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------------------------------------------------------------------------
Map identifier: Mp00036
------------------------------------------------------------------------
Map name: to semistandard tableau
------------------------------------------------------------------------
Domain: Gelfand-Tsetlin patterns
------------------------------------------------------------------------
Codomain: Semistandard tableaux
------------------------------------------------------------------------
Description: Return the Gelfand-Tsetlin pattern as a semistandard Young tableau.
Let $G$ be a Gelfand-Tsetlin pattern and let $\lambda^{(k)}$ be its $(n-k+1)$-st row. The defining inequalities of a Gelfand-Tsetlin pattern imply, regarding each row as a partition,
$$
\lambda^{(0)} \subseteq \lambda^{(1)} \subseteq \cdots \subseteq \lambda^{(n)},
$$
where $\lambda^{(0)}$ is the empty partition.
Each skew shape $\lambda^{(k)} / \lambda^{(k-1)}$ is moreover a horizontal strip.
We now define a semistandard tableau $T(G)$ by inserting $k$ into the cells of the skew shape $\lambda^{(k)} / \lambda^{(k-1)}$, for $k=1,\dots,n$.
------------------------------------------------------------------------
References:
------------------------------------------------------------------------
Code:
def mapping(elt):
ret = []
for i, row in enumerate(reversed(elt)):
for j, val in enumerate(row):
if j >= len(ret):
if val == 0:
break
ret.append([i+1]*val)
else:
ret[j].extend([i+1]*(val-len(ret[j])))
S = SemistandardTableaux()
return S(ret)
------------------------------------------------------------------------
Map images:
[[1,0],[0]] => [[2]]
[[1,0],[1]] => [[1]]
[[2,0],[0]] => [[2,2]]
[[2,0],[1]] => [[1,2]]
[[2,0],[2]] => [[1,1]]
[[1,1],[1]] => [[1],[2]]
[[3,0],[0]] => [[2,2,2]]
[[3,0],[1]] => [[1,2,2]]
[[3,0],[2]] => [[1,1,2]]
[[3,0],[3]] => [[1,1,1]]
[[2,1],[1]] => [[1,2],[2]]
[[2,1],[2]] => [[1,1],[2]]
[[4,0],[0]] => [[2,2,2,2]]
[[4,0],[1]] => [[1,2,2,2]]
[[4,0],[2]] => [[1,1,2,2]]
[[4,0],[3]] => [[1,1,1,2]]
[[4,0],[4]] => [[1,1,1,1]]
[[3,1],[1]] => [[1,2,2],[2]]
[[3,1],[2]] => [[1,1,2],[2]]
[[3,1],[3]] => [[1,1,1],[2]]
[[2,2],[2]] => [[1,1],[2,2]]
[[5,0],[0]] => [[2,2,2,2,2]]
[[5,0],[1]] => [[1,2,2,2,2]]
[[5,0],[2]] => [[1,1,2,2,2]]
[[5,0],[3]] => [[1,1,1,2,2]]
[[5,0],[4]] => [[1,1,1,1,2]]
[[5,0],[5]] => [[1,1,1,1,1]]
[[4,1],[1]] => [[1,2,2,2],[2]]
[[4,1],[2]] => [[1,1,2,2],[2]]
[[4,1],[3]] => [[1,1,1,2],[2]]
[[4,1],[4]] => [[1,1,1,1],[2]]
[[3,2],[2]] => [[1,1,2],[2,2]]
[[3,2],[3]] => [[1,1,1],[2,2]]
[[6,0],[0]] => [[2,2,2,2,2,2]]
[[6,0],[1]] => [[1,2,2,2,2,2]]
[[6,0],[2]] => [[1,1,2,2,2,2]]
[[6,0],[3]] => [[1,1,1,2,2,2]]
[[6,0],[4]] => [[1,1,1,1,2,2]]
[[6,0],[5]] => [[1,1,1,1,1,2]]
[[6,0],[6]] => [[1,1,1,1,1,1]]
[[5,1],[1]] => [[1,2,2,2,2],[2]]
[[5,1],[2]] => [[1,1,2,2,2],[2]]
[[5,1],[3]] => [[1,1,1,2,2],[2]]
[[5,1],[4]] => [[1,1,1,1,2],[2]]
[[5,1],[5]] => [[1,1,1,1,1],[2]]
[[4,2],[2]] => [[1,1,2,2],[2,2]]
[[4,2],[3]] => [[1,1,1,2],[2,2]]
[[4,2],[4]] => [[1,1,1,1],[2,2]]
[[3,3],[3]] => [[1,1,1],[2,2,2]]
[[7,0],[0]] => [[2,2,2,2,2,2,2]]
[[7,0],[1]] => [[1,2,2,2,2,2,2]]
[[7,0],[2]] => [[1,1,2,2,2,2,2]]
[[7,0],[3]] => [[1,1,1,2,2,2,2]]
[[7,0],[4]] => [[1,1,1,1,2,2,2]]
[[7,0],[5]] => [[1,1,1,1,1,2,2]]
[[7,0],[6]] => [[1,1,1,1,1,1,2]]
[[7,0],[7]] => [[1,1,1,1,1,1,1]]
[[6,1],[1]] => [[1,2,2,2,2,2],[2]]
[[6,1],[2]] => [[1,1,2,2,2,2],[2]]
[[6,1],[3]] => [[1,1,1,2,2,2],[2]]
[[6,1],[4]] => [[1,1,1,1,2,2],[2]]
[[6,1],[5]] => [[1,1,1,1,1,2],[2]]
[[6,1],[6]] => [[1,1,1,1,1,1],[2]]
[[5,2],[2]] => [[1,1,2,2,2],[2,2]]
[[5,2],[3]] => [[1,1,1,2,2],[2,2]]
[[5,2],[4]] => [[1,1,1,1,2],[2,2]]
[[5,2],[5]] => [[1,1,1,1,1],[2,2]]
[[4,3],[3]] => [[1,1,1,2],[2,2,2]]
[[4,3],[4]] => [[1,1,1,1],[2,2,2]]
[[1,0,0],[0,0],[0]] => [[3]]
[[1,0,0],[1,0],[0]] => [[2]]
[[1,0,0],[1,0],[1]] => [[1]]
[[2,0,0],[0,0],[0]] => [[3,3]]
[[2,0,0],[1,0],[0]] => [[2,3]]
[[2,0,0],[1,0],[1]] => [[1,3]]
[[2,0,0],[2,0],[0]] => [[2,2]]
[[2,0,0],[2,0],[1]] => [[1,2]]
[[2,0,0],[2,0],[2]] => [[1,1]]
[[1,1,0],[1,0],[0]] => [[2],[3]]
[[1,1,0],[1,0],[1]] => [[1],[3]]
[[1,1,0],[1,1],[1]] => [[1],[2]]
[[3,0,0],[0,0],[0]] => [[3,3,3]]
[[3,0,0],[1,0],[0]] => [[2,3,3]]
[[3,0,0],[1,0],[1]] => [[1,3,3]]
[[3,0,0],[2,0],[0]] => [[2,2,3]]
[[3,0,0],[2,0],[1]] => [[1,2,3]]
[[3,0,0],[2,0],[2]] => [[1,1,3]]
[[3,0,0],[3,0],[0]] => [[2,2,2]]
[[3,0,0],[3,0],[1]] => [[1,2,2]]
[[3,0,0],[3,0],[2]] => [[1,1,2]]
[[3,0,0],[3,0],[3]] => [[1,1,1]]
[[2,1,0],[1,0],[0]] => [[2,3],[3]]
[[2,1,0],[1,0],[1]] => [[1,3],[3]]
[[2,1,0],[1,1],[1]] => [[1,3],[2]]
[[2,1,0],[2,0],[0]] => [[2,2],[3]]
[[2,1,0],[2,0],[1]] => [[1,2],[3]]
[[2,1,0],[2,0],[2]] => [[1,1],[3]]
[[2,1,0],[2,1],[1]] => [[1,2],[2]]
[[2,1,0],[2,1],[2]] => [[1,1],[2]]
[[1,1,1],[1,1],[1]] => [[1],[2],[3]]
[[4,0,0],[0,0],[0]] => [[3,3,3,3]]
[[4,0,0],[1,0],[0]] => [[2,3,3,3]]
[[4,0,0],[1,0],[1]] => [[1,3,3,3]]
[[4,0,0],[2,0],[0]] => [[2,2,3,3]]
[[4,0,0],[2,0],[1]] => [[1,2,3,3]]
[[4,0,0],[2,0],[2]] => [[1,1,3,3]]
[[4,0,0],[3,0],[0]] => [[2,2,2,3]]
[[4,0,0],[3,0],[1]] => [[1,2,2,3]]
[[4,0,0],[3,0],[2]] => [[1,1,2,3]]
[[4,0,0],[3,0],[3]] => [[1,1,1,3]]
[[4,0,0],[4,0],[0]] => [[2,2,2,2]]
[[4,0,0],[4,0],[1]] => [[1,2,2,2]]
[[4,0,0],[4,0],[2]] => [[1,1,2,2]]
[[4,0,0],[4,0],[3]] => [[1,1,1,2]]
[[4,0,0],[4,0],[4]] => [[1,1,1,1]]
[[3,1,0],[1,0],[0]] => [[2,3,3],[3]]
[[3,1,0],[1,0],[1]] => [[1,3,3],[3]]
[[3,1,0],[1,1],[1]] => [[1,3,3],[2]]
[[3,1,0],[2,0],[0]] => [[2,2,3],[3]]
[[3,1,0],[2,0],[1]] => [[1,2,3],[3]]
[[3,1,0],[2,0],[2]] => [[1,1,3],[3]]
[[3,1,0],[2,1],[1]] => [[1,2,3],[2]]
[[3,1,0],[2,1],[2]] => [[1,1,3],[2]]
[[3,1,0],[3,0],[0]] => [[2,2,2],[3]]
[[3,1,0],[3,0],[1]] => [[1,2,2],[3]]
[[3,1,0],[3,0],[2]] => [[1,1,2],[3]]
[[3,1,0],[3,0],[3]] => [[1,1,1],[3]]
[[3,1,0],[3,1],[1]] => [[1,2,2],[2]]
[[3,1,0],[3,1],[2]] => [[1,1,2],[2]]
[[3,1,0],[3,1],[3]] => [[1,1,1],[2]]
[[2,2,0],[2,0],[0]] => [[2,2],[3,3]]
[[2,2,0],[2,0],[1]] => [[1,2],[3,3]]
[[2,2,0],[2,0],[2]] => [[1,1],[3,3]]
[[2,2,0],[2,1],[1]] => [[1,2],[2,3]]
[[2,2,0],[2,1],[2]] => [[1,1],[2,3]]
[[2,2,0],[2,2],[2]] => [[1,1],[2,2]]
[[2,1,1],[1,1],[1]] => [[1,3],[2],[3]]
[[2,1,1],[2,1],[1]] => [[1,2],[2],[3]]
[[2,1,1],[2,1],[2]] => [[1,1],[2],[3]]
[[5,0,0],[0,0],[0]] => [[3,3,3,3,3]]
[[5,0,0],[1,0],[0]] => [[2,3,3,3,3]]
[[5,0,0],[1,0],[1]] => [[1,3,3,3,3]]
[[5,0,0],[2,0],[0]] => [[2,2,3,3,3]]
[[5,0,0],[2,0],[1]] => [[1,2,3,3,3]]
[[5,0,0],[2,0],[2]] => [[1,1,3,3,3]]
[[5,0,0],[3,0],[0]] => [[2,2,2,3,3]]
[[5,0,0],[3,0],[1]] => [[1,2,2,3,3]]
[[5,0,0],[3,0],[2]] => [[1,1,2,3,3]]
[[5,0,0],[3,0],[3]] => [[1,1,1,3,3]]
[[5,0,0],[4,0],[0]] => [[2,2,2,2,3]]
[[5,0,0],[4,0],[1]] => [[1,2,2,2,3]]
[[5,0,0],[4,0],[2]] => [[1,1,2,2,3]]
[[5,0,0],[4,0],[3]] => [[1,1,1,2,3]]
[[5,0,0],[4,0],[4]] => [[1,1,1,1,3]]
[[5,0,0],[5,0],[0]] => [[2,2,2,2,2]]
[[5,0,0],[5,0],[1]] => [[1,2,2,2,2]]
[[5,0,0],[5,0],[2]] => [[1,1,2,2,2]]
[[5,0,0],[5,0],[3]] => [[1,1,1,2,2]]
[[5,0,0],[5,0],[4]] => [[1,1,1,1,2]]
[[5,0,0],[5,0],[5]] => [[1,1,1,1,1]]
[[4,1,0],[1,0],[0]] => [[2,3,3,3],[3]]
[[4,1,0],[1,0],[1]] => [[1,3,3,3],[3]]
[[4,1,0],[1,1],[1]] => [[1,3,3,3],[2]]
[[4,1,0],[2,0],[0]] => [[2,2,3,3],[3]]
[[4,1,0],[2,0],[1]] => [[1,2,3,3],[3]]
[[4,1,0],[2,0],[2]] => [[1,1,3,3],[3]]
[[4,1,0],[2,1],[1]] => [[1,2,3,3],[2]]
[[4,1,0],[2,1],[2]] => [[1,1,3,3],[2]]
[[4,1,0],[3,0],[0]] => [[2,2,2,3],[3]]
[[4,1,0],[3,0],[1]] => [[1,2,2,3],[3]]
[[4,1,0],[3,0],[2]] => [[1,1,2,3],[3]]
[[4,1,0],[3,0],[3]] => [[1,1,1,3],[3]]
[[4,1,0],[3,1],[1]] => [[1,2,2,3],[2]]
[[4,1,0],[3,1],[2]] => [[1,1,2,3],[2]]
[[4,1,0],[3,1],[3]] => [[1,1,1,3],[2]]
[[4,1,0],[4,0],[0]] => [[2,2,2,2],[3]]
[[4,1,0],[4,0],[1]] => [[1,2,2,2],[3]]
[[4,1,0],[4,0],[2]] => [[1,1,2,2],[3]]
[[4,1,0],[4,0],[3]] => [[1,1,1,2],[3]]
[[4,1,0],[4,0],[4]] => [[1,1,1,1],[3]]
[[4,1,0],[4,1],[1]] => [[1,2,2,2],[2]]
[[4,1,0],[4,1],[2]] => [[1,1,2,2],[2]]
[[4,1,0],[4,1],[3]] => [[1,1,1,2],[2]]
[[4,1,0],[4,1],[4]] => [[1,1,1,1],[2]]
[[3,2,0],[2,0],[0]] => [[2,2,3],[3,3]]
[[3,2,0],[2,0],[1]] => [[1,2,3],[3,3]]
[[3,2,0],[2,0],[2]] => [[1,1,3],[3,3]]
[[3,2,0],[2,1],[1]] => [[1,2,3],[2,3]]
[[3,2,0],[2,1],[2]] => [[1,1,3],[2,3]]
[[3,2,0],[2,2],[2]] => [[1,1,3],[2,2]]
[[3,2,0],[3,0],[0]] => [[2,2,2],[3,3]]
[[3,2,0],[3,0],[1]] => [[1,2,2],[3,3]]
[[3,2,0],[3,0],[2]] => [[1,1,2],[3,3]]
[[3,2,0],[3,0],[3]] => [[1,1,1],[3,3]]
[[3,2,0],[3,1],[1]] => [[1,2,2],[2,3]]
[[3,2,0],[3,1],[2]] => [[1,1,2],[2,3]]
[[3,2,0],[3,1],[3]] => [[1,1,1],[2,3]]
[[3,2,0],[3,2],[2]] => [[1,1,2],[2,2]]
[[3,2,0],[3,2],[3]] => [[1,1,1],[2,2]]
[[3,1,1],[1,1],[1]] => [[1,3,3],[2],[3]]
[[3,1,1],[2,1],[1]] => [[1,2,3],[2],[3]]
[[3,1,1],[2,1],[2]] => [[1,1,3],[2],[3]]
[[3,1,1],[3,1],[1]] => [[1,2,2],[2],[3]]
[[3,1,1],[3,1],[2]] => [[1,1,2],[2],[3]]
[[3,1,1],[3,1],[3]] => [[1,1,1],[2],[3]]
[[2,2,1],[2,1],[1]] => [[1,2],[2,3],[3]]
[[2,2,1],[2,1],[2]] => [[1,1],[2,3],[3]]
[[2,2,1],[2,2],[2]] => [[1,1],[2,2],[3]]
[[6,0,0],[0,0],[0]] => [[3,3,3,3,3,3]]
[[6,0,0],[1,0],[0]] => [[2,3,3,3,3,3]]
[[6,0,0],[1,0],[1]] => [[1,3,3,3,3,3]]
[[6,0,0],[2,0],[0]] => [[2,2,3,3,3,3]]
[[6,0,0],[2,0],[1]] => [[1,2,3,3,3,3]]
[[6,0,0],[2,0],[2]] => [[1,1,3,3,3,3]]
[[6,0,0],[3,0],[0]] => [[2,2,2,3,3,3]]
[[6,0,0],[3,0],[1]] => [[1,2,2,3,3,3]]
[[6,0,0],[3,0],[2]] => [[1,1,2,3,3,3]]
[[6,0,0],[3,0],[3]] => [[1,1,1,3,3,3]]
[[6,0,0],[4,0],[0]] => [[2,2,2,2,3,3]]
[[6,0,0],[4,0],[1]] => [[1,2,2,2,3,3]]
[[6,0,0],[4,0],[2]] => [[1,1,2,2,3,3]]
[[6,0,0],[4,0],[3]] => [[1,1,1,2,3,3]]
[[6,0,0],[4,0],[4]] => [[1,1,1,1,3,3]]
[[6,0,0],[5,0],[0]] => [[2,2,2,2,2,3]]
[[6,0,0],[5,0],[1]] => [[1,2,2,2,2,3]]
[[6,0,0],[5,0],[2]] => [[1,1,2,2,2,3]]
[[6,0,0],[5,0],[3]] => [[1,1,1,2,2,3]]
[[6,0,0],[5,0],[4]] => [[1,1,1,1,2,3]]
[[6,0,0],[5,0],[5]] => [[1,1,1,1,1,3]]
[[6,0,0],[6,0],[0]] => [[2,2,2,2,2,2]]
[[6,0,0],[6,0],[1]] => [[1,2,2,2,2,2]]
[[6,0,0],[6,0],[2]] => [[1,1,2,2,2,2]]
[[6,0,0],[6,0],[3]] => [[1,1,1,2,2,2]]
[[6,0,0],[6,0],[4]] => [[1,1,1,1,2,2]]
[[6,0,0],[6,0],[5]] => [[1,1,1,1,1,2]]
[[6,0,0],[6,0],[6]] => [[1,1,1,1,1,1]]
[[5,1,0],[1,0],[0]] => [[2,3,3,3,3],[3]]
[[5,1,0],[1,0],[1]] => [[1,3,3,3,3],[3]]
[[5,1,0],[1,1],[1]] => [[1,3,3,3,3],[2]]
[[5,1,0],[2,0],[0]] => [[2,2,3,3,3],[3]]
[[5,1,0],[2,0],[1]] => [[1,2,3,3,3],[3]]
[[5,1,0],[2,0],[2]] => [[1,1,3,3,3],[3]]
[[5,1,0],[2,1],[1]] => [[1,2,3,3,3],[2]]
[[5,1,0],[2,1],[2]] => [[1,1,3,3,3],[2]]
[[5,1,0],[3,0],[0]] => [[2,2,2,3,3],[3]]
[[5,1,0],[3,0],[1]] => [[1,2,2,3,3],[3]]
[[5,1,0],[3,0],[2]] => [[1,1,2,3,3],[3]]
[[5,1,0],[3,0],[3]] => [[1,1,1,3,3],[3]]
[[5,1,0],[3,1],[1]] => [[1,2,2,3,3],[2]]
[[5,1,0],[3,1],[2]] => [[1,1,2,3,3],[2]]
[[5,1,0],[3,1],[3]] => [[1,1,1,3,3],[2]]
[[5,1,0],[4,0],[0]] => [[2,2,2,2,3],[3]]
[[5,1,0],[4,0],[1]] => [[1,2,2,2,3],[3]]
[[5,1,0],[4,0],[2]] => [[1,1,2,2,3],[3]]
[[5,1,0],[4,0],[3]] => [[1,1,1,2,3],[3]]
[[5,1,0],[4,0],[4]] => [[1,1,1,1,3],[3]]
[[5,1,0],[4,1],[1]] => [[1,2,2,2,3],[2]]
[[5,1,0],[4,1],[2]] => [[1,1,2,2,3],[2]]
[[5,1,0],[4,1],[3]] => [[1,1,1,2,3],[2]]
[[5,1,0],[4,1],[4]] => [[1,1,1,1,3],[2]]
[[5,1,0],[5,0],[0]] => [[2,2,2,2,2],[3]]
[[5,1,0],[5,0],[1]] => [[1,2,2,2,2],[3]]
[[5,1,0],[5,0],[2]] => [[1,1,2,2,2],[3]]
[[5,1,0],[5,0],[3]] => [[1,1,1,2,2],[3]]
[[5,1,0],[5,0],[4]] => [[1,1,1,1,2],[3]]
[[5,1,0],[5,0],[5]] => [[1,1,1,1,1],[3]]
[[5,1,0],[5,1],[1]] => [[1,2,2,2,2],[2]]
[[5,1,0],[5,1],[2]] => [[1,1,2,2,2],[2]]
[[5,1,0],[5,1],[3]] => [[1,1,1,2,2],[2]]
[[5,1,0],[5,1],[4]] => [[1,1,1,1,2],[2]]
[[5,1,0],[5,1],[5]] => [[1,1,1,1,1],[2]]
[[4,2,0],[2,0],[0]] => [[2,2,3,3],[3,3]]
[[4,2,0],[2,0],[1]] => [[1,2,3,3],[3,3]]
[[4,2,0],[2,0],[2]] => [[1,1,3,3],[3,3]]
[[4,2,0],[2,1],[1]] => [[1,2,3,3],[2,3]]
[[4,2,0],[2,1],[2]] => [[1,1,3,3],[2,3]]
[[4,2,0],[2,2],[2]] => [[1,1,3,3],[2,2]]
[[4,2,0],[3,0],[0]] => [[2,2,2,3],[3,3]]
[[4,2,0],[3,0],[1]] => [[1,2,2,3],[3,3]]
[[4,2,0],[3,0],[2]] => [[1,1,2,3],[3,3]]
[[4,2,0],[3,0],[3]] => [[1,1,1,3],[3,3]]
[[4,2,0],[3,1],[1]] => [[1,2,2,3],[2,3]]
[[4,2,0],[3,1],[2]] => [[1,1,2,3],[2,3]]
[[4,2,0],[3,1],[3]] => [[1,1,1,3],[2,3]]
[[4,2,0],[3,2],[2]] => [[1,1,2,3],[2,2]]
[[4,2,0],[3,2],[3]] => [[1,1,1,3],[2,2]]
[[4,2,0],[4,0],[0]] => [[2,2,2,2],[3,3]]
[[4,2,0],[4,0],[1]] => [[1,2,2,2],[3,3]]
[[4,2,0],[4,0],[2]] => [[1,1,2,2],[3,3]]
[[4,2,0],[4,0],[3]] => [[1,1,1,2],[3,3]]
[[4,2,0],[4,0],[4]] => [[1,1,1,1],[3,3]]
[[4,2,0],[4,1],[1]] => [[1,2,2,2],[2,3]]
[[4,2,0],[4,1],[2]] => [[1,1,2,2],[2,3]]
[[4,2,0],[4,1],[3]] => [[1,1,1,2],[2,3]]
[[4,2,0],[4,1],[4]] => [[1,1,1,1],[2,3]]
[[4,2,0],[4,2],[2]] => [[1,1,2,2],[2,2]]
[[4,2,0],[4,2],[3]] => [[1,1,1,2],[2,2]]
[[4,2,0],[4,2],[4]] => [[1,1,1,1],[2,2]]
[[4,1,1],[1,1],[1]] => [[1,3,3,3],[2],[3]]
[[4,1,1],[2,1],[1]] => [[1,2,3,3],[2],[3]]
[[4,1,1],[2,1],[2]] => [[1,1,3,3],[2],[3]]
[[4,1,1],[3,1],[1]] => [[1,2,2,3],[2],[3]]
[[4,1,1],[3,1],[2]] => [[1,1,2,3],[2],[3]]
[[4,1,1],[3,1],[3]] => [[1,1,1,3],[2],[3]]
[[4,1,1],[4,1],[1]] => [[1,2,2,2],[2],[3]]
[[4,1,1],[4,1],[2]] => [[1,1,2,2],[2],[3]]
[[4,1,1],[4,1],[3]] => [[1,1,1,2],[2],[3]]
[[4,1,1],[4,1],[4]] => [[1,1,1,1],[2],[3]]
[[3,3,0],[3,0],[0]] => [[2,2,2],[3,3,3]]
[[3,3,0],[3,0],[1]] => [[1,2,2],[3,3,3]]
[[3,3,0],[3,0],[2]] => [[1,1,2],[3,3,3]]
[[3,3,0],[3,0],[3]] => [[1,1,1],[3,3,3]]
[[3,3,0],[3,1],[1]] => [[1,2,2],[2,3,3]]
[[3,3,0],[3,1],[2]] => [[1,1,2],[2,3,3]]
[[3,3,0],[3,1],[3]] => [[1,1,1],[2,3,3]]
[[3,3,0],[3,2],[2]] => [[1,1,2],[2,2,3]]
[[3,3,0],[3,2],[3]] => [[1,1,1],[2,2,3]]
[[3,3,0],[3,3],[3]] => [[1,1,1],[2,2,2]]
[[3,2,1],[2,1],[1]] => [[1,2,3],[2,3],[3]]
[[3,2,1],[2,1],[2]] => [[1,1,3],[2,3],[3]]
[[3,2,1],[2,2],[2]] => [[1,1,3],[2,2],[3]]
[[3,2,1],[3,1],[1]] => [[1,2,2],[2,3],[3]]
[[3,2,1],[3,1],[2]] => [[1,1,2],[2,3],[3]]
[[3,2,1],[3,1],[3]] => [[1,1,1],[2,3],[3]]
[[3,2,1],[3,2],[2]] => [[1,1,2],[2,2],[3]]
[[3,2,1],[3,2],[3]] => [[1,1,1],[2,2],[3]]
[[2,2,2],[2,2],[2]] => [[1,1],[2,2],[3,3]]
[[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]]
[[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]]
[[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]]
[[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]]
[[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]]
[[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]]
[[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]]
[[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]]
[[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3]]
[[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3]]
[[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3]]
[[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]]
[[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]]
[[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]]
[[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]]
[[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]]
[[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]]
[[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]]
[[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]]
[[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]]
[[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4]]
[[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4]]
[[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4]]
[[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4]]
[[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4]]
[[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4]]
[[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4]]
[[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4]]
[[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4]]
[[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4]]
[[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]]
[[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]]
[[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]]
[[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]]
[[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]]
[[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]]
[[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]]
[[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]]
[[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]]
[[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]]
[[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4]]
[[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4]]
[[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4]]
[[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3]]
[[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3]]
[[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2]]
[[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4]]
[[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4]]
[[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4]]
[[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4]]
[[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4]]
[[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4]]
[[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]]
[[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]]
[[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2]]
[[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]]
[[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3]]
[[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3]]
[[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2]]
[[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2]]
[[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4]]
[[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4]]
[[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4]]
[[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3]]
[[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4]]
[[4,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4]]
[[4,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4]]
[[4,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4]]
[[4,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4]]
[[4,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4]]
[[4,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4]]
[[4,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4]]
[[4,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4]]
[[4,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4]]
[[4,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4]]
[[4,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4]]
[[4,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4]]
[[4,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4]]
[[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4]]
[[4,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4]]
[[4,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4]]
[[4,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4]]
[[4,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4]]
[[4,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4]]
[[4,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3]]
[[4,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3]]
[[4,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3]]
[[4,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3]]
[[4,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3]]
[[4,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3]]
[[4,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3]]
[[4,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3]]
[[4,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3]]
[[4,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3]]
[[4,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2]]
[[4,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2]]
[[4,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2]]
[[4,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2]]
[[4,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1]]
[[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[4]]
[[3,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[4]]
[[3,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[4]]
[[3,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3]]
[[3,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3]]
[[3,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2]]
[[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4]]
[[3,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4]]
[[3,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4]]
[[3,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4]]
[[3,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4]]
[[3,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4]]
[[3,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3]]
[[3,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3]]
[[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2]]
[[3,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3]]
[[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3]]
[[3,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3]]
[[3,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2]]
[[3,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2]]
[[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4]]
[[3,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4]]
[[3,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4]]
[[3,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4]]
[[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4]]
[[3,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4]]
[[3,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4]]
[[3,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4]]
[[3,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4]]
[[3,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4]]
[[3,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3]]
[[3,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3]]
[[3,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2]]
[[3,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3]]
[[3,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3]]
[[3,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3]]
[[3,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2]]
[[3,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2]]
[[3,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3]]
[[3,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3]]
[[3,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3]]
[[3,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3]]
[[3,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2]]
[[3,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2]]
[[3,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2]]
[[2,2,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,4]]
[[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,4]]
[[2,2,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,4]]
[[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,4]]
[[2,2,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,4]]
[[2,2,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,4]]
[[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4]]
[[2,2,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4]]
[[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4]]
[[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4]]
[[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4]]
[[2,2,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4]]
[[2,2,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4]]
[[2,2,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4]]
[[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3]]
[[2,2,0,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3]]
[[2,2,0,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3]]
[[2,2,0,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3]]
[[2,2,0,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3]]
[[2,2,0,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2]]
[[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[4]]
[[2,1,1,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[4]]
[[2,1,1,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[4]]
[[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3]]
[[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[4]]
[[2,1,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[4]]
[[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4]]
[[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[4]]
[[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4]]
[[2,1,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[4]]
[[2,1,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[4]]
[[2,1,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[4]]
[[2,1,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2],[3]]
[[2,1,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2],[3]]
[[2,1,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2],[3]]
[[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4]]
[[5,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4,4]]
[[5,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4,4]]
[[5,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4,4]]
[[5,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4,4]]
[[5,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4,4]]
[[5,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4,4]]
[[5,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4,4]]
[[5,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4,4]]
[[5,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4,4]]
[[5,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4,4]]
[[5,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4,4]]
[[5,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4,4]]
[[5,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4,4]]
[[5,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4,4]]
[[5,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,4]]
[[5,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4,4]]
[[5,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4,4]]
[[5,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4,4]]
[[5,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4,4]]
[[5,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4,4]]
[[5,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3,4]]
[[5,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3,4]]
[[5,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3,4]]
[[5,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3,4]]
[[5,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3,4]]
[[5,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3,4]]
[[5,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3,4]]
[[5,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3,4]]
[[5,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3,4]]
[[5,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3,4]]
[[5,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2,4]]
[[5,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2,4]]
[[5,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2,4]]
[[5,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2,4]]
[[5,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1,4]]
[[5,0,0,0],[5,0,0],[0,0],[0]] => [[3,3,3,3,3]]
[[5,0,0,0],[5,0,0],[1,0],[0]] => [[2,3,3,3,3]]
[[5,0,0,0],[5,0,0],[1,0],[1]] => [[1,3,3,3,3]]
[[5,0,0,0],[5,0,0],[2,0],[0]] => [[2,2,3,3,3]]
[[5,0,0,0],[5,0,0],[2,0],[1]] => [[1,2,3,3,3]]
[[5,0,0,0],[5,0,0],[2,0],[2]] => [[1,1,3,3,3]]
[[5,0,0,0],[5,0,0],[3,0],[0]] => [[2,2,2,3,3]]
[[5,0,0,0],[5,0,0],[3,0],[1]] => [[1,2,2,3,3]]
[[5,0,0,0],[5,0,0],[3,0],[2]] => [[1,1,2,3,3]]
[[5,0,0,0],[5,0,0],[3,0],[3]] => [[1,1,1,3,3]]
[[5,0,0,0],[5,0,0],[4,0],[0]] => [[2,2,2,2,3]]
[[5,0,0,0],[5,0,0],[4,0],[1]] => [[1,2,2,2,3]]
[[5,0,0,0],[5,0,0],[4,0],[2]] => [[1,1,2,2,3]]
[[5,0,0,0],[5,0,0],[4,0],[3]] => [[1,1,1,2,3]]
[[5,0,0,0],[5,0,0],[4,0],[4]] => [[1,1,1,1,3]]
[[5,0,0,0],[5,0,0],[5,0],[0]] => [[2,2,2,2,2]]
[[5,0,0,0],[5,0,0],[5,0],[1]] => [[1,2,2,2,2]]
[[5,0,0,0],[5,0,0],[5,0],[2]] => [[1,1,2,2,2]]
[[5,0,0,0],[5,0,0],[5,0],[3]] => [[1,1,1,2,2]]
[[5,0,0,0],[5,0,0],[5,0],[4]] => [[1,1,1,1,2]]
[[5,0,0,0],[5,0,0],[5,0],[5]] => [[1,1,1,1,1]]
[[4,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4],[4]]
[[4,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4],[4]]
[[4,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4],[4]]
[[4,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4,4],[3]]
[[4,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4,4],[3]]
[[4,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4,4],[2]]
[[4,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4],[4]]
[[4,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4],[4]]
[[4,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4],[4]]
[[4,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4],[4]]
[[4,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4],[4]]
[[4,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4],[4]]
[[4,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4,4],[3]]
[[4,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4,4],[3]]
[[4,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,4],[2]]
[[4,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4,4],[3]]
[[4,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,4],[3]]
[[4,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4,4],[3]]
[[4,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4,4],[2]]
[[4,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4,4],[2]]
[[4,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4],[4]]
[[4,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4],[4]]
[[4,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4],[4]]
[[4,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4],[4]]
[[4,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[4]]
[[4,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4],[4]]
[[4,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4],[4]]
[[4,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4],[4]]
[[4,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4],[4]]
[[4,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4],[4]]
[[4,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3,4],[3]]
[[4,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3,4],[3]]
[[4,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3,4],[2]]
[[4,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3,4],[3]]
[[4,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3,4],[3]]
[[4,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3,4],[3]]
[[4,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3,4],[2]]
[[4,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3,4],[2]]
[[4,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2,4],[3]]
[[4,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2,4],[3]]
[[4,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2,4],[3]]
[[4,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1,4],[3]]
[[4,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2,4],[2]]
[[4,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2,4],[2]]
[[4,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1,4],[2]]
[[4,1,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3],[4]]
[[4,1,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3],[4]]
[[4,1,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3],[4]]
[[4,1,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3],[4]]
[[4,1,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3],[4]]
[[4,1,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3],[4]]
[[4,1,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3],[4]]
[[4,1,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3],[4]]
[[4,1,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3],[4]]
[[4,1,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3],[4]]
[[4,1,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2],[4]]
[[4,1,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2],[4]]
[[4,1,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2],[4]]
[[4,1,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2],[4]]
[[4,1,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1],[4]]
[[4,1,0,0],[4,1,0],[1,0],[0]] => [[2,3,3,3],[3]]
[[4,1,0,0],[4,1,0],[1,0],[1]] => [[1,3,3,3],[3]]
[[4,1,0,0],[4,1,0],[1,1],[1]] => [[1,3,3,3],[2]]
[[4,1,0,0],[4,1,0],[2,0],[0]] => [[2,2,3,3],[3]]
[[4,1,0,0],[4,1,0],[2,0],[1]] => [[1,2,3,3],[3]]
[[4,1,0,0],[4,1,0],[2,0],[2]] => [[1,1,3,3],[3]]
[[4,1,0,0],[4,1,0],[2,1],[1]] => [[1,2,3,3],[2]]
[[4,1,0,0],[4,1,0],[2,1],[2]] => [[1,1,3,3],[2]]
[[4,1,0,0],[4,1,0],[3,0],[0]] => [[2,2,2,3],[3]]
[[4,1,0,0],[4,1,0],[3,0],[1]] => [[1,2,2,3],[3]]
[[4,1,0,0],[4,1,0],[3,0],[2]] => [[1,1,2,3],[3]]
[[4,1,0,0],[4,1,0],[3,0],[3]] => [[1,1,1,3],[3]]
[[4,1,0,0],[4,1,0],[3,1],[1]] => [[1,2,2,3],[2]]
[[4,1,0,0],[4,1,0],[3,1],[2]] => [[1,1,2,3],[2]]
[[4,1,0,0],[4,1,0],[3,1],[3]] => [[1,1,1,3],[2]]
[[4,1,0,0],[4,1,0],[4,0],[0]] => [[2,2,2,2],[3]]
[[4,1,0,0],[4,1,0],[4,0],[1]] => [[1,2,2,2],[3]]
[[4,1,0,0],[4,1,0],[4,0],[2]] => [[1,1,2,2],[3]]
[[4,1,0,0],[4,1,0],[4,0],[3]] => [[1,1,1,2],[3]]
[[4,1,0,0],[4,1,0],[4,0],[4]] => [[1,1,1,1],[3]]
[[4,1,0,0],[4,1,0],[4,1],[1]] => [[1,2,2,2],[2]]
[[4,1,0,0],[4,1,0],[4,1],[2]] => [[1,1,2,2],[2]]
[[4,1,0,0],[4,1,0],[4,1],[3]] => [[1,1,1,2],[2]]
[[4,1,0,0],[4,1,0],[4,1],[4]] => [[1,1,1,1],[2]]
[[3,2,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4,4]]
[[3,2,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4,4]]
[[3,2,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4,4]]
[[3,2,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4,4]]
[[3,2,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4,4]]
[[3,2,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4,4]]
[[3,2,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3,4]]
[[3,2,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3,4]]
[[3,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,4]]
[[3,2,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3,4]]
[[3,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,4]]
[[3,2,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3,4]]
[[3,2,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2,4]]
[[3,2,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2,4]]
[[3,2,0,0],[2,2,0],[2,0],[0]] => [[2,2,4],[3,3]]
[[3,2,0,0],[2,2,0],[2,0],[1]] => [[1,2,4],[3,3]]
[[3,2,0,0],[2,2,0],[2,0],[2]] => [[1,1,4],[3,3]]
[[3,2,0,0],[2,2,0],[2,1],[1]] => [[1,2,4],[2,3]]
[[3,2,0,0],[2,2,0],[2,1],[2]] => [[1,1,4],[2,3]]
[[3,2,0,0],[2,2,0],[2,2],[2]] => [[1,1,4],[2,2]]
[[3,2,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4,4]]
[[3,2,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4,4]]
[[3,2,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4,4]]
[[3,2,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4,4]]
[[3,2,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,4]]
[[3,2,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4,4]]
[[3,2,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4,4]]
[[3,2,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4,4]]
[[3,2,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4,4]]
[[3,2,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4,4]]
[[3,2,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3,4]]
[[3,2,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3,4]]
[[3,2,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2,4]]
[[3,2,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3,4]]
[[3,2,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3,4]]
[[3,2,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3,4]]
[[3,2,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2,4]]
[[3,2,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2,4]]
[[3,2,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3,4]]
[[3,2,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3,4]]
[[3,2,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3,4]]
[[3,2,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3,4]]
[[3,2,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2,4]]
[[3,2,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2,4]]
[[3,2,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2,4]]
[[3,2,0,0],[3,2,0],[2,0],[0]] => [[2,2,3],[3,3]]
[[3,2,0,0],[3,2,0],[2,0],[1]] => [[1,2,3],[3,3]]
[[3,2,0,0],[3,2,0],[2,0],[2]] => [[1,1,3],[3,3]]
[[3,2,0,0],[3,2,0],[2,1],[1]] => [[1,2,3],[2,3]]
[[3,2,0,0],[3,2,0],[2,1],[2]] => [[1,1,3],[2,3]]
[[3,2,0,0],[3,2,0],[2,2],[2]] => [[1,1,3],[2,2]]
[[3,2,0,0],[3,2,0],[3,0],[0]] => [[2,2,2],[3,3]]
[[3,2,0,0],[3,2,0],[3,0],[1]] => [[1,2,2],[3,3]]
[[3,2,0,0],[3,2,0],[3,0],[2]] => [[1,1,2],[3,3]]
[[3,2,0,0],[3,2,0],[3,0],[3]] => [[1,1,1],[3,3]]
[[3,2,0,0],[3,2,0],[3,1],[1]] => [[1,2,2],[2,3]]
[[3,2,0,0],[3,2,0],[3,1],[2]] => [[1,1,2],[2,3]]
[[3,2,0,0],[3,2,0],[3,1],[3]] => [[1,1,1],[2,3]]
[[3,2,0,0],[3,2,0],[3,2],[2]] => [[1,1,2],[2,2]]
[[3,2,0,0],[3,2,0],[3,2],[3]] => [[1,1,1],[2,2]]
[[3,1,1,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3],[4]]
[[3,1,1,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3],[4]]
[[3,1,1,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2],[4]]
[[3,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,4],[2],[3]]
[[3,1,1,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3],[4]]
[[3,1,1,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3],[4]]
[[3,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2],[4]]
[[3,1,1,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3],[4]]
[[3,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3],[4]]
[[3,1,1,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3],[4]]
[[3,1,1,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2],[4]]
[[3,1,1,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2],[4]]
[[3,1,1,0],[2,1,1],[1,1],[1]] => [[1,3,4],[2],[3]]
[[3,1,1,0],[2,1,1],[2,1],[1]] => [[1,2,4],[2],[3]]
[[3,1,1,0],[2,1,1],[2,1],[2]] => [[1,1,4],[2],[3]]
[[3,1,1,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3],[4]]
[[3,1,1,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3],[4]]
[[3,1,1,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2],[4]]
[[3,1,1,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3],[4]]
[[3,1,1,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3],[4]]
[[3,1,1,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3],[4]]
[[3,1,1,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2],[4]]
[[3,1,1,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2],[4]]
[[3,1,1,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3],[4]]
[[3,1,1,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3],[4]]
[[3,1,1,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3],[4]]
[[3,1,1,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3],[4]]
[[3,1,1,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2],[4]]
[[3,1,1,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2],[4]]
[[3,1,1,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2],[4]]
[[3,1,1,0],[3,1,1],[1,1],[1]] => [[1,3,3],[2],[3]]
[[3,1,1,0],[3,1,1],[2,1],[1]] => [[1,2,3],[2],[3]]
[[3,1,1,0],[3,1,1],[2,1],[2]] => [[1,1,3],[2],[3]]
[[3,1,1,0],[3,1,1],[3,1],[1]] => [[1,2,2],[2],[3]]
[[3,1,1,0],[3,1,1],[3,1],[2]] => [[1,1,2],[2],[3]]
[[3,1,1,0],[3,1,1],[3,1],[3]] => [[1,1,1],[2],[3]]
[[2,2,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4],[4]]
[[2,2,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4],[4]]
[[2,2,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[4]]
[[2,2,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4],[4]]
[[2,2,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[4]]
[[2,2,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4],[4]]
[[2,2,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4],[4]]
[[2,2,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4],[4]]
[[2,2,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2,4],[3]]
[[2,2,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2,4],[3]]
[[2,2,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2,4],[3]]
[[2,2,1,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3],[4]]
[[2,2,1,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3],[4]]
[[2,2,1,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3],[4]]
[[2,2,1,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3],[4]]
[[2,2,1,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3],[4]]
[[2,2,1,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2],[4]]
[[2,2,1,0],[2,2,1],[2,1],[1]] => [[1,2],[2,3],[3]]
[[2,2,1,0],[2,2,1],[2,1],[2]] => [[1,1],[2,3],[3]]
[[2,2,1,0],[2,2,1],[2,2],[2]] => [[1,1],[2,2],[3]]
[[2,1,1,1],[1,1,1],[1,1],[1]] => [[1,4],[2],[3],[4]]
[[2,1,1,1],[2,1,1],[1,1],[1]] => [[1,3],[2],[3],[4]]
[[2,1,1,1],[2,1,1],[2,1],[1]] => [[1,2],[2],[3],[4]]
[[2,1,1,1],[2,1,1],[2,1],[2]] => [[1,1],[2],[3],[4]]
[[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5]]
[[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]]
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]]
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]]
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]]
[[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5]]
[[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5]]
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5]]
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5]]
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5]]
[[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]]
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]]
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]]
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]]
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3]]
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3]]
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3]]
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]]
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]]
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]]
[[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5]]
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5]]
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5]]
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5]]
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]]
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]]
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]]
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]]
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]]
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]]
[[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,5]]
[[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5]]
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5]]
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5]]
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5]]
[[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5]]
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5]]
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5]]
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5]]
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5]]
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5]]
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5]]
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5]]
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5]]
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5]]
[[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4]]
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4]]
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4]]
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4]]
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4]]
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4]]
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4]]
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4]]
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4]]
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]]
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]]
[[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5],[5]]
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5],[5]]
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5],[5]]
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5],[5]]
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5],[4]]
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5],[4]]
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5],[4]]
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5],[3]]
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5],[3]]
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5],[2]]
[[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[5]]
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[5]]
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[5]]
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[5]]
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[5]]
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[5]]
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[5]]
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[5]]
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[5]]
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[5]]
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4]]
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4]]
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4]]
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3]]
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3]]
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2]]
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4]]
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4]]
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4]]
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4]]
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4]]
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4]]
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]]
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]]
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2]]
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]]
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3]]
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3]]
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2]]
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2]]
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4],[5]]
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4],[5]]
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4],[5]]
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3],[5]]
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3],[5]]
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2],[5]]
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4]]
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4]]
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4]]
[[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3]]
[[4,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,5,5]]
[[4,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5,5]]
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5,5]]
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5,5]]
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5,5]]
[[4,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5,5]]
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5,5]]
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5,5]]
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5,5]]
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5,5]]
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5,5]]
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5,5]]
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5,5]]
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5,5]]
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5,5]]
[[4,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,5]]
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,5]]
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,5]]
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,5]]
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,5]]
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,5]]
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,5]]
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,5]]
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,5]]
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,5]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,5]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,5]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,5]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,5]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,5]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,5]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,5]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,5]]
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,5]]
[[4,0,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4]]
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4]]
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4]]
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4]]
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4]]
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4]]
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4]]
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4]]
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4]]
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4]]
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2]]
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1]]
[[3,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5],[5]]
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5],[5]]
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5],[5]]
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5],[5]]
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5,5],[4]]
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5,5],[4]]
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5,5],[4]]
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5,5],[3]]
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5,5],[3]]
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5,5],[2]]
[[3,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5],[5]]
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5],[5]]
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5],[5]]
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5],[5]]
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5],[5]]
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5],[5]]
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5],[5]]
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5],[5]]
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5],[5]]
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5],[5]]
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,5],[4]]
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,5],[4]]
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,5],[4]]
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,5],[3]]
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,5],[3]]
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,5],[2]]
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,5],[4]]
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,5],[4]]
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,5],[4]]
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,5],[4]]
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,5],[4]]
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,5],[4]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,5],[3]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,5],[3]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,5],[3]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,5],[3]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,5],[2]]
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,5],[2]]
[[3,1,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4],[5]]
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[5]]
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[5]]
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[5]]
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[5]]
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[5]]
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[5]]
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[5]]
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[5]]
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[5]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[5]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[5]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[5]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[5]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[5]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[5]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[5]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[5]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[5]]
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[5]]
[[3,1,0,0,0],[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[4]]
[[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[4]]
[[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[4]]
[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3]]
[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3]]
[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2]]
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4]]
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4]]
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4]]
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4]]
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4]]
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2]]
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4]]
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2]]
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2]]
[[2,2,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[5,5]]
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[5,5]]
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[5,5]]
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[5,5]]
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[5,5]]
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[5,5]]
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[5,5]]
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[5,5]]
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[5,5]]
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[5,5]]
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4,5]]
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4,5]]
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4,5]]
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3,5]]
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3,5]]
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2,5]]
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,5]]
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,5]]
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,5]]
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,5]]
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,5]]
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,5]]
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,5]]
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,5]]
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,5]]
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,5]]
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,5]]
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,5]]
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,5]]
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,5]]
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,4]]
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,4]]
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,4]]
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,4]]
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,4]]
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,4]]
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4]]
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4]]
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4]]
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4]]
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4]]
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4]]
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4]]
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4]]
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3]]
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3]]
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3]]
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3]]
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3]]
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2]]
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5],[4],[5]]
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5],[4],[5]]
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5],[4],[5]]
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5],[3],[5]]
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5],[3],[5]]
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5],[2],[5]]
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2,5],[3],[4]]
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1,5],[3],[4]]
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1,5],[2],[4]]
[[2,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1,5],[2],[3]]
[[2,1,1,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4],[5]]
[[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4],[5]]
[[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4],[5]]
[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[5]]
[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[5]]
[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[5]]
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4],[5]]
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4],[5]]
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4],[5]]
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4],[5]]
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4],[5]]
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4],[5]]
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[5]]
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[5]]
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[5]]
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[5]]
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[5]]
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[5]]
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[5]]
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[5]]
[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[4]]
[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[4]]
[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[4]]
[[2,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3]]
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[4]]
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[4]]
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4]]
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[4]]
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4]]
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[4]]
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[4]]
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[4]]
[[2,1,1,0,0],[2,1,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2],[3]]
[[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2],[3]]
[[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6]]
[[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5]]
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]]
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]]
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]]
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]]
[[2,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6,6]]
[[2,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,6]]
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6]]
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6]]
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6]]
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6]]
[[2,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5]]
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5]]
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5]]
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5]]
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5]]
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]]
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]]
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]]
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]]
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3]]
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3]]
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3]]
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]]
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]]
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]]
[[1,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5],[6]]
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[6]]
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[6]]
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[6]]
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[6]]
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5]]
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5]]
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5]]
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5]]
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]]
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]]
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]]
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]]
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]]
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]]
[[1,0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[7]]
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6]]
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5]]
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]]
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]]
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]]
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]]
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Created: Jan 19, 2020 at 07:28 by FindStatCrew
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Last Updated: Jan 19, 2020 at 07:28 by Martin Rubey