1,2,1] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,1,1,2,1] => 1
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,1,1,2,1] => 1
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,1,1,3] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0] => [4,1,2,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,1,2,2] => 1
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,1,2,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,1,2,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,1,2,1,1] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,1,2,1,1] => 1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,1,3,1] => 1
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,1,3,1] => 1
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,1,4] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,0] => [4,2,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [4,2,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [4,2,1,2] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,2,1,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [4,2,1,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,2,1,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0] => [4,2,1,2] => 1
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [4,2,2,1] => 1
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [4,2,3] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0] => [4,3,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0] => [4,3,2] => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0] => [4,3,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,3,2] => 2
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [4,3,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [4,3,2] => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [4,3,1,1] => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,3,1,1] => 1
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,1,1] => 1
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [4,3,2] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [4,4,1] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [4,4,1] => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4,4,1] => 1
[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,4,1] => 1
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [4,4,1] => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,5] => 4
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0] => [5,1,2,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0] => [5,1,3] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0] => [5,2,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0] => [5,3,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,4] => 4
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0] => [5,1,1,2] => 1
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [5,1,3] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [5,2,2] => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0] => [5,3,1] => 1
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0] => [5,3,1] => 1
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0] => [5,4] => 4
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0] => [5,1,3] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [5,1,1,2] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [5,2,2] => 2
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0] => [5,2,1,1] => 1
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [5,2,2] => 2
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,3,1] => 1
[1,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,0] => [5,3,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0] => [5,1,1,2] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [5,1,3] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [5,1,2,1] => 1
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [5,1,2,1] => 1
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [5,1,3] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [5,1,1,2] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [5,1,1,2] => 1
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [5,1,2,1] => 1
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [5,1,2,1] => 1
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [5,1,3] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [5,2,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [5,2,2] => 2
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [5,2,1,1] => 1
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [5,2,1,1] => 1
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [5,2,2] => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [5,3,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [5,3,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,3,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [5,3,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [5,3,1] => 1
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [5,3,1] => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [5,4] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0] => [6,1,2] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0] => [6,2,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [6,2,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [6,3] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [6,2,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [6,3] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [6,1,2] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,2,1] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [6,2,1] => 1
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [6,3] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0] => [6,1,2] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [6,1,2] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [6,1,2] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [6,2,1] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [6,2,1] => 1
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [6,2,1] => 1
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [6,3] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [6,1,2] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [6,1,2] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [6,1,2] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [6,1,2] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [6,2,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,2,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [6,2,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [6,2,1] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [6,2,1] => 1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [6,3] => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,2] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [7,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [7,2] => 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0] => [7,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [7,2] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0] => [7,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [7,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [7,2] => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,1,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0] => [7,1,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => [7,1,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [7,1,1] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [7,1,1] => 1
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [7,2] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [7,1,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [7,1,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [7,1,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [7,1,1] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,1,1] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,2] => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [8,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [8,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [8,1] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,1] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9] => 9
[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
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,2] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,2,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,3] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,3,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,3,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,3,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,3,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,3,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,3,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,4] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,3,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,4,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,3,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,4,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,3,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,3,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,3,2] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,3,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,4,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,3,2,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,4,1,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,4,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,4,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,3,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,3,1,2] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,5] => 1
[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,3,2,1] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,3,1,2,1,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,5,1,1] => 1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,3,2,1,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,4,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,3,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,3,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,3,1,1,2] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,5,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,3,3,1,1] => 1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,3,1,2,1,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,5,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,4,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,3,1,1,1,2] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,5,1] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,5,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,6] => 1
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,3,3,1,1] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,6,1,1] => 1
[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,3,2,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,4,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,3,3,1] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,6,1] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,5,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,2,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,2,2] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,3,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,2,1,2] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,2,2,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,2,3] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,3,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,3,2] => 1
[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
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1,2,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,2,2,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2,2] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,2,4] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,3,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,3,2,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,3,3] => 1
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,5,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,1,2] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,2,1,1,2,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,2,1,1,3] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,2,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,2,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,2,4,1] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,2,5] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,3,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,4,1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,4,3] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,5,1,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,5,2] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,6,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,1,2] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,1,3] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,1,2,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,2,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,1,5] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,2,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,2,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2,2] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,3,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,5,1] => 1
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,6] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,2,1] => 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] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,4,4] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,5,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,5,3] => 1
[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] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,1,3] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,1,2,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,1,2,2] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,1,3,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,1,4] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,1,2,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,1,2,3] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,1,4,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,1,5] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,5,1] => 1
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,6] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,2,1,1,1,2] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,2,1,2] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,2,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,2,3] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,2,3,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,2,3,2] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,5] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,1,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,3,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,4,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,4,3] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,5,1,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,5,2] => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,6,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,1,2] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,1,2,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,1,3] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,2,1,2] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,2,2,2] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,3,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,4,2] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,5,1] => 1
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,6] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [4,1,1,1,2] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] => [4,1,1,3] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [4,1,3,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,1,4] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [4,2,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0] => [4,2,3] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [4,3,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,3,2] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,4,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0] => [5,1,1,2] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0] => [5,1,2,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => [5,1,3] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,2,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [5,4] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [6,1,2] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [6,3] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,1,1,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,1,1,2,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [6,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,1,1,2] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,6] => 1
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,4] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,3] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,4,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,1,1,2] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,1,1,2] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,1,1,3] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,1,1,4] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,4,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,4,1,1] => 1
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,4,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,5] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [3,4,2] => 2
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3] => 3
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [4,2,3] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,4,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,2,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [5,3,1] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,5,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,2,1,2,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [6,1,2] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,6,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0] => [5,1,3] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,5,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,2,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,2,1,2] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,1,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [2,2,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [2,2,2,2,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,2,2,1,2] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,2,1,2,2] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2,2] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [2,3,1,2,1] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [2,2,3,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [2,2,2,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,2,1,3,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,3,1,2] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,1,2,2] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,1,2,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => 1
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,2,5] => 1
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,2,4] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,2,3] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,2,2] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [4,2,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,1,2,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,1,1,2,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,1,1,1,2] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,1,2,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,4,1,1] => 1
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [3,4,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,1,0] => [4,2,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [5,1,2,1] => 1
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,5] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,1,2] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,1,2] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,1,2] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,3,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,2,1,1,2,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,3,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,2,2,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,4,1,1,2] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,4,1,2] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,4,2] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,1,3,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,2,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,2,1,1,2] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,1,1,2] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,2,1,1,1,2] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,5,2] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,4,2] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,5,1,1] => 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,4,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,2,2,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,2,2,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2,2] => 2
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,5,1] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,5,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,1,1,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,2,1,3] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,1,2] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,2,1,2,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,1,1,2,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,1,1,3] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,1,4] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,1,5] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,2,1,4] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,2,4,1] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,2,4,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,1,1,3,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,4,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,1,2,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,1,2,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,1,2,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,2,2,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,2,2,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,2,2,1,1,1] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,2,1,1,1,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,1,3,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0] => [4,2,1,2] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0] => [4,1,1,2,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [4,2,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [2,3,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => 1
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,5,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,1,4,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,1,3,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,2,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,2,2,1,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,1,2,2] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,4] => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,5,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,2,2,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,2,3,1] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,2,4,1] => 1
[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,1,5] => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,1,1,2,3] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,1,1,3,2] => 1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,1,1,4,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [3,2,1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [6,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,2,2,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,1,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,2,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,2,2,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0] => [5,1,3] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,1,2,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,4,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [3,1,3,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,1,0,0] => [4,1,2,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,3,2] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,4,3] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,4,2] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0] => [4,2,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,4,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,2,3,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [3,1,1,2,1,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,5,3] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0] => [5,3,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,1,1,2,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,2,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,3,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,3,1,1,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,3,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,2,1,1,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,4,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0] => [4,2,3] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,4,2,2] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,2] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,6,2] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,2,1,1,3] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,4,1] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,4,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,1,1,2] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [2,3,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,1,2,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,2,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,2,2] => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2,2] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [3,2,1,2,1] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,2,2,1,1] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,2,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,2,2] => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [3,2,2,2] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2,2] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [2,3,2,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [2,3,1,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [2,3,1,1,1,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,1,4,1,1] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,4,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,1,3,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,3,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,3,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,1,1,2,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,1,1,2,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,1,2,3] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,2,3,1] => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,5,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,1,1,2,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,4,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,1,2,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,1,2,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,1,2,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,1,5] => 1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,5,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => [6,2,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,4,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,3,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,3,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,4,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [3,3,3] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0] => [5,2,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0] => [5,3,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,1,1,2,1] => 1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,5,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,4,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,4,3] => 2
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4] => 2
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [2,3,3,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [3,3,2,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,2,3,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,3,2,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,2,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,2,2,2,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,2,2,2,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,3,2,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,3,2,2,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,2,2,2,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [2,2,2,2,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,2,2,2,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,4,1] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,4,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0] => [5,1,2,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,1,2,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,1,1,3] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,2,2,1,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,3,1,1,1] => 1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,1,1,2,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,1,3,1] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,1,2,1] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,2,2,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,1,2,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0] => [4,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,1,2,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,2,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,2,2,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,2,2,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,3,2,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,2,2,2,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,2,3,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,3,2,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,1,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [2,2,1,2,2] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,2,2,2] => 1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,2,2,2,2] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [2,2,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,3,1,2] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,1,2,2] => 1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,2,5,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,2,1,1,1,2] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [3,2,4] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,2,1,2] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,2,4,2] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,3,3,2] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,5,1,2] => 1
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,5,1,1] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,5,1,1] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,5,1,1,1] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [2,4,1,2] => 1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,3,3,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,1,3,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,1,3,2] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,3,2,2] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,3,1,2] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,1,4] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,1,1,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,1,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,2,2,2] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,3,1,2] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,4,1,2] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,2,1,2,2] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,3,1,1,2] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,4,1,2] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,3,1,1,1,1] => 1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [3,3,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,1,2,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,2,1,2,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,1,2,1] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [3,3,1,1,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,2,1,3] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,4,1,2] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,3,1,3] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,2,1,4] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,3,1,3] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,5,1,2] => 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,4,1,3] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,1,4] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,1,3,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,1,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,1,1,3,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,1,3,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,3,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,3,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,1,3,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,3,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,1,4,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,3,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,4,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,4,1,1,1] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,4,1,1,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [3,2,1,2,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [3,2,2,1,1] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [3,2,2,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,2,1,1,2,2] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,1,2,2] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,1,1,2,2] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,2,1,2,2] => 1
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,3,1,1,2,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0] => [4,4,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,1,4] => 1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0] => [4,2,2,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,2,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [2,2,2,2,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,1,2,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [2,2,1,1,2,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,3,1,1,1,2] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,1,1,2] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,1,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,1,1,2,1,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,5,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,3,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0] => [5,1,2,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,3,1] => 1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,1,4,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0] => [5,1,2,1] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,1,3,1] => 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,4,1,2,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,1,1,2,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,1,1,2,1] => 1
[1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,4,1,2,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,1,2,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,1,1,3] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,2,1,1,2,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,2,2,1,2] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,2,2,2,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [3,2,1,2,1] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,2,2,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,2,2,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,2,2,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,2,1,1,2,1] => 1
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,2,4,1,1] => 1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0] => [4,3,1,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,4,3] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,1,1,1,1,2] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,2,2,2] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,2,2,2] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,2,2,2,2] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,3,2,2] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,2,3,2] => 2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,2,3,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,2,3,1,2] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,1,3,2] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,2,3,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,1,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,2,3,1] => 1
[1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,4,2,2] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [3,2,2,2] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,3,1,1,1,2] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,2,1,1,2] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,4,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,2,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,4,2,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,1,2,2] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [3,3,1,2] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,3,2,1,2] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [2,2,2,2,1] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,3,1,2] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [2,2,1,4] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,1,2,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,1,2,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,3,1,2,2] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,1,1] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,1,3,2] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,3,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,2,2,2,2] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,2,2,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,2,2,1,2,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,1,2,2,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,2,3,1,2] => 1
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,2,2,3,1] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,2,2,2,1,1] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,2,2,1,3] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,1,3,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,3,1,2,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,3,2,1] => 1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,3,2,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,1,1,2,1] => 1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [2,2,1,1,2,1] => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,2,1,1,1,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,2,1,1,2] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,1,3] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,3,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,3,1,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,2,2,2] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,2,1,2,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,1,2] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,3,1,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,1,2,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0] => [4,2,1,1,1] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [3,3,1,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,2,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0] => [4,2,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0] => [6,1,1,1] => 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,1,1,2] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,4,1,1,1] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [3,3,1,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [3,2,2,1,1] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [1,3,1,2,2] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,2,1,1,2,2] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,1,2,2] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,1,2,2] => 1
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [3,2,1,2,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,1,1,2,1] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,4,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,1,1,2,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,3,1,1] => 1
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,4,1,1,1] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,5,1,1,1] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,4,1,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,1,3,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,1,1,2] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,1,2,2,1] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,3,2,1,1] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,4,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,4,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,1,2,1,2] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,1,2,2] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [2,5,1,1] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,2,2,1] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [1,3,1,1,1,1,1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,3,3,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,2,4,1,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,1,2,2,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,1,3,1] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1] => 1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,2,3,2,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,2,3,1,2] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,2,1,1,2,2] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0] => [4,2,1,2] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,1,1,1,2] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,1,1,2,2] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,1,2,2,1] => 1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,2,1,3,1,1] => 1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,2,3,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,5,1,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,4,2,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [4,2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1,1] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,1,3,2,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,1,2,3] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [2,2,3,2] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [2,4,1,2] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,2,3,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,2,1,1,3] => 1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,3,3,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,5,1,1] => 1
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,1,4] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,1,3,1,1] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,2,2,2,2] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,2,2,2,2] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,2,1,2,1] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0] => [5,1,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,1,1,2,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1,1] => 1
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,4,1,1] => 1
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,2,2,3,1] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,4,1,1,1] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [2,4,1,1,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,1,1,2,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,1,0,0] => [4,1,2,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2,2] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,1,2,2] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,3,1,2,1,1] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [1,3,2,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,2,1,2,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,2,1,3,1] => 1
[1,0,1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,2,1,4,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [2,3,3,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,2,2,3] => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [2,3,2,1,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [3,2,2,2] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,2,2,2,1] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,1,3,2] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,1,2,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,2,1,3,1] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,2,3,2,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,2,1,2,2,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,3,1,1,1] => 1
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,1,4] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0] => [5,1,3] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [4,2,1,1,1] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [2,3,2,1,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,4,1,2,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,2,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0] => [4,2,3] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [3,3,3] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0] => [5,2,2] => 2
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,5,2] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,2,2,1,1,1,1] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,2,1,1,2,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,1,1,3,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,1,1,3] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,1,1,3] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,4,1,1,2] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,1,3] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [1,3,1,2,2] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,1,2,2] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [2,4,1,1,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [2,2,1,1,2,1] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,1,3,1,1,1] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,4,2,1,1] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,4,1,1,1,1] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 4,0,1 11,2,0,1 36,5,0,0,1 117,11,3,0,0,1 393,28,7,0,0,0,1 1339,78,8,4,0,0,0,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = 4\ q + q^{3}$
$F_{4} = 11\ q + 2\ q^{2} + q^{4}$
$F_{5} = 36\ q + 5\ q^{2} + q^{5}$
$F_{6} = 117\ q + 11\ q^{2} + 3\ q^{3} + q^{6}$
$F_{7} = 393\ q + 28\ q^{2} + 7\ q^{3} + q^{7}$
$F_{8} = 1339\ q + 78\ q^{2} + 8\ q^{3} + 4\ q^{4} + q^{8}$
Description
The smallest part of an integer composition.
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.
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