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------------------------------------------------------------------------
Map identifier: Mp00233
------------------------------------------------------------------------
Map name: skew partition
------------------------------------------------------------------------
Domain: Dyck paths
------------------------------------------------------------------------
Codomain: Skew partitions
------------------------------------------------------------------------
Description: The parallelogram polyomino corresponding to a Dyck path, interpreted as a skew partition.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
This map returns the skew partition definded by the diagram of $\gamma(D)$.
------------------------------------------------------------------------
References:
------------------------------------------------------------------------
Code:
def mapping(D):
p = ParallelogramPolyomino.from_dyck_word(D)
return SkewPartitions(p.area()).from_row_and_column_length(p.widths()[::-1], p.heights())
------------------------------------------------------------------------
Map images:
[1,0] => [[1],[]]
[1,0,1,0] => [[1,1],[]]
[1,1,0,0] => [[2],[]]
[1,0,1,0,1,0] => [[1,1,1],[]]
[1,0,1,1,0,0] => [[2,1],[]]
[1,1,0,0,1,0] => [[2,2],[1]]
[1,1,0,1,0,0] => [[3],[]]
[1,1,1,0,0,0] => [[2,2],[]]
[1,0,1,0,1,0,1,0] => [[1,1,1,1],[]]
[1,0,1,0,1,1,0,0] => [[2,1,1],[]]
[1,0,1,1,0,0,1,0] => [[2,2,1],[1]]
[1,0,1,1,0,1,0,0] => [[3,1],[]]
[1,0,1,1,1,0,0,0] => [[2,2,1],[]]
[1,1,0,0,1,0,1,0] => [[2,2,2],[1,1]]
[1,1,0,0,1,1,0,0] => [[3,2],[1]]
[1,1,0,1,0,0,1,0] => [[3,3],[2]]
[1,1,0,1,0,1,0,0] => [[4],[]]
[1,1,0,1,1,0,0,0] => [[3,3],[1]]
[1,1,1,0,0,0,1,0] => [[2,2,2],[1]]
[1,1,1,0,0,1,0,0] => [[3,2],[]]
[1,1,1,0,1,0,0,0] => [[2,2,2],[]]
[1,1,1,1,0,0,0,0] => [[3,3],[]]
[1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1],[]]
[1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1],[]]
[1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1],[1]]
[1,0,1,0,1,1,0,1,0,0] => [[3,1,1],[]]
[1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1],[]]
[1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1],[1,1]]
[1,0,1,1,0,0,1,1,0,0] => [[3,2,1],[1]]
[1,0,1,1,0,1,0,0,1,0] => [[3,3,1],[2]]
[1,0,1,1,0,1,0,1,0,0] => [[4,1],[]]
[1,0,1,1,0,1,1,0,0,0] => [[3,3,1],[1]]
[1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1],[1]]
[1,0,1,1,1,0,0,1,0,0] => [[3,2,1],[]]
[1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1],[]]
[1,0,1,1,1,1,0,0,0,0] => [[3,3,1],[]]
[1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2],[1,1,1]]
[1,1,0,0,1,0,1,1,0,0] => [[3,2,2],[1,1]]
[1,1,0,0,1,1,0,0,1,0] => [[3,3,2],[2,1]]
[1,1,0,0,1,1,0,1,0,0] => [[4,2],[1]]
[1,1,0,0,1,1,1,0,0,0] => [[3,3,2],[1,1]]
[1,1,0,1,0,0,1,0,1,0] => [[3,3,3],[2,2]]
[1,1,0,1,0,0,1,1,0,0] => [[4,3],[2]]
[1,1,0,1,0,1,0,0,1,0] => [[4,4],[3]]
[1,1,0,1,0,1,0,1,0,0] => [[5],[]]
[1,1,0,1,0,1,1,0,0,0] => [[4,4],[2]]
[1,1,0,1,1,0,0,0,1,0] => [[3,3,3],[2,1]]
[1,1,0,1,1,0,0,1,0,0] => [[4,3],[1]]
[1,1,0,1,1,0,1,0,0,0] => [[3,3,3],[1,1]]
[1,1,0,1,1,1,0,0,0,0] => [[4,4],[1]]
[1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2],[1,1]]
[1,1,1,0,0,0,1,1,0,0] => [[3,2,2],[1]]
[1,1,1,0,0,1,0,0,1,0] => [[3,3,2],[2]]
[1,1,1,0,0,1,0,1,0,0] => [[4,2],[]]
[1,1,1,0,0,1,1,0,0,0] => [[3,3,2],[1]]
[1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2],[1]]
[1,1,1,0,1,0,0,1,0,0] => [[3,2,2],[]]
[1,1,1,0,1,0,1,0,0,0] => [[2,2,2,2],[]]
[1,1,1,0,1,1,0,0,0,0] => [[3,3,2],[]]
[1,1,1,1,0,0,0,0,1,0] => [[3,3,3],[2]]
[1,1,1,1,0,0,0,1,0,0] => [[4,3],[]]
[1,1,1,1,0,0,1,0,0,0] => [[3,3,3],[1]]
[1,1,1,1,0,1,0,0,0,0] => [[4,4],[]]
[1,1,1,1,1,0,0,0,0,0] => [[3,3,3],[]]
[1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1],[]]
[1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1],[1]]
[1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1],[]]
[1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1],[]]
[1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1],[1,1]]
[1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1],[1]]
[1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1],[2]]
[1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1],[]]
[1,0,1,0,1,1,0,1,1,0,0,0] => [[3,3,1,1],[1]]
[1,0,1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1,1],[1]]
[1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1],[]]
[1,0,1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1,1],[]]
[1,0,1,0,1,1,1,1,0,0,0,0] => [[3,3,1,1],[]]
[1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1],[1,1,1]]
[1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1],[1,1]]
[1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1],[2,1]]
[1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1],[1]]
[1,0,1,1,0,0,1,1,1,0,0,0] => [[3,3,2,1],[1,1]]
[1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1],[2,2]]
[1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1],[2]]
[1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1],[3]]
[1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1],[]]
[1,0,1,1,0,1,0,1,1,0,0,0] => [[4,4,1],[2]]
[1,0,1,1,0,1,1,0,0,0,1,0] => [[3,3,3,1],[2,1]]
[1,0,1,1,0,1,1,0,0,1,0,0] => [[4,3,1],[1]]
[1,0,1,1,0,1,1,0,1,0,0,0] => [[3,3,3,1],[1,1]]
[1,0,1,1,0,1,1,1,0,0,0,0] => [[4,4,1],[1]]
[1,0,1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2,1],[1,1]]
[1,0,1,1,1,0,0,0,1,1,0,0] => [[3,2,2,1],[1]]
[1,0,1,1,1,0,0,1,0,0,1,0] => [[3,3,2,1],[2]]
[1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1],[]]
[1,0,1,1,1,0,0,1,1,0,0,0] => [[3,3,2,1],[1]]
[1,0,1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2,1],[1]]
[1,0,1,1,1,0,1,0,0,1,0,0] => [[3,2,2,1],[]]
[1,0,1,1,1,0,1,0,1,0,0,0] => [[2,2,2,2,1],[]]
[1,0,1,1,1,0,1,1,0,0,0,0] => [[3,3,2,1],[]]
[1,0,1,1,1,1,0,0,0,0,1,0] => [[3,3,3,1],[2]]
[1,0,1,1,1,1,0,0,0,1,0,0] => [[4,3,1],[]]
[1,0,1,1,1,1,0,0,1,0,0,0] => [[3,3,3,1],[1]]
[1,0,1,1,1,1,0,1,0,0,0,0] => [[4,4,1],[]]
[1,0,1,1,1,1,1,0,0,0,0,0] => [[3,3,3,1],[]]
[1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1,1]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1,1]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2],[1,1]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [[3,3,2,2],[1,1,1]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2,1]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2],[2,1]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2],[3,1]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2],[1]]
[1,1,0,0,1,1,0,1,1,0,0,0] => [[4,4,2],[2,1]]
[1,1,0,0,1,1,1,0,0,0,1,0] => [[3,3,3,2],[2,1,1]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [[4,3,2],[1,1]]
[1,1,0,0,1,1,1,0,1,0,0,0] => [[3,3,3,2],[1,1,1]]
[1,1,0,0,1,1,1,1,0,0,0,0] => [[4,4,2],[1,1]]
[1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3],[2,2,2]]
[1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3],[2,2]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3],[3,2]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3],[2]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [[4,4,3],[2,2]]
[1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4],[3,3]]
[1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4],[3]]
[1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5],[4]]
[1,1,0,1,0,1,0,1,0,1,0,0] => [[6],[]]
[1,1,0,1,0,1,0,1,1,0,0,0] => [[5,5],[3]]
[1,1,0,1,0,1,1,0,0,0,1,0] => [[4,4,4],[3,2]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [[5,4],[2]]
[1,1,0,1,0,1,1,0,1,0,0,0] => [[4,4,4],[2,2]]
[1,1,0,1,0,1,1,1,0,0,0,0] => [[5,5],[2]]
[1,1,0,1,1,0,0,0,1,0,1,0] => [[3,3,3,3],[2,2,1]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [[4,3,3],[2,1]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [[4,4,3],[3,1]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [[5,3],[1]]
[1,1,0,1,1,0,0,1,1,0,0,0] => [[4,4,3],[2,1]]
[1,1,0,1,1,0,1,0,0,0,1,0] => [[3,3,3,3],[2,1,1]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [[4,3,3],[1,1]]
[1,1,0,1,1,0,1,0,1,0,0,0] => [[3,3,3,3],[1,1,1]]
[1,1,0,1,1,0,1,1,0,0,0,0] => [[4,4,3],[1,1]]
[1,1,0,1,1,1,0,0,0,0,1,0] => [[4,4,4],[3,1]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [[5,4],[1]]
[1,1,0,1,1,1,0,0,1,0,0,0] => [[4,4,4],[2,1]]
[1,1,0,1,1,1,0,1,0,0,0,0] => [[5,5],[1]]
[1,1,0,1,1,1,1,0,0,0,0,0] => [[4,4,4],[1,1]]
[1,1,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1]]
[1,1,1,0,0,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [[4,2,2],[1]]
[1,1,1,0,0,0,1,1,1,0,0,0] => [[3,3,2,2],[1,1]]
[1,1,1,0,0,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [[4,3,2],[2]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [[4,4,2],[3]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2],[]]
[1,1,1,0,0,1,0,1,1,0,0,0] => [[4,4,2],[2]]
[1,1,1,0,0,1,1,0,0,0,1,0] => [[3,3,3,2],[2,1]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [[4,3,2],[1]]
[1,1,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2],[1,1]]
[1,1,1,0,0,1,1,1,0,0,0,0] => [[4,4,2],[1]]
[1,1,1,0,1,0,0,0,1,0,1,0] => [[2,2,2,2,2],[1,1]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [[3,2,2,2],[1]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [[3,3,2,2],[2]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [[4,2,2],[]]
[1,1,1,0,1,0,0,1,1,0,0,0] => [[3,3,2,2],[1]]
[1,1,1,0,1,0,1,0,0,0,1,0] => [[2,2,2,2,2],[1]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2],[]]
[1,1,1,0,1,0,1,0,1,0,0,0] => [[2,2,2,2,2],[]]
[1,1,1,0,1,0,1,1,0,0,0,0] => [[3,3,2,2],[]]
[1,1,1,0,1,1,0,0,0,0,1,0] => [[3,3,3,2],[2]]
[1,1,1,0,1,1,0,0,0,1,0,0] => [[4,3,2],[]]
[1,1,1,0,1,1,0,0,1,0,0,0] => [[3,3,3,2],[1]]
[1,1,1,0,1,1,0,1,0,0,0,0] => [[4,4,2],[]]
[1,1,1,0,1,1,1,0,0,0,0,0] => [[3,3,3,2],[]]
[1,1,1,1,0,0,0,0,1,0,1,0] => [[3,3,3,3],[2,2]]
[1,1,1,1,0,0,0,0,1,1,0,0] => [[4,3,3],[2]]
[1,1,1,1,0,0,0,1,0,0,1,0] => [[4,4,3],[3]]
[1,1,1,1,0,0,0,1,0,1,0,0] => [[5,3],[]]
[1,1,1,1,0,0,0,1,1,0,0,0] => [[4,4,3],[2]]
[1,1,1,1,0,0,1,0,0,0,1,0] => [[3,3,3,3],[2,1]]
[1,1,1,1,0,0,1,0,0,1,0,0] => [[4,3,3],[1]]
[1,1,1,1,0,0,1,0,1,0,0,0] => [[3,3,3,3],[1,1]]
[1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3],[1]]
[1,1,1,1,0,1,0,0,0,0,1,0] => [[4,4,4],[3]]
[1,1,1,1,0,1,0,0,0,1,0,0] => [[5,4],[]]
[1,1,1,1,0,1,0,0,1,0,0,0] => [[4,4,4],[2]]
[1,1,1,1,0,1,0,1,0,0,0,0] => [[5,5],[]]
[1,1,1,1,0,1,1,0,0,0,0,0] => [[4,4,4],[1]]
[1,1,1,1,1,0,0,0,0,0,1,0] => [[3,3,3,3],[2]]
[1,1,1,1,1,0,0,0,0,1,0,0] => [[4,3,3],[]]
[1,1,1,1,1,0,0,0,1,0,0,0] => [[3,3,3,3],[1]]
[1,1,1,1,1,0,0,1,0,0,0,0] => [[4,4,3],[]]
[1,1,1,1,1,0,1,0,0,0,0,0] => [[3,3,3,3],[]]
[1,1,1,1,1,1,0,0,0,0,0,0] => [[4,4,4],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1,1],[1]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1,1],[]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1,1],[1,1]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1,1],[1]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1,1],[2]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1],[]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[3,3,1,1,1],[1]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1,1,1],[1]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1,1],[]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1,1,1],[]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[3,3,1,1,1],[]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1,1],[1,1,1]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1,1],[1,1]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1,1],[2,1]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1,1],[1]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[3,3,2,1,1],[1,1]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1,1],[2,2]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1,1],[2]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1,1],[3]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1],[]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[4,4,1,1],[2]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[3,3,3,1,1],[2,1]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[4,3,1,1],[1]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[3,3,3,1,1],[1,1]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[4,4,1,1],[1]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2,1,1],[1,1]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[3,2,2,1,1],[1]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[3,3,2,1,1],[2]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1,1],[]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[3,3,2,1,1],[1]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2,1,1],[1]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[3,2,2,1,1],[]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[2,2,2,2,1,1],[]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[3,3,2,1,1],[]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[3,3,3,1,1],[2]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[4,3,1,1],[]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[3,3,3,1,1],[1]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[4,4,1,1],[]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[3,3,3,1,1],[]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,1],[1,1,1,1]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,1],[1,1,1]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,1],[2,1,1]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2,1],[1,1]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[3,3,2,2,1],[1,1,1]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,1],[2,2,1]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2,1],[2,1]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2,1],[3,1]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2,1],[1]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[4,4,2,1],[2,1]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[3,3,3,2,1],[2,1,1]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[4,3,2,1],[1,1]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[3,3,3,2,1],[1,1,1]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[4,4,2,1],[1,1]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,1],[2,2,2]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3,1],[2,2]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3,1],[3,2]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3,1],[2]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[4,4,3,1],[2,2]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4,1],[3,3]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4,1],[3]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5,1],[4]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1],[]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[5,5,1],[3]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[4,4,4,1],[3,2]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[5,4,1],[2]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[4,4,4,1],[2,2]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[5,5,1],[2]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[3,3,3,3,1],[2,2,1]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[4,3,3,1],[2,1]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[4,4,3,1],[3,1]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[5,3,1],[1]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[4,4,3,1],[2,1]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[3,3,3,3,1],[2,1,1]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[4,3,3,1],[1,1]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[3,3,3,3,1],[1,1,1]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,1],[1,1]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[4,4,4,1],[3,1]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[5,4,1],[1]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,1],[2,1]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[5,5,1],[1]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[4,4,4,1],[1,1]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2,1],[1,1,1]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[3,2,2,2,1],[1,1]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[3,3,2,2,1],[2,1]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[4,2,2,1],[1]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[3,3,2,2,1],[1,1]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[3,3,3,2,1],[2,2]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[4,3,2,1],[2]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[4,4,2,1],[3]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2,1],[]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[4,4,2,1],[2]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[3,3,3,2,1],[2,1]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[4,3,2,1],[1]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2,1],[1,1]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[4,4,2,1],[1]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[2,2,2,2,2,1],[1,1]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[3,2,2,2,1],[1]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[3,3,2,2,1],[2]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[4,2,2,1],[]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [[3,3,2,2,1],[1]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[2,2,2,2,2,1],[1]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2,1],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[2,2,2,2,2,1],[]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[3,3,2,2,1],[]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[3,3,3,2,1],[2]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[4,3,2,1],[]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[3,3,3,2,1],[1]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[4,4,2,1],[]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[3,3,3,2,1],[]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[3,3,3,3,1],[2,2]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[4,3,3,1],[2]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[4,4,3,1],[3]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[5,3,1],[]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,1],[2]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[3,3,3,3,1],[2,1]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[4,3,3,1],[1]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[3,3,3,3,1],[1,1]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1],[1]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[4,4,4,1],[3]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[5,4,1],[]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[4,4,4,1],[2]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[5,5,1],[]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[4,4,4,1],[1]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[3,3,3,3,1],[2]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[4,3,3,1],[]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[3,3,3,3,1],[1]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[4,4,3,1],[]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[3,3,3,3,1],[]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[4,4,4,1],[]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1,1,1,1]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2],[1,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2],[2,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[4,2,2,2],[1,1,1]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[3,3,2,2,2],[1,1,1,1]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2],[2,2,1,1]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[4,3,2,2],[2,1,1]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[4,4,2,2],[3,1,1]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[5,2,2],[1,1]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[4,4,2,2],[2,1,1]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[3,3,3,2,2],[2,1,1,1]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[4,3,2,2],[1,1,1]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[3,3,3,2,2],[1,1,1,1]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[4,4,2,2],[1,1,1]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2],[2,2,2,1]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[4,3,3,2],[2,2,1]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[4,4,3,2],[3,2,1]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2],[2,1]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[4,4,3,2],[2,2,1]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[4,4,4,2],[3,3,1]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[5,4,2],[3,1]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[5,5,2],[4,1]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[6,2],[1]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[5,5,2],[3,1]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[4,4,4,2],[3,2,1]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[5,4,2],[2,1]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[4,4,4,2],[2,2,1]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[5,5,2],[2,1]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[3,3,3,3,2],[2,2,1,1]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[4,3,3,2],[2,1,1]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[4,4,3,2],[3,1,1]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[5,3,2],[1,1]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[4,4,3,2],[2,1,1]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[3,3,3,3,2],[2,1,1,1]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[4,3,3,2],[1,1,1]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[3,3,3,3,2],[1,1,1,1]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[4,4,3,2],[1,1,1]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[4,4,4,2],[3,1,1]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[5,4,2],[1,1]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[4,4,4,2],[2,1,1]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[5,5,2],[1,1]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[4,4,4,2],[1,1,1]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3],[2,2,2,2]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3],[2,2,2]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[4,4,3,3],[3,2,2]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3],[2,2]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[4,4,3,3],[2,2,2]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[4,4,4,3],[3,3,2]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[5,4,3],[3,2]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[5,5,3],[4,2]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[6,3],[2]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[5,5,3],[3,2]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[4,4,4,3],[3,2,2]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[5,4,3],[2,2]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[4,4,4,3],[2,2,2]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[5,5,3],[2,2]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4],[3,3,3]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[5,4,4],[3,3]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4],[4,3]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[6,4],[3]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[5,5,4],[3,3]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[5,5,5],[4,4]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[6,5],[4]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[6,6],[5]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7],[]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[6,6],[4]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[5,5,5],[4,3]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[6,5],[3]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[5,5,5],[3,3]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[6,6],[3]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[4,4,4,4],[3,3,2]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[5,4,4],[3,2]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[5,5,4],[4,2]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[6,4],[2]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[5,5,4],[3,2]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[4,4,4,4],[3,2,2]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[5,4,4],[2,2]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[4,4,4,4],[2,2,2]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[5,5,4],[2,2]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[5,5,5],[4,2]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[6,5],[2]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[5,5,5],[3,2]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[6,6],[2]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[5,5,5],[2,2]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[3,3,3,3,3],[2,2,2,1]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[4,3,3,3],[2,2,1]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[4,4,3,3],[3,2,1]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[5,3,3],[2,1]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[4,4,3,3],[2,2,1]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[4,4,4,3],[3,3,1]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[5,4,3],[3,1]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[5,5,3],[4,1]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[6,3],[1]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3,1]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[4,4,4,3],[3,2,1]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2,1]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[4,4,4,3],[2,2,1]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2,1]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[3,3,3,3,3],[2,2,1,1]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[4,3,3,3],[2,1,1]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[4,4,3,3],[3,1,1]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[5,3,3],[1,1]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1,1]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[3,3,3,3,3],[2,1,1,1]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[4,3,3,3],[1,1,1]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3],[1,1,1,1]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1,1]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1,1]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1,1]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1,1]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[5,5,3],[1,1]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[4,4,4,3],[1,1,1]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[4,4,4,4],[3,3,1]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[5,4,4],[3,1]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[5,5,4],[4,1]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[6,4],[1]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3,1]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[4,4,4,4],[3,2,1]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[5,4,4],[2,1]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[4,4,4,4],[2,2,1]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2,1]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[5,5,5],[4,1]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[6,5],[1]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[5,5,5],[3,1]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[6,6],[1]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[5,5,5],[2,1]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[4,4,4,4],[3,1,1]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[5,4,4],[1,1]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[4,4,4,4],[2,1,1]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[5,5,4],[1,1]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[4,4,4,4],[1,1,1]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[5,5,5],[1,1]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1,1,1]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2],[1,1,1]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2],[2,1,1]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[4,2,2,2],[1,1]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[3,3,2,2,2],[1,1,1]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2],[2,2,1]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[4,3,2,2],[2,1]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[4,4,2,2],[3,1]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[5,2,2],[1]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[4,4,2,2],[2,1]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[3,3,3,2,2],[2,1,1]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[4,3,2,2],[1,1]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[3,3,3,2,2],[1,1,1]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[4,4,2,2],[1,1]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2],[2,2,2]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[4,3,3,2],[2,2]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[4,4,3,2],[3,2]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[5,3,2],[2]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[4,4,3,2],[2,2]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[4,4,4,2],[3,3]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[5,4,2],[3]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[5,5,2],[4]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[6,2],[]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[5,5,2],[3]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[4,4,4,2],[3,2]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[5,4,2],[2]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[4,4,4,2],[2,2]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[5,5,2],[2]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[3,3,3,3,2],[2,2,1]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[4,3,3,2],[2,1]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[4,4,3,2],[3,1]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[5,3,2],[1]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[4,4,3,2],[2,1]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[3,3,3,3,2],[2,1,1]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[4,3,3,2],[1,1]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[3,3,3,3,2],[1,1,1]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,2],[1,1]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[4,4,4,2],[3,1]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[5,4,2],[1]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,2],[2,1]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[5,5,2],[1]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[4,4,4,2],[1,1]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1,1]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[3,2,2,2,2],[1,1]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[3,3,2,2,2],[2,1]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[4,2,2,2],[1]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[3,3,2,2,2],[1,1]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[3,3,3,2,2],[2,2]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[4,3,2,2],[2]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[4,4,2,2],[3]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[5,2,2],[]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[4,4,2,2],[2]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[3,3,3,2,2],[2,1]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[4,3,2,2],[1]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2,2],[1,1]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[4,4,2,2],[1]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[3,2,2,2,2],[1]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[3,3,2,2,2],[2]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[4,2,2,2],[]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[3,3,2,2,2],[1]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[2,2,2,2,2,2],[1]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2,2],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[2,2,2,2,2,2],[]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[3,3,2,2,2],[]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[3,3,3,2,2],[2]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[4,3,2,2],[]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[3,3,3,2,2],[1]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[4,4,2,2],[]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[3,3,3,2,2],[]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[3,3,3,3,2],[2,2]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[4,3,3,2],[2]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[4,4,3,2],[3]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[5,3,2],[]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,2],[2]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[3,3,3,3,2],[2,1]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[4,3,3,2],[1]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[3,3,3,3,2],[1,1]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2],[1]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[4,4,4,2],[3]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[5,4,2],[]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[4,4,4,2],[2]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[5,5,2],[]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[4,4,4,2],[1]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[3,3,3,3,2],[2]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[4,3,3,2],[]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[3,3,3,3,2],[1]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[4,4,3,2],[]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[3,3,3,3,2],[]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[4,4,4,2],[]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[3,3,3,3,3],[2,2,2]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[4,3,3,3],[2,2]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[4,4,3,3],[3,2]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[5,3,3],[2]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[4,4,3,3],[2,2]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[4,4,4,3],[3,3]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[5,4,3],[3]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[5,5,3],[4]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[6,3],[]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[5,5,3],[3]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[4,4,4,3],[3,2]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[5,4,3],[2]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[4,4,4,3],[2,2]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3],[2]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[3,3,3,3,3],[2,2,1]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[4,3,3,3],[2,1]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[4,4,3,3],[3,1]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[5,3,3],[1]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[4,4,3,3],[2,1]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[3,3,3,3,3],[2,1,1]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[4,3,3,3],[1,1]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3],[1,1,1]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3],[1,1]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3],[3,1]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3],[1]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3],[2,1]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[5,5,3],[1]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[4,4,4,3],[1,1]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[4,4,4,4],[3,3]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[5,4,4],[3]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[5,5,4],[4]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[6,4],[]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[5,5,4],[3]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[4,4,4,4],[3,2]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[5,4,4],[2]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[4,4,4,4],[2,2]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[5,5,4],[2]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[5,5,5],[4]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[6,5],[]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[5,5,5],[3]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[6,6],[]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[5,5,5],[2]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[4,4,4,4],[3,1]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[5,4,4],[1]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[4,4,4,4],[2,1]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[5,5,4],[1]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[4,4,4,4],[1,1]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[5,5,5],[1]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[3,3,3,3,3],[2,2]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[4,3,3,3],[2]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[4,4,3,3],[3]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[5,3,3],[]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[4,4,3,3],[2]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[3,3,3,3,3],[2,1]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[4,3,3,3],[1]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[3,3,3,3,3],[1,1]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[4,4,3,3],[1]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[4,4,4,3],[3]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[5,4,3],[]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[4,4,4,3],[2]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[5,5,3],[]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[4,4,4,3],[1]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[3,3,3,3,3],[2]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[4,3,3,3],[]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[3,3,3,3,3],[1]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[4,4,3,3],[]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[3,3,3,3,3],[]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[4,4,4,3],[]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[4,4,4,4],[3]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[5,4,4],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[4,4,4,4],[2]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[5,5,4],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[4,4,4,4],[1]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[5,5,5],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[4,4,4,4],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1,1,1],[1]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1,1,1],[1,1]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1,1,1],[1]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1,1,1],[2]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[3,3,1,1,1,1],[1]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1,1,1,1],[1]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1,1,1,1],[]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[3,3,1,1,1,1],[]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1,1,1],[1,1,1]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1,1,1],[1,1]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1,1,1],[2,1]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1,1,1],[1]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[3,3,2,1,1,1],[1,1]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1,1,1],[2,2]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1,1,1],[2]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1,1,1],[3]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1,1],[]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[4,4,1,1,1],[2]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[3,3,3,1,1,1],[2,1]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[4,3,1,1,1],[1]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[3,3,3,1,1,1],[1,1]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[4,4,1,1,1],[1]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2,1,1,1],[1,1]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[3,2,2,1,1,1],[1]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[3,3,2,1,1,1],[2]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1,1,1],[]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[3,3,2,1,1,1],[1]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2,1,1,1],[1]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[3,2,2,1,1,1],[]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[2,2,2,2,1,1,1],[]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[3,3,2,1,1,1],[]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[3,3,3,1,1,1],[2]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[4,3,1,1,1],[]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[3,3,3,1,1,1],[1]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[4,4,1,1,1],[]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[3,3,3,1,1,1],[]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,1,1],[1,1,1,1]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,1,1],[1,1,1]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,1,1],[2,1,1]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2,1,1],[1,1]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[3,3,2,2,1,1],[1,1,1]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,1,1],[2,2,1]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2,1,1],[2,1]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2,1,1],[3,1]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2,1,1],[1]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[4,4,2,1,1],[2,1]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[3,3,3,2,1,1],[2,1,1]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[4,3,2,1,1],[1,1]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[3,3,3,2,1,1],[1,1,1]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[4,4,2,1,1],[1,1]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,1,1],[2,2,2]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3,1,1],[2,2]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3,1,1],[3,2]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3,1,1],[2]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[4,4,3,1,1],[2,2]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4,1,1],[3,3]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4,1,1],[3]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5,1,1],[4]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1,1],[]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[5,5,1,1],[3]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[4,4,4,1,1],[3,2]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[5,4,1,1],[2]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[4,4,4,1,1],[2,2]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[5,5,1,1],[2]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[3,3,3,3,1,1],[2,2,1]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[4,3,3,1,1],[2,1]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[4,4,3,1,1],[3,1]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[5,3,1,1],[1]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[4,4,3,1,1],[2,1]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[3,3,3,3,1,1],[2,1,1]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[4,3,3,1,1],[1,1]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[3,3,3,3,1,1],[1,1,1]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,1,1],[1,1]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[4,4,4,1,1],[3,1]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[5,4,1,1],[1]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,1,1],[2,1]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[5,5,1,1],[1]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[4,4,4,1,1],[1,1]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2,1,1],[1,1,1]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[3,2,2,2,1,1],[1,1]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[3,3,2,2,1,1],[2,1]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[4,2,2,1,1],[1]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[3,3,2,2,1,1],[1,1]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[3,3,3,2,1,1],[2,2]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[4,3,2,1,1],[2]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[4,4,2,1,1],[3]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2,1,1],[]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[4,4,2,1,1],[2]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[3,3,3,2,1,1],[2,1]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[4,3,2,1,1],[1]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2,1,1],[1,1]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[4,4,2,1,1],[1]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[2,2,2,2,2,1,1],[1,1]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[3,2,2,2,1,1],[1]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[3,3,2,2,1,1],[2]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[4,2,2,1,1],[]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [[3,3,2,2,1,1],[1]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[2,2,2,2,2,1,1],[1]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2,1,1],[]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[2,2,2,2,2,1,1],[]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[3,3,2,2,1,1],[]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[3,3,3,2,1,1],[2]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[4,3,2,1,1],[]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[3,3,3,2,1,1],[1]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[4,4,2,1,1],[]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[3,3,3,2,1,1],[]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[3,3,3,3,1,1],[2,2]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[4,3,3,1,1],[2]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[4,4,3,1,1],[3]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[5,3,1,1],[]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,1,1],[2]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[3,3,3,3,1,1],[2,1]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[4,3,3,1,1],[1]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[3,3,3,3,1,1],[1,1]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,1,1],[1]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[4,4,4,1,1],[3]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[5,4,1,1],[]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[4,4,4,1,1],[2]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[5,5,1,1],[]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[4,4,4,1,1],[1]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[3,3,3,3,1,1],[2]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[4,3,3,1,1],[]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[3,3,3,3,1,1],[1]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[4,4,3,1,1],[]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[3,3,3,3,1,1],[]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[4,4,4,1,1],[]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,1],[1,1,1,1,1]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2,1],[1,1,1,1]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2,1],[2,1,1,1]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[4,2,2,2,1],[1,1,1]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[3,3,2,2,2,1],[1,1,1,1]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2,1],[2,2,1,1]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[4,3,2,2,1],[2,1,1]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[4,4,2,2,1],[3,1,1]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[5,2,2,1],[1,1]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[4,4,2,2,1],[2,1,1]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[3,3,3,2,2,1],[2,1,1,1]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[4,3,2,2,1],[1,1,1]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[3,3,3,2,2,1],[1,1,1,1]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[4,4,2,2,1],[1,1,1]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2,1],[2,2,2,1]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[4,3,3,2,1],[2,2,1]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[4,4,3,2,1],[3,2,1]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2,1],[2,1]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[4,4,3,2,1],[2,2,1]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[4,4,4,2,1],[3,3,1]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[5,4,2,1],[3,1]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[5,5,2,1],[4,1]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[6,2,1],[1]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[5,5,2,1],[3,1]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[4,4,4,2,1],[3,2,1]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[5,4,2,1],[2,1]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[4,4,4,2,1],[2,2,1]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[5,5,2,1],[2,1]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[3,3,3,3,2,1],[2,2,1,1]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[4,3,3,2,1],[2,1,1]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[4,4,3,2,1],[3,1,1]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[5,3,2,1],[1,1]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[4,4,3,2,1],[2,1,1]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[3,3,3,3,2,1],[2,1,1,1]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[4,3,3,2,1],[1,1,1]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[3,3,3,3,2,1],[1,1,1,1]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[4,4,3,2,1],[1,1,1]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[4,4,4,2,1],[3,1,1]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[5,4,2,1],[1,1]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[4,4,4,2,1],[2,1,1]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[5,5,2,1],[1,1]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[4,4,4,2,1],[1,1,1]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,1],[2,2,2,2]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3,1],[2,2,2]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[4,4,3,3,1],[3,2,2]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3,1],[2,2]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[4,4,3,3,1],[2,2,2]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[4,4,4,3,1],[3,3,2]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[5,4,3,1],[3,2]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[5,5,3,1],[4,2]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[6,3,1],[2]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[5,5,3,1],[3,2]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[4,4,4,3,1],[3,2,2]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[5,4,3,1],[2,2]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[4,4,4,3,1],[2,2,2]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[5,5,3,1],[2,2]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4,1],[3,3,3]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[5,4,4,1],[3,3]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4,1],[4,3]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[6,4,1],[3]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[5,5,4,1],[3,3]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[5,5,5,1],[4,4]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[6,5,1],[4]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[6,6,1],[5]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,1],[]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[6,6,1],[4]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[5,5,5,1],[4,3]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[6,5,1],[3]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[5,5,5,1],[3,3]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[6,6,1],[3]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[4,4,4,4,1],[3,3,2]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[5,4,4,1],[3,2]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[5,5,4,1],[4,2]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[6,4,1],[2]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[5,5,4,1],[3,2]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[4,4,4,4,1],[3,2,2]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[5,4,4,1],[2,2]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[4,4,4,4,1],[2,2,2]]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[5,5,4,1],[2,2]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[5,5,5,1],[4,2]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[6,5,1],[2]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[5,5,5,1],[3,2]]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[6,6,1],[2]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[5,5,5,1],[2,2]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[3,3,3,3,3,1],[2,2,2,1]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[4,3,3,3,1],[2,2,1]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[4,4,3,3,1],[3,2,1]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[5,3,3,1],[2,1]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[4,4,3,3,1],[2,2,1]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[4,4,4,3,1],[3,3,1]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[5,4,3,1],[3,1]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[5,5,3,1],[4,1]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[6,3,1],[1]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[5,5,3,1],[3,1]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[4,4,4,3,1],[3,2,1]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[5,4,3,1],[2,1]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[4,4,4,3,1],[2,2,1]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[5,5,3,1],[2,1]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[3,3,3,3,3,1],[2,2,1,1]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[4,3,3,3,1],[2,1,1]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[4,4,3,3,1],[3,1,1]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[5,3,3,1],[1,1]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[4,4,3,3,1],[2,1,1]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[3,3,3,3,3,1],[2,1,1,1]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[4,3,3,3,1],[1,1,1]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3,1],[1,1,1,1]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[4,4,3,3,1],[1,1,1]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[4,4,4,3,1],[3,1,1]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[5,4,3,1],[1,1]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[4,4,4,3,1],[2,1,1]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[5,5,3,1],[1,1]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[4,4,4,3,1],[1,1,1]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[4,4,4,4,1],[3,3,1]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[5,4,4,1],[3,1]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[5,5,4,1],[4,1]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[6,4,1],[1]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[5,5,4,1],[3,1]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[4,4,4,4,1],[3,2,1]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[5,4,4,1],[2,1]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[4,4,4,4,1],[2,2,1]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4,1],[2,1]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[5,5,5,1],[4,1]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[6,5,1],[1]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[5,5,5,1],[3,1]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[6,6,1],[1]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[5,5,5,1],[2,1]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[4,4,4,4,1],[3,1,1]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[5,4,4,1],[1,1]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[4,4,4,4,1],[2,1,1]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[5,5,4,1],[1,1]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[4,4,4,4,1],[1,1,1]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[5,5,5,1],[1,1]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,1],[1,1,1,1]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2,1],[1,1,1]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2,1],[2,1,1]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[4,2,2,2,1],[1,1]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[3,3,2,2,2,1],[1,1,1]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2,1],[2,2,1]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[4,3,2,2,1],[2,1]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[4,4,2,2,1],[3,1]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[5,2,2,1],[1]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[4,4,2,2,1],[2,1]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[3,3,3,2,2,1],[2,1,1]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[4,3,2,2,1],[1,1]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[3,3,3,2,2,1],[1,1,1]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[4,4,2,2,1],[1,1]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2,1],[2,2,2]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[4,3,3,2,1],[2,2]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[4,4,3,2,1],[3,2]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[5,3,2,1],[2]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[4,4,3,2,1],[2,2]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[4,4,4,2,1],[3,3]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[5,4,2,1],[3]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[5,5,2,1],[4]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[6,2,1],[]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[5,5,2,1],[3]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[4,4,4,2,1],[3,2]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[5,4,2,1],[2]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[4,4,4,2,1],[2,2]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[5,5,2,1],[2]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[3,3,3,3,2,1],[2,2,1]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[4,3,3,2,1],[2,1]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[4,4,3,2,1],[3,1]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[5,3,2,1],[1]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[4,4,3,2,1],[2,1]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[3,3,3,3,2,1],[2,1,1]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[4,3,3,2,1],[1,1]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[3,3,3,3,2,1],[1,1,1]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[4,4,3,2,1],[1,1]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[4,4,4,2,1],[3,1]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[5,4,2,1],[1]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[4,4,4,2,1],[2,1]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[5,5,2,1],[1]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[4,4,4,2,1],[1,1]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,1],[1,1,1]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[3,2,2,2,2,1],[1,1]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[3,3,2,2,2,1],[2,1]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[4,2,2,2,1],[1]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[3,3,2,2,2,1],[1,1]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[3,3,3,2,2,1],[2,2]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[4,3,2,2,1],[2]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[4,4,2,2,1],[3]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[5,2,2,1],[]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[4,4,2,2,1],[2]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[3,3,3,2,2,1],[2,1]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[4,3,2,2,1],[1]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2,2,1],[1,1]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[4,4,2,2,1],[1]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[2,2,2,2,2,2,1],[1,1]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[3,2,2,2,2,1],[1]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[3,3,2,2,2,1],[2]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[4,2,2,2,1],[]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[3,3,2,2,2,1],[1]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[2,2,2,2,2,2,1],[1]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2,2,1],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[2,2,2,2,2,2,1],[]]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[3,3,2,2,2,1],[]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[3,3,3,2,2,1],[2]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[4,3,2,2,1],[]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[3,3,3,2,2,1],[1]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[4,4,2,2,1],[]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[3,3,3,2,2,1],[]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[3,3,3,3,2,1],[2,2]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[4,3,3,2,1],[2]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[4,4,3,2,1],[3]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[5,3,2,1],[]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[4,4,3,2,1],[2]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[3,3,3,3,2,1],[2,1]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[4,3,3,2,1],[1]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[3,3,3,3,2,1],[1,1]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[4,4,3,2,1],[1]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[4,4,4,2,1],[3]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[5,4,2,1],[]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[4,4,4,2,1],[2]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[5,5,2,1],[]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[4,4,4,2,1],[1]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[3,3,3,3,2,1],[2]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[4,3,3,2,1],[]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[3,3,3,3,2,1],[1]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[4,4,3,2,1],[]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[3,3,3,3,2,1],[]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[4,4,4,2,1],[]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[3,3,3,3,3,1],[2,2,2]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[4,3,3,3,1],[2,2]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[4,4,3,3,1],[3,2]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[5,3,3,1],[2]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[4,4,3,3,1],[2,2]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[4,4,4,3,1],[3,3]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[5,4,3,1],[3]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[5,5,3,1],[4]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[6,3,1],[]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[5,5,3,1],[3]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[4,4,4,3,1],[3,2]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[5,4,3,1],[2]]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[4,4,4,3,1],[2,2]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[5,5,3,1],[2]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[3,3,3,3,3,1],[2,2,1]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[4,3,3,3,1],[2,1]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[4,4,3,3,1],[3,1]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[5,3,3,1],[1]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[4,4,3,3,1],[2,1]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[3,3,3,3,3,1],[2,1,1]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[4,3,3,3,1],[1,1]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3,1],[1,1,1]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[4,4,3,3,1],[1,1]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[4,4,4,3,1],[3,1]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[5,4,3,1],[1]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[4,4,4,3,1],[2,1]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[5,5,3,1],[1]]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[4,4,4,3,1],[1,1]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[4,4,4,4,1],[3,3]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[5,4,4,1],[3]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[5,5,4,1],[4]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[6,4,1],[]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[5,5,4,1],[3]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[4,4,4,4,1],[3,2]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[5,4,4,1],[2]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[4,4,4,4,1],[2,2]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[5,5,4,1],[2]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[5,5,5,1],[4]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[6,5,1],[]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[5,5,5,1],[3]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[6,6,1],[]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[5,5,5,1],[2]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[4,4,4,4,1],[3,1]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[5,4,4,1],[1]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[4,4,4,4,1],[2,1]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[5,5,4,1],[1]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[4,4,4,4,1],[1,1]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[5,5,5,1],[1]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[3,3,3,3,3,1],[2,2]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[4,3,3,3,1],[2]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[4,4,3,3,1],[3]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[5,3,3,1],[]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[4,4,3,3,1],[2]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[3,3,3,3,3,1],[2,1]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[4,3,3,3,1],[1]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[3,3,3,3,3,1],[1,1]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[4,4,3,3,1],[1]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[4,4,4,3,1],[3]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[5,4,3,1],[]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[4,4,4,3,1],[2]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[5,5,3,1],[]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[4,4,4,3,1],[1]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[3,3,3,3,3,1],[2]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[4,3,3,3,1],[]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[3,3,3,3,3,1],[1]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[4,4,3,3,1],[]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[3,3,3,3,3,1],[]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[4,4,4,3,1],[]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[4,4,4,4,1],[3]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[5,4,4,1],[]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[4,4,4,4,1],[2]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[5,5,4,1],[]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[4,4,4,4,1],[1]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[5,5,5,1],[]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[4,4,4,4,1],[]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2,2],[1,1,1,1,1]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2,2],[2,1,1,1,1]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[4,2,2,2,2],[1,1,1,1]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[3,3,2,2,2,2],[1,1,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2,2],[2,2,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[4,3,2,2,2],[2,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[4,4,2,2,2],[3,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[5,2,2,2],[1,1,1]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[4,4,2,2,2],[2,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[3,3,3,2,2,2],[2,1,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[4,3,2,2,2],[1,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[3,3,3,2,2,2],[1,1,1,1,1]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[4,4,2,2,2],[1,1,1,1]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2,2],[2,2,2,1,1]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[4,3,3,2,2],[2,2,1,1]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[4,4,3,2,2],[3,2,1,1]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2,2],[2,1,1]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[4,4,3,2,2],[2,2,1,1]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[4,4,4,2,2],[3,3,1,1]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[5,4,2,2],[3,1,1]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[5,5,2,2],[4,1,1]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[6,2,2],[1,1]]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[5,5,2,2],[3,1,1]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[4,4,4,2,2],[3,2,1,1]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[5,4,2,2],[2,1,1]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[4,4,4,2,2],[2,2,1,1]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[5,5,2,2],[2,1,1]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[3,3,3,3,2,2],[2,2,1,1,1]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[4,3,3,2,2],[2,1,1,1]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[4,4,3,2,2],[3,1,1,1]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[5,3,2,2],[1,1,1]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[4,4,3,2,2],[2,1,1,1]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[3,3,3,3,2,2],[2,1,1,1,1]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[4,3,3,2,2],[1,1,1,1]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[3,3,3,3,2,2],[1,1,1,1,1]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[4,4,3,2,2],[1,1,1,1]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[4,4,4,2,2],[3,1,1,1]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[5,4,2,2],[1,1,1]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[4,4,4,2,2],[2,1,1,1]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[5,5,2,2],[1,1,1]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[4,4,4,2,2],[1,1,1,1]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,2],[2,2,2,2,1]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3,2],[2,2,2,1]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[4,4,3,3,2],[3,2,2,1]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3,2],[2,2,1]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[4,4,3,3,2],[2,2,2,1]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[4,4,4,3,2],[3,3,2,1]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[5,4,3,2],[3,2,1]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[5,5,3,2],[4,2,1]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[6,3,2],[2,1]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[5,5,3,2],[3,2,1]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[4,4,4,3,2],[3,2,2,1]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[5,4,3,2],[2,2,1]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[4,4,4,3,2],[2,2,2,1]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[5,5,3,2],[2,2,1]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4,2],[3,3,3,1]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[5,4,4,2],[3,3,1]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4,2],[4,3,1]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[6,4,2],[3,1]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[5,5,4,2],[3,3,1]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[5,5,5,2],[4,4,1]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[6,5,2],[4,1]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[6,6,2],[5,1]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[7,2],[1]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[6,6,2],[4,1]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[5,5,5,2],[4,3,1]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[6,5,2],[3,1]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[5,5,5,2],[3,3,1]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[6,6,2],[3,1]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[4,4,4,4,2],[3,3,2,1]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[5,4,4,2],[3,2,1]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[5,5,4,2],[4,2,1]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[6,4,2],[2,1]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[5,5,4,2],[3,2,1]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[4,4,4,4,2],[3,2,2,1]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[5,4,4,2],[2,2,1]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[4,4,4,4,2],[2,2,2,1]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[5,5,4,2],[2,2,1]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[5,5,5,2],[4,2,1]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[6,5,2],[2,1]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[5,5,5,2],[3,2,1]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[6,6,2],[2,1]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[5,5,5,2],[2,2,1]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[3,3,3,3,3,2],[2,2,2,1,1]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[4,3,3,3,2],[2,2,1,1]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[4,4,3,3,2],[3,2,1,1]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[5,3,3,2],[2,1,1]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[4,4,3,3,2],[2,2,1,1]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[4,4,4,3,2],[3,3,1,1]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[5,4,3,2],[3,1,1]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[5,5,3,2],[4,1,1]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[6,3,2],[1,1]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[5,5,3,2],[3,1,1]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[4,4,4,3,2],[3,2,1,1]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[5,4,3,2],[2,1,1]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[4,4,4,3,2],[2,2,1,1]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[5,5,3,2],[2,1,1]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[3,3,3,3,3,2],[2,2,1,1,1]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[4,3,3,3,2],[2,1,1,1]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[4,4,3,3,2],[3,1,1,1]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[5,3,3,2],[1,1,1]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [[4,4,3,3,2],[2,1,1,1]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[3,3,3,3,3,2],[2,1,1,1,1]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[4,3,3,3,2],[1,1,1,1]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[3,3,3,3,3,2],[1,1,1,1,1]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[4,4,3,3,2],[1,1,1,1]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[4,4,4,3,2],[3,1,1,1]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[5,4,3,2],[1,1,1]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[4,4,4,3,2],[2,1,1,1]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[5,5,3,2],[1,1,1]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[4,4,4,3,2],[1,1,1,1]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[4,4,4,4,2],[3,3,1,1]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[5,4,4,2],[3,1,1]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[5,5,4,2],[4,1,1]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[6,4,2],[1,1]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[5,5,4,2],[3,1,1]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[4,4,4,4,2],[3,2,1,1]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[5,4,4,2],[2,1,1]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[4,4,4,4,2],[2,2,1,1]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[5,5,4,2],[2,1,1]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[5,5,5,2],[4,1,1]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[6,5,2],[1,1]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[5,5,5,2],[3,1,1]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[6,6,2],[1,1]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[5,5,5,2],[2,1,1]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[4,4,4,4,2],[3,1,1,1]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[5,4,4,2],[1,1,1]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[4,4,4,4,2],[2,1,1,1]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[5,5,4,2],[1,1,1]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[4,4,4,4,2],[1,1,1,1]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[5,5,5,2],[1,1,1]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3,3],[2,2,2,2,2]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[4,3,3,3,3],[2,2,2,2]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[4,4,3,3,3],[3,2,2,2]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[5,3,3,3],[2,2,2]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[4,4,3,3,3],[2,2,2,2]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[4,4,4,3,3],[3,3,2,2]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[5,4,3,3],[3,2,2]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[5,5,3,3],[4,2,2]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[6,3,3],[2,2]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[5,5,3,3],[3,2,2]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[4,4,4,3,3],[3,2,2,2]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[5,4,3,3],[2,2,2]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[4,4,4,3,3],[2,2,2,2]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[5,5,3,3],[2,2,2]]
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Created: May 13, 2021 at 15:12 by Martin Rubey
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Last Updated: May 13, 2021 at 15:12 by Martin Rubey