Identifier
-
Mp00102:
Dyck paths
—rise composition⟶
Integer compositions
St000805: Integer compositions ⟶ ℤ
Values
[1,0] => [1] => 1
[1,0,1,0] => [1,1] => 1
[1,1,0,0] => [2] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,2,1] => 1
[1,1,0,0,1,1,0,1,0,0] => [2,2,1] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,3] => 1
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,1] => 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] => 2
[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] => 2
[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] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,2,1] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,2,1] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,2,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,3] => 2
[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] => 2
[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] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,2,1] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,2,1] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,2,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,3] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => 1
[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] => 2
[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] => 2
[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] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,2,2,1] => 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] => 2
[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] => 2
[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] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,2,1] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,2,1] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => 2
[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] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,1,2,1] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,2,1] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,3] => 2
[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] => 2
[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] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,2,1] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,2,1] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,2,1] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,3] => 2
[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] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,1] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,2,1] => 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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,1,2] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => 1
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4] => 2
[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] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,2,1] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,2,1] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,3] => 2
[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] => 2
[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] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,2,1] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,2,1] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,2,1] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,3] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,2,1,1] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,2,2] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,2,1,1] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,2,1,1] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,2,2] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,2,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,2,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,2,1,1] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,2,2] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,3,1] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,3,1] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,3,1] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4] => 2
[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] => 2
[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] => 1
[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] => 2
[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] => 2
[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] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,1] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,2,1] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,2,1] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,3] => 2
[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] => 2
[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] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,2,1] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,2,1] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,2,1] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,3] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,2,1] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,2,1] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,3] => 2
[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] => 2
[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] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,2,1] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,1,2,1] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,1,2,1] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,3] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,2,1] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,2,1] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,2,1] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,2,1] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,3] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,2,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3] => 1
[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] => 2
[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] => 2
[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] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [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] => 2
[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] => 2
[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] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,2,1,2,1] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,2,1,3] => 2
[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] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,2,1,2,1] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,2,1,3] => 2
[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] => 2
[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] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,2,1,2,1] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,2,1,2,1] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,2,1,2,1] => 2
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,2,1,3] => 2
[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] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,3,2,1] => 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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,2,1,1] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,2,1,1] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,2,2] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,1,3,1] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,3,1] => 2
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,2,1] => 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] => 2
[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] => 2
[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] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,2,1,2,1,1] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,2,1,2,1,1] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,2,1,2,2] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,2,1,3,1] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,2,1,3,1] => 2
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => 2
[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] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,1,3] => 2
[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] => 2
[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] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,1,2,1] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,1,2,1] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,1,2,1] => 2
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,1,3] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,2,1,2,1,1] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,2,1,2,2] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,2,1,2,1,1] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,2,1,2,1,1] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,2,1,2,2] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,2,1,2,1,1] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,2,1,2,1,1] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,2,1,2,1,1] => 2
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,2,1,2,2] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,2,1,3,1] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,2,1,3,1] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,2,1,3,1] => 2
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,2,1,3,1] => 2
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,2,1,4] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,3,1,2,1] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => 2
[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] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,3,1,2,1] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,3,1,2,1] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,3,1,3] => 2
[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] => 2
[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] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,3,1,2,1] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,3,1,2,1] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,3,1,2,1] => 2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,3,1,3] => 2
[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] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,3,1,2,1] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,3,1,2,1] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,3,1,3] => 2
[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] => 2
[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] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,3,1,2,1] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,3,1,2,1] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,3,1,2,1] => 2
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,3,1,3] => 2
[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] => 2
[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] => 2
[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] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,3,1,2,1] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,3,1,2,1] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,3,1,2,1] => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,3,1,2,1] => 2
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,3,1,3] => 2
[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] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,4,2,1] => 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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => 2
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,2,3] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,1,1] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,1,1] => 2
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,2] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,1,1] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,1,1] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,1,1] => 2
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,2] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,1] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,1] => 2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,1] => 2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,2,1,2,1] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => 2
[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] => 1
[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] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [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] => 1
[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] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,2,1,3] => 2
[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] => 2
[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] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,1,3] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,2,1] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,3] => 1
[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] => 2
[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] => 2
[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] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => 2
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => 2
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,2,3] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,1,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,1,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,2] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,1,1] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,1,1] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,1,1] => 2
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,2] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,1] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,1] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,1] => 2
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => 2
[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] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => 2
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => 2
[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] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,1,3] => 2
[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] => 2
[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] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,1,2,1] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,1,2,1] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,1,2,1] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,1,3] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,1,2,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,1,2,2] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,1,2,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,1,2,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,1,2,2] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,1,2,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,1,2,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,1,2,1,1] => 2
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,1,2,2] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,1,3,1] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,1,3,1] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,1,3,1] => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,3,1] => 2
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,1,4] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,1,2,3] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => 2
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,1,2,3] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,1,2,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,1,2,1,2] => 3
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,1,2,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,1,2,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,1,2,1,2] => 3
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,1,2,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,1,2,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,1,2,1,1,1] => 2
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,1,2,1,2] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,1,2,2,1] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,1,2,2,1] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,1,2,2,1] => 2
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,1,2,2,1] => 2
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,1,2,3] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,2] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,2] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,3,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,1,3,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,1,3,2] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,1,1] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,1,3,1,1] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,1,3,1,1] => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,1,3,1,1] => 2
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,1,3,2] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,1,4,1] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,1,4,1] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,1,4,1] => 2
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,1,4,1] => 2
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,4,1] => 2
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,1,5] => 2
[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] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,2,1,2,1] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,2,1,3] => 2
[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] => 2
[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] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => 2
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [2,2,1,3] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,2,1,3] => 2
[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] => 2
[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] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => 2
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,2,1,3] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [2,2,1,2,1] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,2,1,2,1] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,2,1,2,1] => 2
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,2,1,2,1] => 2
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,1,3] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 2
[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] => 2
[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] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => 2
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4] => 2
[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] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,2,1] => 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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [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] => 1
[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] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,1,4] => 2
[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] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,1,1,3] => 2
[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] => 2
[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] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => 2
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [3,1,1,3] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,1,1] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,2] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,1,1] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [3,1,2,1,1] => 2
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,1,2,2] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,1,1] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,1,2,1,1] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,2,1,1] => 2
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,1,2,2] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,3,1] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,1,3,1] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [3,1,3,1] => 2
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,1,3,1] => 2
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,1,4] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,4] => 2
[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] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,1,3] => 2
[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] => 2
[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] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => 2
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,1,3] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,2,1,1] => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,2,2] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,2,1,1] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,2,1,1] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,2,2] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,2,1,1] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,2,1,1] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,2,1,1] => 2
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,2,2] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,3,1] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,3,1] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,3,1] => 2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,3,1] => 2
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,4] => 2
[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] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,1,3] => 2
[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] => 2
[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] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => 2
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,1,3] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,1,2,1] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,1,2,1] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,1,2,1] => 2
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,1,2,1] => 2
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,1,3] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [3,1,2,1,1] => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,1,2,2] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,1,2,1,1] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,1,2,1,1] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [3,1,2,2] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [3,1,2,1,1] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,1,2,1,1] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,1,2,1,1] => 2
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [3,1,2,2] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [3,1,2,1,1] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,1,2,1,1] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,1,2,1,1] => 2
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,1,2,1,1] => 2
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,1,2,2] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,1,3,1] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,1,3,1] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,1,3,1] => 2
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,3,1] => 2
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,1,3,1] => 2
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,1,4] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,1,2,1] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,1,2,1] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,1,3] => 2
[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] => 2
[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] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,1] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,1,2,1] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,1,2,1] => 2
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,1,3] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,1] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,1,3] => 2
[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] => 2
[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] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,2,1] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [4,1,2,1] => 2
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,1,3] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [4,1,2,1] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,1,2,1] => 2
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,1,2,1] => 2
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [4,1,3] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,1] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,1,3] => 2
[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] => 2
[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] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,1] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,1] => 2
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,1,3] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,1,2,1] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,1,2,1] => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,1,2,1] => 2
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,1,3] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,1,2,1] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,1,2,1] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [4,1,2,1] => 2
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,1,2,1] => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,1,2,1] => 2
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,1,3] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => 2
[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] => 1
[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] => 2
[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] => 2
[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] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,2] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [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] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,8] => 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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [5,2,2] => 1
[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] => 1
[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] => 2
[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] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => [5,1,1,2] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0] => [4,3,2] => 1
[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] => 2
[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] => 2
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,4,3] => 1
[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] => 2
[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] => 2
[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] => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,1,1,3] => 2
[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] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,1,1,2,2] => 2
[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] => 2
[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] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,1,1,2,2] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,1,1,3,1] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,1,1,3,1] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1,3,1] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,1,1,4] => 2
[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] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,1,1,2,1,2] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,1,1,2,3] => 2
[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] => 2
[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] => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,1,1,2,1,2] => 3
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,1,1,2,3] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,1,1,3,1,1] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,1,1,3,1,1] => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,1,1,3,1,1] => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,1,1,3,1,1] => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,1,1,3,1,1] => 2
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,1,1,4,1] => 2
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,1,1,4,1] => 2
[1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,4,1] => 2
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,1,1,5] => 2
[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] => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,1,2,1,1,2] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,1,2,1,2,1] => 3
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,1,2,1,2,1] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,1,2,2,1,1] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,1,2,2,1,1] => 2
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,1,2,2,1,1] => 2
[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,1,2,4] => 2
[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] => 2
[1,1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,1,2,1,3] => 3
[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] => 2
[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] => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,1,2,1,1,2] => 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,1,2,2,1,1] => 2
[1,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,1,2,2,1,1] => 2
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,1,2,4] => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,1,3,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,1,3,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,1,3,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,1,3,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,1,3,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,1,3,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,1,3,1,1,1] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,1,4,2] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,1,4,1,1] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,1,4,2] => 2
[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,1,4,1,1] => 2
[1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1,4,1,1] => 2
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,1,5,1] => 2
[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,5,1] => 2
[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,5,1] => 2
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,5,1] => 2
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,6] => 2
[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] => 2
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [2,2,1,1,2,1] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [2,2,1,2,1,1] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [2,2,1,2,1,1] => 2
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [2,2,1,2,1,1] => 2
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [2,2,1,3,1] => 2
[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] => 2
[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] => 1
[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] => 1
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,5] => 1
[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] => 2
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [2,2,1,1,2,1] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [2,2,1,2,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [2,2,1,2,1,1] => 2
[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,1,4] => 2
[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] => 2
[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [2,2,1,1,2,1] => 2
[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,1,1,3] => 2
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [2,2,1,3,1] => 2
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,1,4] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [2,2,2,1,2] => 2
[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] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [2,5,2] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,1,1,2,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,1,1,2,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,1,1,1,3] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [3,1,1,2,1,1] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,1,2,1,1] => 2
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [3,1,2,1,1,1] => 2
[1,1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,1,3,1,1] => 2
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,1,3,2] => 2
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,1,4,1] => 2
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,5] => 2
[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] => 1
[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] => 1
[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] => 2
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,2,1,3] => 2
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,2,2,2] => 1
[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] => 1
[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] => 1
[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] => 2
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,1,1,2,1] => 2
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,1,2,1,1] => 2
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,1,1,4] => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,1,3,1,1] => 2
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,1,4,1] => 2
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,1,5] => 2
[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] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,1,1,2,1] => 2
[1,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,1,1,3] => 2
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,1,2,1,1] => 2
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,1,1,4] => 2
[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] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,1,1,3] => 2
[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] => 2
[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] => 2
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,1,1,2,1] => 2
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,1,1,2,1] => 2
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,1,1,2,1] => 2
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,1,1,3] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,1,1,2,1,1] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,1,1,2,1,1] => 2
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,1,1,2,1,1] => 2
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,1,1,2,1,1] => 2
[1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,1,1,2,2] => 2
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,1,1,3,1] => 2
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,1,1,3,1] => 2
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,1,1,4] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,1,2,1,1,1] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,1,2,1,1,1] => 2
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,1,2,1,1,1] => 2
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,1,2,1,1,1] => 2
[1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,1,2,2,1] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,1,3,1,1] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,1,3,1,1] => 2
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,1,3,1,1] => 2
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,1,3,1,1] => 2
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,1,4,1] => 2
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,1,4,1] => 2
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,5] => 2
[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] => 2
[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] => 1
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,2,2,2] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [3,3,1,2] => 2
[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] => 2
[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] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [3,4,2] => 1
[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] => 1
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,4,2] => 1
[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] => 1
[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] => 1
[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] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0] => [4,1,1,2,1] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0] => [4,1,1,3] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0,0] => [4,1,2,1,1] => 2
[1,1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0,0] => [4,1,3,1] => 2
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,1,4] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,1,4] => 2
[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] => 2
[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] => 2
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0] => [4,1,1,2,1] => 2
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,1,1,3] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0] => [4,1,2,2] => 2
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0] => [4,1,2,1,1] => 2
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0] => [4,1,2,2] => 2
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,3,1] => 2
[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] => 1
[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] => 2
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,1,4] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,1,2,1] => 2
[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] => 2
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,1,4] => 2
[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] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,1,1,2,1] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,1,1,3] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,1,1,2,1] => 2
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,1,1,2,1] => 2
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,1,1,2,1] => 2
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,1,1,3] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0] => [4,1,2,1,1] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,1,2,2] => 2
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,1,2,1,1] => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,1,2,1,1] => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,1,2,1,1] => 2
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,1,2,1,1] => 2
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,1,3,1] => 2
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,1,3,1] => 2
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,1,4] => 2
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0] => [5,1,3] => 2
[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] => 1
[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] => 2
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [5,1,3] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [5,2,2] => 1
[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] => 1
[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] => 2
[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] => 2
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [5,2,2] => 1
[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] => 1
[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] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0] => [5,1,3] => 2
[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] => 2
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [5,1,2,1] => 2
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [5,1,3] => 2
[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] => 2
[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] => 2
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [5,1,2,1] => 2
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [5,1,2,1] => 2
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [5,1,3] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0] => [6,1,2] => 2
[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] => 2
[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] => 2
[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] => 1
[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] => 2
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [6,1,2] => 2
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,2,1,1,3] => 2
[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] => 2
[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] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,1,3] => 2
[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] => 2
[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] => 2
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,1,5] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,1,3] => 2
[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] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,1,2,2] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,1,3,1] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,1,4] => 2
[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] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,1,2,3] => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,1,4,1] => 2
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,1,5] => 2
[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] => 2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,5,1] => 2
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,6] => 2
[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] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,2,1,2] => 2
[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] => 1
[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] => 1
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,5] => 1
[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] => 1
[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] => 1
[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] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,1,2,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,1,3] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,2,1,2] => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => 2
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,1] => 2
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5] => 2
[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] => 1
[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] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,4,2] => 1
[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] => 1
[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] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] => [4,1,1,3] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [4,1,3,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,1,4] => 2
[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] => 1
[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] => 1
[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] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0] => [5,1,2,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => [5,1,3] => 2
[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] => 1
[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] => 2
[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] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,1,4] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [5,1,3] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,1,1,4] => 2
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,4,1] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,4,1,1] => 2
[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] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [3,4,2] => 1
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3] => 1
[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] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [6,1,2] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,2,1,2,2] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2,2] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [2,3,1,2,1] => 2
[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] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,3,1,2] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,1,2,2] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,1,1,2,1] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,1,1,1,2] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,1,2] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,1,2] => 2
[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] => 2
[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] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,4,1,1,2] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,4,1,2] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 1
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,5,1] => 2
[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] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,2,1,3] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,1,2] => 2
[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] => 2
[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] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,1,1,3] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,1,1,4] => 2
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,1,5] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,2,1,4] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,1,1,3,1] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0] => [4,2,1,2] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0] => [4,1,1,2,1] => 2
[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] => 2
[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] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,1,3,1] => 2
[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] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => 2
[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] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,1,1,2,3] => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,1,1,3,2] => 2
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,1,1,4,1] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,4,1,1] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [3,1,3,1,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,1,0,0] => [4,1,2,1,1] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,4,1] => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,4,1] => 2
[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] => 2
[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] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,1,2,1] => 2
[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] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2,2] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [3,2,1,2,1] => 2
[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] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [3,2,2,2] => 1
[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] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,4,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,1,3,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,1,3,1,1,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,1,3,1,1,1] => 2
[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] => 2
[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] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,1,2,3] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,5,1] => 2
[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] => 1
[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] => 2
[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] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4] => 1
[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] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,1,2,1] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,1,1,3] => 2
[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] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,1,3,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,1,2,1] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,2,2,2] => 2
[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] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,1,2,2] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,1,3,2] => 2
[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] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,1,4] => 2
[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] => 2
[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] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,4,1,2] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,2,1,2,2] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,3,1,1,2] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,4,1,2] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,4,1,2] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,3,1,3] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,2,1,4] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,3,1,3] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,5,1,2] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,4,1,3] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,1,4] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,1,3,1,1] => 2
[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] => 2
[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] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,1,1,3,1] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,1,3,1,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,3,1,1,1] => 2
[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] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,3,1,1,1] => 2
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,1,4,1] => 2
[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] => 2
[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] => 2
[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] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,1,2,2] => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,1,1,2,2] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,2,1,2,2] => 2
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,3,1,1,2,1] => 2
[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] => 2
[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] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [2,2,1,1,2,1] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,3,1,1,1,2] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,1,1,2] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,1] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,1,3,1] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0] => [5,1,2,1] => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,1] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,3,1] => 2
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,1,4,1] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0] => [5,1,2,1] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,1,3,1] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,4,1,2,1] => 2
[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] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,1,1,2,1] => 2
[1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,4,1,2,1] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1] => 2
[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] => 2
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,1,1,3] => 2
[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] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,2,2,1,2] => 2
[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] => 2
[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] => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => 2
[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] => 2
[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] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,1,1,1,1,2] => 2
[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] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,2,3,2] => 1
[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] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,1,3,2] => 2
[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] => 2
[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] => 2
[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] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,3,1,1,1,2] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,2,1,1,2] => 2
[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] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [3,3,1,2] => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,3,2,1,2] => 2
[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] => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [2,2,1,4] => 2
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,1,2,1] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,1,2,1] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,3,1,2,2] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,1,1] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,1,3,2] => 2
[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] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,1,2,2,1] => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,2,3,1,2] => 2
[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] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,1,3,1,1] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,3,1,2,1] => 2
[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] => 2
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [2,2,1,1,2,1] => 2
[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] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,1,3] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,3,1,1] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,3,1,2,1] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,2,1,1,2,2] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,1,2,2] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,1,2,2] => 2
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [3,2,1,2,1] => 2
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,1,1,2,1] => 2
[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] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,3,1,1] => 2
[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] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,1,3,1] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,1,1,2] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,1,2,2,1] => 2
[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] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,1,2,2] => 2
[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] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,1,3,1] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1] => 2
[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] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,2,1,1,2,2] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0] => [4,2,1,2] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,1,1,1,2] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,1,1,2,2] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,1,2,2,1] => 2
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,2,1,3,1,1] => 2
[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] => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,1,3,2,1] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,1,2,3] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [2,2,3,2] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [2,4,1,2] => 2
[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] => 2
[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] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,1,3,1,1] => 2
[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] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0] => [5,1,2,1] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,1,1,2,1] => 2
[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] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,1,0,0] => [4,1,2,1,1] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,1,2,1,1,1] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2,2] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,1,2,2] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,3,1,2,1,1] => 2
[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] => 2
[1,0,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,2,1,3,1] => 2
[1,0,1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,2,1,4,1] => 2
[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] => 1
[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] => 1
[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] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,1,2,1,1] => 2
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,2,1,3,1] => 2
[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] => 2
[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] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,1,4] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0] => [5,1,3] => 2
[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] => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,2,1,1] => 2
[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] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0] => [5,2,2] => 1
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,5,2] => 1
[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] => 2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,1,1,3,1] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,1,1,3] => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,1,1,3] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,4,1,1,2] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,1,3] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [1,3,1,2,2] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,1,2,2] => 2
[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] => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,1,3,1,1,1] => 2
[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:
39,3 109,23 305,124 849,569,12
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 5\ q$
$F_{4} = 14\ q$
$F_{5} = 39\ q + 3\ q^{2}$
$F_{6} = 109\ q + 23\ q^{2}$
$F_{7} = 305\ q + 124\ q^{2}$
$F_{8} = 849\ q + 569\ q^{2} + 12\ q^{3}$
Description
The number of peaks of the associated bargraph.
Interpret the composition as the sequence of heights of the bars of a bargraph. This statistic is the number of contiguous subsequences consisting of an up step, a sequence of horizontal steps, and a down step.
Interpret the composition as the sequence of heights of the bars of a bargraph. This statistic is the number of contiguous subsequences consisting of an up step, a sequence of horizontal steps, and a down step.
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.
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