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------------------------------------------------------------------------
Map identifier: Mp00294
------------------------------------------------------------------------
Map name: peak composition
------------------------------------------------------------------------
Domain: Standard tableaux
------------------------------------------------------------------------
Codomain: Integer compositions
------------------------------------------------------------------------
Description: The composition corresponding to the peak set of a standard tableau.
Let $T$ be a standard tableau of size $n$.
An entry $i$ of $T$ is a descent if $i+1$ is in a lower row (in English notation), otherwise $i$ is an ascent.
An entry $2 \leq i \leq n-1$ is a peak, if $i-1$ is an ascent and $i$ is a descent.
This map returns the composition $c_1,\dots,c_k$ of $n$ such that $\{c_1, c_1+c_2,\dots, c_1+\dots+c_k\}$ is the peak set of $T$.
------------------------------------------------------------------------
References: [1] Zhou, R. D. P., Yan, S. H. F. Equidistribution of set-valued statistics on standard Young tableaux and transversals [[arXiv:2306.04382]]
------------------------------------------------------------------------
Code:
def mapping(T):
d = T.standard_descents()
c = [i for i in range(2, T.size()) if i in d and i-1 not in d]
return Composition(from_subset=(c, T.size()))
------------------------------------------------------------------------
Map images:
[[1]] => [1]
[[1,2]] => [2]
[[1],[2]] => [2]
[[1,2,3]] => [3]
[[1,3],[2]] => [3]
[[1,2],[3]] => [2,1]
[[1],[2],[3]] => [3]
[[1,2,3,4]] => [4]
[[1,3,4],[2]] => [4]
[[1,2,4],[3]] => [2,2]
[[1,2,3],[4]] => [3,1]
[[1,3],[2,4]] => [3,1]
[[1,2],[3,4]] => [2,2]
[[1,4],[2],[3]] => [4]
[[1,3],[2],[4]] => [3,1]
[[1,2],[3],[4]] => [2,2]
[[1],[2],[3],[4]] => [4]
[[1,2,3,4,5]] => [5]
[[1,3,4,5],[2]] => [5]
[[1,2,4,5],[3]] => [2,3]
[[1,2,3,5],[4]] => [3,2]
[[1,2,3,4],[5]] => [4,1]
[[1,3,5],[2,4]] => [3,2]
[[1,2,5],[3,4]] => [2,3]
[[1,3,4],[2,5]] => [4,1]
[[1,2,4],[3,5]] => [2,2,1]
[[1,2,3],[4,5]] => [3,2]
[[1,4,5],[2],[3]] => [5]
[[1,3,5],[2],[4]] => [3,2]
[[1,2,5],[3],[4]] => [2,3]
[[1,3,4],[2],[5]] => [4,1]
[[1,2,4],[3],[5]] => [2,2,1]
[[1,2,3],[4],[5]] => [3,2]
[[1,4],[2,5],[3]] => [4,1]
[[1,3],[2,5],[4]] => [3,2]
[[1,2],[3,5],[4]] => [2,3]
[[1,3],[2,4],[5]] => [3,2]
[[1,2],[3,4],[5]] => [2,2,1]
[[1,5],[2],[3],[4]] => [5]
[[1,4],[2],[3],[5]] => [4,1]
[[1,3],[2],[4],[5]] => [3,2]
[[1,2],[3],[4],[5]] => [2,3]
[[1],[2],[3],[4],[5]] => [5]
[[1,2,3,4,5,6]] => [6]
[[1,3,4,5,6],[2]] => [6]
[[1,2,4,5,6],[3]] => [2,4]
[[1,2,3,5,6],[4]] => [3,3]
[[1,2,3,4,6],[5]] => [4,2]
[[1,2,3,4,5],[6]] => [5,1]
[[1,3,5,6],[2,4]] => [3,3]
[[1,2,5,6],[3,4]] => [2,4]
[[1,3,4,6],[2,5]] => [4,2]
[[1,2,4,6],[3,5]] => [2,2,2]
[[1,2,3,6],[4,5]] => [3,3]
[[1,3,4,5],[2,6]] => [5,1]
[[1,2,4,5],[3,6]] => [2,3,1]
[[1,2,3,5],[4,6]] => [3,2,1]
[[1,2,3,4],[5,6]] => [4,2]
[[1,4,5,6],[2],[3]] => [6]
[[1,3,5,6],[2],[4]] => [3,3]
[[1,2,5,6],[3],[4]] => [2,4]
[[1,3,4,6],[2],[5]] => [4,2]
[[1,2,4,6],[3],[5]] => [2,2,2]
[[1,2,3,6],[4],[5]] => [3,3]
[[1,3,4,5],[2],[6]] => [5,1]
[[1,2,4,5],[3],[6]] => [2,3,1]
[[1,2,3,5],[4],[6]] => [3,2,1]
[[1,2,3,4],[5],[6]] => [4,2]
[[1,3,5],[2,4,6]] => [3,2,1]
[[1,2,5],[3,4,6]] => [2,3,1]
[[1,3,4],[2,5,6]] => [4,2]
[[1,2,4],[3,5,6]] => [2,2,2]
[[1,2,3],[4,5,6]] => [3,3]
[[1,4,6],[2,5],[3]] => [4,2]
[[1,3,6],[2,5],[4]] => [3,3]
[[1,2,6],[3,5],[4]] => [2,4]
[[1,3,6],[2,4],[5]] => [3,3]
[[1,2,6],[3,4],[5]] => [2,2,2]
[[1,4,5],[2,6],[3]] => [5,1]
[[1,3,5],[2,6],[4]] => [3,2,1]
[[1,2,5],[3,6],[4]] => [2,3,1]
[[1,3,4],[2,6],[5]] => [4,2]
[[1,2,4],[3,6],[5]] => [2,2,2]
[[1,2,3],[4,6],[5]] => [3,3]
[[1,3,5],[2,4],[6]] => [3,2,1]
[[1,2,5],[3,4],[6]] => [2,3,1]
[[1,3,4],[2,5],[6]] => [4,2]
[[1,2,4],[3,5],[6]] => [2,2,2]
[[1,2,3],[4,5],[6]] => [3,2,1]
[[1,5,6],[2],[3],[4]] => [6]
[[1,4,6],[2],[3],[5]] => [4,2]
[[1,3,6],[2],[4],[5]] => [3,3]
[[1,2,6],[3],[4],[5]] => [2,4]
[[1,4,5],[2],[3],[6]] => [5,1]
[[1,3,5],[2],[4],[6]] => [3,2,1]
[[1,2,5],[3],[4],[6]] => [2,3,1]
[[1,3,4],[2],[5],[6]] => [4,2]
[[1,2,4],[3],[5],[6]] => [2,2,2]
[[1,2,3],[4],[5],[6]] => [3,3]
[[1,4],[2,5],[3,6]] => [4,2]
[[1,3],[2,5],[4,6]] => [3,2,1]
[[1,2],[3,5],[4,6]] => [2,3,1]
[[1,3],[2,4],[5,6]] => [3,3]
[[1,2],[3,4],[5,6]] => [2,2,2]
[[1,5],[2,6],[3],[4]] => [5,1]
[[1,4],[2,6],[3],[5]] => [4,2]
[[1,3],[2,6],[4],[5]] => [3,3]
[[1,2],[3,6],[4],[5]] => [2,4]
[[1,4],[2,5],[3],[6]] => [4,2]
[[1,3],[2,5],[4],[6]] => [3,2,1]
[[1,2],[3,5],[4],[6]] => [2,3,1]
[[1,3],[2,4],[5],[6]] => [3,3]
[[1,2],[3,4],[5],[6]] => [2,2,2]
[[1,6],[2],[3],[4],[5]] => [6]
[[1,5],[2],[3],[4],[6]] => [5,1]
[[1,4],[2],[3],[5],[6]] => [4,2]
[[1,3],[2],[4],[5],[6]] => [3,3]
[[1,2],[3],[4],[5],[6]] => [2,4]
[[1],[2],[3],[4],[5],[6]] => [6]
[[1,2,3,4,5,6,7]] => [7]
[[1,3,4,5,6,7],[2]] => [7]
[[1,2,4,5,6,7],[3]] => [2,5]
[[1,2,3,5,6,7],[4]] => [3,4]
[[1,2,3,4,6,7],[5]] => [4,3]
[[1,2,3,4,5,7],[6]] => [5,2]
[[1,2,3,4,5,6],[7]] => [6,1]
[[1,3,5,6,7],[2,4]] => [3,4]
[[1,2,5,6,7],[3,4]] => [2,5]
[[1,3,4,6,7],[2,5]] => [4,3]
[[1,2,4,6,7],[3,5]] => [2,2,3]
[[1,2,3,6,7],[4,5]] => [3,4]
[[1,3,4,5,7],[2,6]] => [5,2]
[[1,2,4,5,7],[3,6]] => [2,3,2]
[[1,2,3,5,7],[4,6]] => [3,2,2]
[[1,2,3,4,7],[5,6]] => [4,3]
[[1,3,4,5,6],[2,7]] => [6,1]
[[1,2,4,5,6],[3,7]] => [2,4,1]
[[1,2,3,5,6],[4,7]] => [3,3,1]
[[1,2,3,4,6],[5,7]] => [4,2,1]
[[1,2,3,4,5],[6,7]] => [5,2]
[[1,4,5,6,7],[2],[3]] => [7]
[[1,3,5,6,7],[2],[4]] => [3,4]
[[1,2,5,6,7],[3],[4]] => [2,5]
[[1,3,4,6,7],[2],[5]] => [4,3]
[[1,2,4,6,7],[3],[5]] => [2,2,3]
[[1,2,3,6,7],[4],[5]] => [3,4]
[[1,3,4,5,7],[2],[6]] => [5,2]
[[1,2,4,5,7],[3],[6]] => [2,3,2]
[[1,2,3,5,7],[4],[6]] => [3,2,2]
[[1,2,3,4,7],[5],[6]] => [4,3]
[[1,3,4,5,6],[2],[7]] => [6,1]
[[1,2,4,5,6],[3],[7]] => [2,4,1]
[[1,2,3,5,6],[4],[7]] => [3,3,1]
[[1,2,3,4,6],[5],[7]] => [4,2,1]
[[1,2,3,4,5],[6],[7]] => [5,2]
[[1,3,5,7],[2,4,6]] => [3,2,2]
[[1,2,5,7],[3,4,6]] => [2,3,2]
[[1,3,4,7],[2,5,6]] => [4,3]
[[1,2,4,7],[3,5,6]] => [2,2,3]
[[1,2,3,7],[4,5,6]] => [3,4]
[[1,3,5,6],[2,4,7]] => [3,3,1]
[[1,2,5,6],[3,4,7]] => [2,4,1]
[[1,3,4,6],[2,5,7]] => [4,2,1]
[[1,2,4,6],[3,5,7]] => [2,2,2,1]
[[1,2,3,6],[4,5,7]] => [3,3,1]
[[1,3,4,5],[2,6,7]] => [5,2]
[[1,2,4,5],[3,6,7]] => [2,3,2]
[[1,2,3,5],[4,6,7]] => [3,2,2]
[[1,2,3,4],[5,6,7]] => [4,3]
[[1,4,6,7],[2,5],[3]] => [4,3]
[[1,3,6,7],[2,5],[4]] => [3,4]
[[1,2,6,7],[3,5],[4]] => [2,5]
[[1,3,6,7],[2,4],[5]] => [3,4]
[[1,2,6,7],[3,4],[5]] => [2,2,3]
[[1,4,5,7],[2,6],[3]] => [5,2]
[[1,3,5,7],[2,6],[4]] => [3,2,2]
[[1,2,5,7],[3,6],[4]] => [2,3,2]
[[1,3,4,7],[2,6],[5]] => [4,3]
[[1,2,4,7],[3,6],[5]] => [2,2,3]
[[1,2,3,7],[4,6],[5]] => [3,4]
[[1,3,5,7],[2,4],[6]] => [3,2,2]
[[1,2,5,7],[3,4],[6]] => [2,3,2]
[[1,3,4,7],[2,5],[6]] => [4,3]
[[1,2,4,7],[3,5],[6]] => [2,2,3]
[[1,2,3,7],[4,5],[6]] => [3,2,2]
[[1,4,5,6],[2,7],[3]] => [6,1]
[[1,3,5,6],[2,7],[4]] => [3,3,1]
[[1,2,5,6],[3,7],[4]] => [2,4,1]
[[1,3,4,6],[2,7],[5]] => [4,2,1]
[[1,2,4,6],[3,7],[5]] => [2,2,2,1]
[[1,2,3,6],[4,7],[5]] => [3,3,1]
[[1,3,4,5],[2,7],[6]] => [5,2]
[[1,2,4,5],[3,7],[6]] => [2,3,2]
[[1,2,3,5],[4,7],[6]] => [3,2,2]
[[1,2,3,4],[5,7],[6]] => [4,3]
[[1,3,5,6],[2,4],[7]] => [3,3,1]
[[1,2,5,6],[3,4],[7]] => [2,4,1]
[[1,3,4,6],[2,5],[7]] => [4,2,1]
[[1,2,4,6],[3,5],[7]] => [2,2,2,1]
[[1,2,3,6],[4,5],[7]] => [3,3,1]
[[1,3,4,5],[2,6],[7]] => [5,2]
[[1,2,4,5],[3,6],[7]] => [2,3,2]
[[1,2,3,5],[4,6],[7]] => [3,2,2]
[[1,2,3,4],[5,6],[7]] => [4,2,1]
[[1,5,6,7],[2],[3],[4]] => [7]
[[1,4,6,7],[2],[3],[5]] => [4,3]
[[1,3,6,7],[2],[4],[5]] => [3,4]
[[1,2,6,7],[3],[4],[5]] => [2,5]
[[1,4,5,7],[2],[3],[6]] => [5,2]
[[1,3,5,7],[2],[4],[6]] => [3,2,2]
[[1,2,5,7],[3],[4],[6]] => [2,3,2]
[[1,3,4,7],[2],[5],[6]] => [4,3]
[[1,2,4,7],[3],[5],[6]] => [2,2,3]
[[1,2,3,7],[4],[5],[6]] => [3,4]
[[1,4,5,6],[2],[3],[7]] => [6,1]
[[1,3,5,6],[2],[4],[7]] => [3,3,1]
[[1,2,5,6],[3],[4],[7]] => [2,4,1]
[[1,3,4,6],[2],[5],[7]] => [4,2,1]
[[1,2,4,6],[3],[5],[7]] => [2,2,2,1]
[[1,2,3,6],[4],[5],[7]] => [3,3,1]
[[1,3,4,5],[2],[6],[7]] => [5,2]
[[1,2,4,5],[3],[6],[7]] => [2,3,2]
[[1,2,3,5],[4],[6],[7]] => [3,2,2]
[[1,2,3,4],[5],[6],[7]] => [4,3]
[[1,4,6],[2,5,7],[3]] => [4,2,1]
[[1,3,6],[2,5,7],[4]] => [3,3,1]
[[1,2,6],[3,5,7],[4]] => [2,4,1]
[[1,3,6],[2,4,7],[5]] => [3,3,1]
[[1,2,6],[3,4,7],[5]] => [2,2,2,1]
[[1,4,5],[2,6,7],[3]] => [5,2]
[[1,3,5],[2,6,7],[4]] => [3,2,2]
[[1,2,5],[3,6,7],[4]] => [2,3,2]
[[1,3,4],[2,6,7],[5]] => [4,3]
[[1,2,4],[3,6,7],[5]] => [2,2,3]
[[1,2,3],[4,6,7],[5]] => [3,4]
[[1,3,5],[2,4,7],[6]] => [3,2,2]
[[1,2,5],[3,4,7],[6]] => [2,3,2]
[[1,3,4],[2,5,7],[6]] => [4,3]
[[1,2,4],[3,5,7],[6]] => [2,2,3]
[[1,2,3],[4,5,7],[6]] => [3,2,2]
[[1,3,5],[2,4,6],[7]] => [3,2,2]
[[1,2,5],[3,4,6],[7]] => [2,3,2]
[[1,3,4],[2,5,6],[7]] => [4,2,1]
[[1,2,4],[3,5,6],[7]] => [2,2,2,1]
[[1,2,3],[4,5,6],[7]] => [3,3,1]
[[1,4,7],[2,5],[3,6]] => [4,3]
[[1,3,7],[2,5],[4,6]] => [3,2,2]
[[1,2,7],[3,5],[4,6]] => [2,3,2]
[[1,3,7],[2,4],[5,6]] => [3,4]
[[1,2,7],[3,4],[5,6]] => [2,2,3]
[[1,4,6],[2,5],[3,7]] => [4,2,1]
[[1,3,6],[2,5],[4,7]] => [3,3,1]
[[1,2,6],[3,5],[4,7]] => [2,4,1]
[[1,3,6],[2,4],[5,7]] => [3,3,1]
[[1,2,6],[3,4],[5,7]] => [2,2,2,1]
[[1,4,5],[2,6],[3,7]] => [5,2]
[[1,3,5],[2,6],[4,7]] => [3,2,2]
[[1,2,5],[3,6],[4,7]] => [2,3,2]
[[1,3,4],[2,6],[5,7]] => [4,2,1]
[[1,2,4],[3,6],[5,7]] => [2,2,2,1]
[[1,2,3],[4,6],[5,7]] => [3,3,1]
[[1,3,5],[2,4],[6,7]] => [3,2,2]
[[1,2,5],[3,4],[6,7]] => [2,3,2]
[[1,3,4],[2,5],[6,7]] => [4,3]
[[1,2,4],[3,5],[6,7]] => [2,2,3]
[[1,2,3],[4,5],[6,7]] => [3,2,2]
[[1,5,7],[2,6],[3],[4]] => [5,2]
[[1,4,7],[2,6],[3],[5]] => [4,3]
[[1,3,7],[2,6],[4],[5]] => [3,4]
[[1,2,7],[3,6],[4],[5]] => [2,5]
[[1,4,7],[2,5],[3],[6]] => [4,3]
[[1,3,7],[2,5],[4],[6]] => [3,2,2]
[[1,2,7],[3,5],[4],[6]] => [2,3,2]
[[1,3,7],[2,4],[5],[6]] => [3,4]
[[1,2,7],[3,4],[5],[6]] => [2,2,3]
[[1,5,6],[2,7],[3],[4]] => [6,1]
[[1,4,6],[2,7],[3],[5]] => [4,2,1]
[[1,3,6],[2,7],[4],[5]] => [3,3,1]
[[1,2,6],[3,7],[4],[5]] => [2,4,1]
[[1,4,5],[2,7],[3],[6]] => [5,2]
[[1,3,5],[2,7],[4],[6]] => [3,2,2]
[[1,2,5],[3,7],[4],[6]] => [2,3,2]
[[1,3,4],[2,7],[5],[6]] => [4,3]
[[1,2,4],[3,7],[5],[6]] => [2,2,3]
[[1,2,3],[4,7],[5],[6]] => [3,4]
[[1,4,6],[2,5],[3],[7]] => [4,2,1]
[[1,3,6],[2,5],[4],[7]] => [3,3,1]
[[1,2,6],[3,5],[4],[7]] => [2,4,1]
[[1,3,6],[2,4],[5],[7]] => [3,3,1]
[[1,2,6],[3,4],[5],[7]] => [2,2,2,1]
[[1,4,5],[2,6],[3],[7]] => [5,2]
[[1,3,5],[2,6],[4],[7]] => [3,2,2]
[[1,2,5],[3,6],[4],[7]] => [2,3,2]
[[1,3,4],[2,6],[5],[7]] => [4,2,1]
[[1,2,4],[3,6],[5],[7]] => [2,2,2,1]
[[1,2,3],[4,6],[5],[7]] => [3,3,1]
[[1,3,5],[2,4],[6],[7]] => [3,2,2]
[[1,2,5],[3,4],[6],[7]] => [2,3,2]
[[1,3,4],[2,5],[6],[7]] => [4,3]
[[1,2,4],[3,5],[6],[7]] => [2,2,3]
[[1,2,3],[4,5],[6],[7]] => [3,2,2]
[[1,6,7],[2],[3],[4],[5]] => [7]
[[1,5,7],[2],[3],[4],[6]] => [5,2]
[[1,4,7],[2],[3],[5],[6]] => [4,3]
[[1,3,7],[2],[4],[5],[6]] => [3,4]
[[1,2,7],[3],[4],[5],[6]] => [2,5]
[[1,5,6],[2],[3],[4],[7]] => [6,1]
[[1,4,6],[2],[3],[5],[7]] => [4,2,1]
[[1,3,6],[2],[4],[5],[7]] => [3,3,1]
[[1,2,6],[3],[4],[5],[7]] => [2,4,1]
[[1,4,5],[2],[3],[6],[7]] => [5,2]
[[1,3,5],[2],[4],[6],[7]] => [3,2,2]
[[1,2,5],[3],[4],[6],[7]] => [2,3,2]
[[1,3,4],[2],[5],[6],[7]] => [4,3]
[[1,2,4],[3],[5],[6],[7]] => [2,2,3]
[[1,2,3],[4],[5],[6],[7]] => [3,4]
[[1,5],[2,6],[3,7],[4]] => [5,2]
[[1,4],[2,6],[3,7],[5]] => [4,2,1]
[[1,3],[2,6],[4,7],[5]] => [3,3,1]
[[1,2],[3,6],[4,7],[5]] => [2,4,1]
[[1,4],[2,5],[3,7],[6]] => [4,3]
[[1,3],[2,5],[4,7],[6]] => [3,2,2]
[[1,2],[3,5],[4,7],[6]] => [2,3,2]
[[1,3],[2,4],[5,7],[6]] => [3,4]
[[1,2],[3,4],[5,7],[6]] => [2,2,3]
[[1,4],[2,5],[3,6],[7]] => [4,3]
[[1,3],[2,5],[4,6],[7]] => [3,2,2]
[[1,2],[3,5],[4,6],[7]] => [2,3,2]
[[1,3],[2,4],[5,6],[7]] => [3,3,1]
[[1,2],[3,4],[5,6],[7]] => [2,2,2,1]
[[1,6],[2,7],[3],[4],[5]] => [6,1]
[[1,5],[2,7],[3],[4],[6]] => [5,2]
[[1,4],[2,7],[3],[5],[6]] => [4,3]
[[1,3],[2,7],[4],[5],[6]] => [3,4]
[[1,2],[3,7],[4],[5],[6]] => [2,5]
[[1,5],[2,6],[3],[4],[7]] => [5,2]
[[1,4],[2,6],[3],[5],[7]] => [4,2,1]
[[1,3],[2,6],[4],[5],[7]] => [3,3,1]
[[1,2],[3,6],[4],[5],[7]] => [2,4,1]
[[1,4],[2,5],[3],[6],[7]] => [4,3]
[[1,3],[2,5],[4],[6],[7]] => [3,2,2]
[[1,2],[3,5],[4],[6],[7]] => [2,3,2]
[[1,3],[2,4],[5],[6],[7]] => [3,4]
[[1,2],[3,4],[5],[6],[7]] => [2,2,3]
[[1,7],[2],[3],[4],[5],[6]] => [7]
[[1,6],[2],[3],[4],[5],[7]] => [6,1]
[[1,5],[2],[3],[4],[6],[7]] => [5,2]
[[1,4],[2],[3],[5],[6],[7]] => [4,3]
[[1,3],[2],[4],[5],[6],[7]] => [3,4]
[[1,2],[3],[4],[5],[6],[7]] => [2,5]
[[1],[2],[3],[4],[5],[6],[7]] => [7]
[[1,2,3,4,5,6,7,8]] => [8]
[[1,3,4,5,6,7,8],[2]] => [8]
[[1,2,4,5,6,7,8],[3]] => [2,6]
[[1,2,3,5,6,7,8],[4]] => [3,5]
[[1,2,3,4,6,7,8],[5]] => [4,4]
[[1,2,3,4,5,7,8],[6]] => [5,3]
[[1,2,3,4,5,6,8],[7]] => [6,2]
[[1,2,3,4,5,6,7],[8]] => [7,1]
[[1,3,5,6,7,8],[2,4]] => [3,5]
[[1,2,5,6,7,8],[3,4]] => [2,6]
[[1,3,4,6,7,8],[2,5]] => [4,4]
[[1,2,4,6,7,8],[3,5]] => [2,2,4]
[[1,2,3,6,7,8],[4,5]] => [3,5]
[[1,3,4,5,7,8],[2,6]] => [5,3]
[[1,2,4,5,7,8],[3,6]] => [2,3,3]
[[1,2,3,5,7,8],[4,6]] => [3,2,3]
[[1,2,3,4,7,8],[5,6]] => [4,4]
[[1,3,4,5,6,8],[2,7]] => [6,2]
[[1,2,4,5,6,8],[3,7]] => [2,4,2]
[[1,2,3,5,6,8],[4,7]] => [3,3,2]
[[1,2,3,4,6,8],[5,7]] => [4,2,2]
[[1,2,3,4,5,8],[6,7]] => [5,3]
[[1,3,4,5,6,7],[2,8]] => [7,1]
[[1,2,4,5,6,7],[3,8]] => [2,5,1]
[[1,2,3,5,6,7],[4,8]] => [3,4,1]
[[1,2,3,4,6,7],[5,8]] => [4,3,1]
[[1,2,3,4,5,7],[6,8]] => [5,2,1]
[[1,2,3,4,5,6],[7,8]] => [6,2]
[[1,4,5,6,7,8],[2],[3]] => [8]
[[1,3,5,6,7,8],[2],[4]] => [3,5]
[[1,2,5,6,7,8],[3],[4]] => [2,6]
[[1,3,4,6,7,8],[2],[5]] => [4,4]
[[1,2,4,6,7,8],[3],[5]] => [2,2,4]
[[1,2,3,6,7,8],[4],[5]] => [3,5]
[[1,3,4,5,7,8],[2],[6]] => [5,3]
[[1,2,4,5,7,8],[3],[6]] => [2,3,3]
[[1,2,3,5,7,8],[4],[6]] => [3,2,3]
[[1,2,3,4,7,8],[5],[6]] => [4,4]
[[1,3,4,5,6,8],[2],[7]] => [6,2]
[[1,2,4,5,6,8],[3],[7]] => [2,4,2]
[[1,2,3,5,6,8],[4],[7]] => [3,3,2]
[[1,2,3,4,6,8],[5],[7]] => [4,2,2]
[[1,2,3,4,5,8],[6],[7]] => [5,3]
[[1,3,4,5,6,7],[2],[8]] => [7,1]
[[1,2,4,5,6,7],[3],[8]] => [2,5,1]
[[1,2,3,5,6,7],[4],[8]] => [3,4,1]
[[1,2,3,4,6,7],[5],[8]] => [4,3,1]
[[1,2,3,4,5,7],[6],[8]] => [5,2,1]
[[1,2,3,4,5,6],[7],[8]] => [6,2]
[[1,3,5,7,8],[2,4,6]] => [3,2,3]
[[1,2,5,7,8],[3,4,6]] => [2,3,3]
[[1,3,4,7,8],[2,5,6]] => [4,4]
[[1,2,4,7,8],[3,5,6]] => [2,2,4]
[[1,2,3,7,8],[4,5,6]] => [3,5]
[[1,3,5,6,8],[2,4,7]] => [3,3,2]
[[1,2,5,6,8],[3,4,7]] => [2,4,2]
[[1,3,4,6,8],[2,5,7]] => [4,2,2]
[[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[[1,2,3,6,8],[4,5,7]] => [3,3,2]
[[1,3,4,5,8],[2,6,7]] => [5,3]
[[1,2,4,5,8],[3,6,7]] => [2,3,3]
[[1,2,3,5,8],[4,6,7]] => [3,2,3]
[[1,2,3,4,8],[5,6,7]] => [4,4]
[[1,3,5,6,7],[2,4,8]] => [3,4,1]
[[1,2,5,6,7],[3,4,8]] => [2,5,1]
[[1,3,4,6,7],[2,5,8]] => [4,3,1]
[[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[[1,2,3,6,7],[4,5,8]] => [3,4,1]
[[1,3,4,5,7],[2,6,8]] => [5,2,1]
[[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[[1,2,3,4,7],[5,6,8]] => [4,3,1]
[[1,3,4,5,6],[2,7,8]] => [6,2]
[[1,2,4,5,6],[3,7,8]] => [2,4,2]
[[1,2,3,5,6],[4,7,8]] => [3,3,2]
[[1,2,3,4,6],[5,7,8]] => [4,2,2]
[[1,2,3,4,5],[6,7,8]] => [5,3]
[[1,4,6,7,8],[2,5],[3]] => [4,4]
[[1,3,6,7,8],[2,5],[4]] => [3,5]
[[1,2,6,7,8],[3,5],[4]] => [2,6]
[[1,3,6,7,8],[2,4],[5]] => [3,5]
[[1,2,6,7,8],[3,4],[5]] => [2,2,4]
[[1,4,5,7,8],[2,6],[3]] => [5,3]
[[1,3,5,7,8],[2,6],[4]] => [3,2,3]
[[1,2,5,7,8],[3,6],[4]] => [2,3,3]
[[1,3,4,7,8],[2,6],[5]] => [4,4]
[[1,2,4,7,8],[3,6],[5]] => [2,2,4]
[[1,2,3,7,8],[4,6],[5]] => [3,5]
[[1,3,5,7,8],[2,4],[6]] => [3,2,3]
[[1,2,5,7,8],[3,4],[6]] => [2,3,3]
[[1,3,4,7,8],[2,5],[6]] => [4,4]
[[1,2,4,7,8],[3,5],[6]] => [2,2,4]
[[1,2,3,7,8],[4,5],[6]] => [3,2,3]
[[1,4,5,6,8],[2,7],[3]] => [6,2]
[[1,3,5,6,8],[2,7],[4]] => [3,3,2]
[[1,2,5,6,8],[3,7],[4]] => [2,4,2]
[[1,3,4,6,8],[2,7],[5]] => [4,2,2]
[[1,2,4,6,8],[3,7],[5]] => [2,2,2,2]
[[1,2,3,6,8],[4,7],[5]] => [3,3,2]
[[1,3,4,5,8],[2,7],[6]] => [5,3]
[[1,2,4,5,8],[3,7],[6]] => [2,3,3]
[[1,2,3,5,8],[4,7],[6]] => [3,2,3]
[[1,2,3,4,8],[5,7],[6]] => [4,4]
[[1,3,5,6,8],[2,4],[7]] => [3,3,2]
[[1,2,5,6,8],[3,4],[7]] => [2,4,2]
[[1,3,4,6,8],[2,5],[7]] => [4,2,2]
[[1,2,4,6,8],[3,5],[7]] => [2,2,2,2]
[[1,2,3,6,8],[4,5],[7]] => [3,3,2]
[[1,3,4,5,8],[2,6],[7]] => [5,3]
[[1,2,4,5,8],[3,6],[7]] => [2,3,3]
[[1,2,3,5,8],[4,6],[7]] => [3,2,3]
[[1,2,3,4,8],[5,6],[7]] => [4,2,2]
[[1,4,5,6,7],[2,8],[3]] => [7,1]
[[1,3,5,6,7],[2,8],[4]] => [3,4,1]
[[1,2,5,6,7],[3,8],[4]] => [2,5,1]
[[1,3,4,6,7],[2,8],[5]] => [4,3,1]
[[1,2,4,6,7],[3,8],[5]] => [2,2,3,1]
[[1,2,3,6,7],[4,8],[5]] => [3,4,1]
[[1,3,4,5,7],[2,8],[6]] => [5,2,1]
[[1,2,4,5,7],[3,8],[6]] => [2,3,2,1]
[[1,2,3,5,7],[4,8],[6]] => [3,2,2,1]
[[1,2,3,4,7],[5,8],[6]] => [4,3,1]
[[1,3,4,5,6],[2,8],[7]] => [6,2]
[[1,2,4,5,6],[3,8],[7]] => [2,4,2]
[[1,2,3,5,6],[4,8],[7]] => [3,3,2]
[[1,2,3,4,6],[5,8],[7]] => [4,2,2]
[[1,2,3,4,5],[6,8],[7]] => [5,3]
[[1,3,5,6,7],[2,4],[8]] => [3,4,1]
[[1,2,5,6,7],[3,4],[8]] => [2,5,1]
[[1,3,4,6,7],[2,5],[8]] => [4,3,1]
[[1,2,4,6,7],[3,5],[8]] => [2,2,3,1]
[[1,2,3,6,7],[4,5],[8]] => [3,4,1]
[[1,3,4,5,7],[2,6],[8]] => [5,2,1]
[[1,2,4,5,7],[3,6],[8]] => [2,3,2,1]
[[1,2,3,5,7],[4,6],[8]] => [3,2,2,1]
[[1,2,3,4,7],[5,6],[8]] => [4,3,1]
[[1,3,4,5,6],[2,7],[8]] => [6,2]
[[1,2,4,5,6],[3,7],[8]] => [2,4,2]
[[1,2,3,5,6],[4,7],[8]] => [3,3,2]
[[1,2,3,4,6],[5,7],[8]] => [4,2,2]
[[1,2,3,4,5],[6,7],[8]] => [5,2,1]
[[1,5,6,7,8],[2],[3],[4]] => [8]
[[1,4,6,7,8],[2],[3],[5]] => [4,4]
[[1,3,6,7,8],[2],[4],[5]] => [3,5]
[[1,2,6,7,8],[3],[4],[5]] => [2,6]
[[1,4,5,7,8],[2],[3],[6]] => [5,3]
[[1,3,5,7,8],[2],[4],[6]] => [3,2,3]
[[1,2,5,7,8],[3],[4],[6]] => [2,3,3]
[[1,3,4,7,8],[2],[5],[6]] => [4,4]
[[1,2,4,7,8],[3],[5],[6]] => [2,2,4]
[[1,2,3,7,8],[4],[5],[6]] => [3,5]
[[1,4,5,6,8],[2],[3],[7]] => [6,2]
[[1,3,5,6,8],[2],[4],[7]] => [3,3,2]
[[1,2,5,6,8],[3],[4],[7]] => [2,4,2]
[[1,3,4,6,8],[2],[5],[7]] => [4,2,2]
[[1,2,4,6,8],[3],[5],[7]] => [2,2,2,2]
[[1,2,3,6,8],[4],[5],[7]] => [3,3,2]
[[1,3,4,5,8],[2],[6],[7]] => [5,3]
[[1,2,4,5,8],[3],[6],[7]] => [2,3,3]
[[1,2,3,5,8],[4],[6],[7]] => [3,2,3]
[[1,2,3,4,8],[5],[6],[7]] => [4,4]
[[1,4,5,6,7],[2],[3],[8]] => [7,1]
[[1,3,5,6,7],[2],[4],[8]] => [3,4,1]
[[1,2,5,6,7],[3],[4],[8]] => [2,5,1]
[[1,3,4,6,7],[2],[5],[8]] => [4,3,1]
[[1,2,4,6,7],[3],[5],[8]] => [2,2,3,1]
[[1,2,3,6,7],[4],[5],[8]] => [3,4,1]
[[1,3,4,5,7],[2],[6],[8]] => [5,2,1]
[[1,2,4,5,7],[3],[6],[8]] => [2,3,2,1]
[[1,2,3,5,7],[4],[6],[8]] => [3,2,2,1]
[[1,2,3,4,7],[5],[6],[8]] => [4,3,1]
[[1,3,4,5,6],[2],[7],[8]] => [6,2]
[[1,2,4,5,6],[3],[7],[8]] => [2,4,2]
[[1,2,3,5,6],[4],[7],[8]] => [3,3,2]
[[1,2,3,4,6],[5],[7],[8]] => [4,2,2]
[[1,2,3,4,5],[6],[7],[8]] => [5,3]
[[1,3,5,7],[2,4,6,8]] => [3,2,2,1]
[[1,2,5,7],[3,4,6,8]] => [2,3,2,1]
[[1,3,4,7],[2,5,6,8]] => [4,3,1]
[[1,2,4,7],[3,5,6,8]] => [2,2,3,1]
[[1,2,3,7],[4,5,6,8]] => [3,4,1]
[[1,3,5,6],[2,4,7,8]] => [3,3,2]
[[1,2,5,6],[3,4,7,8]] => [2,4,2]
[[1,3,4,6],[2,5,7,8]] => [4,2,2]
[[1,2,4,6],[3,5,7,8]] => [2,2,2,2]
[[1,2,3,6],[4,5,7,8]] => [3,3,2]
[[1,3,4,5],[2,6,7,8]] => [5,3]
[[1,2,4,5],[3,6,7,8]] => [2,3,3]
[[1,2,3,5],[4,6,7,8]] => [3,2,3]
[[1,2,3,4],[5,6,7,8]] => [4,4]
[[1,4,6,8],[2,5,7],[3]] => [4,2,2]
[[1,3,6,8],[2,5,7],[4]] => [3,3,2]
[[1,2,6,8],[3,5,7],[4]] => [2,4,2]
[[1,3,6,8],[2,4,7],[5]] => [3,3,2]
[[1,2,6,8],[3,4,7],[5]] => [2,2,2,2]
[[1,4,5,8],[2,6,7],[3]] => [5,3]
[[1,3,5,8],[2,6,7],[4]] => [3,2,3]
[[1,2,5,8],[3,6,7],[4]] => [2,3,3]
[[1,3,4,8],[2,6,7],[5]] => [4,4]
[[1,2,4,8],[3,6,7],[5]] => [2,2,4]
[[1,2,3,8],[4,6,7],[5]] => [3,5]
[[1,3,5,8],[2,4,7],[6]] => [3,2,3]
[[1,2,5,8],[3,4,7],[6]] => [2,3,3]
[[1,3,4,8],[2,5,7],[6]] => [4,4]
[[1,2,4,8],[3,5,7],[6]] => [2,2,4]
[[1,2,3,8],[4,5,7],[6]] => [3,2,3]
[[1,3,5,8],[2,4,6],[7]] => [3,2,3]
[[1,2,5,8],[3,4,6],[7]] => [2,3,3]
[[1,3,4,8],[2,5,6],[7]] => [4,2,2]
[[1,2,4,8],[3,5,6],[7]] => [2,2,2,2]
[[1,2,3,8],[4,5,6],[7]] => [3,3,2]
[[1,4,6,7],[2,5,8],[3]] => [4,3,1]
[[1,3,6,7],[2,5,8],[4]] => [3,4,1]
[[1,2,6,7],[3,5,8],[4]] => [2,5,1]
[[1,3,6,7],[2,4,8],[5]] => [3,4,1]
[[1,2,6,7],[3,4,8],[5]] => [2,2,3,1]
[[1,4,5,7],[2,6,8],[3]] => [5,2,1]
[[1,3,5,7],[2,6,8],[4]] => [3,2,2,1]
[[1,2,5,7],[3,6,8],[4]] => [2,3,2,1]
[[1,3,4,7],[2,6,8],[5]] => [4,3,1]
[[1,2,4,7],[3,6,8],[5]] => [2,2,3,1]
[[1,2,3,7],[4,6,8],[5]] => [3,4,1]
[[1,3,5,7],[2,4,8],[6]] => [3,2,2,1]
[[1,2,5,7],[3,4,8],[6]] => [2,3,2,1]
[[1,3,4,7],[2,5,8],[6]] => [4,3,1]
[[1,2,4,7],[3,5,8],[6]] => [2,2,3,1]
[[1,2,3,7],[4,5,8],[6]] => [3,2,2,1]
[[1,4,5,6],[2,7,8],[3]] => [6,2]
[[1,3,5,6],[2,7,8],[4]] => [3,3,2]
[[1,2,5,6],[3,7,8],[4]] => [2,4,2]
[[1,3,4,6],[2,7,8],[5]] => [4,2,2]
[[1,2,4,6],[3,7,8],[5]] => [2,2,2,2]
[[1,2,3,6],[4,7,8],[5]] => [3,3,2]
[[1,3,4,5],[2,7,8],[6]] => [5,3]
[[1,2,4,5],[3,7,8],[6]] => [2,3,3]
[[1,2,3,5],[4,7,8],[6]] => [3,2,3]
[[1,2,3,4],[5,7,8],[6]] => [4,4]
[[1,3,5,6],[2,4,8],[7]] => [3,3,2]
[[1,2,5,6],[3,4,8],[7]] => [2,4,2]
[[1,3,4,6],[2,5,8],[7]] => [4,2,2]
[[1,2,4,6],[3,5,8],[7]] => [2,2,2,2]
[[1,2,3,6],[4,5,8],[7]] => [3,3,2]
[[1,3,4,5],[2,6,8],[7]] => [5,3]
[[1,2,4,5],[3,6,8],[7]] => [2,3,3]
[[1,2,3,5],[4,6,8],[7]] => [3,2,3]
[[1,2,3,4],[5,6,8],[7]] => [4,2,2]
[[1,3,5,7],[2,4,6],[8]] => [3,2,2,1]
[[1,2,5,7],[3,4,6],[8]] => [2,3,2,1]
[[1,3,4,7],[2,5,6],[8]] => [4,3,1]
[[1,2,4,7],[3,5,6],[8]] => [2,2,3,1]
[[1,2,3,7],[4,5,6],[8]] => [3,4,1]
[[1,3,5,6],[2,4,7],[8]] => [3,3,2]
[[1,2,5,6],[3,4,7],[8]] => [2,4,2]
[[1,3,4,6],[2,5,7],[8]] => [4,2,2]
[[1,2,4,6],[3,5,7],[8]] => [2,2,2,2]
[[1,2,3,6],[4,5,7],[8]] => [3,3,2]
[[1,3,4,5],[2,6,7],[8]] => [5,2,1]
[[1,2,4,5],[3,6,7],[8]] => [2,3,2,1]
[[1,2,3,5],[4,6,7],[8]] => [3,2,2,1]
[[1,2,3,4],[5,6,7],[8]] => [4,3,1]
[[1,4,7,8],[2,5],[3,6]] => [4,4]
[[1,3,7,8],[2,5],[4,6]] => [3,2,3]
[[1,2,7,8],[3,5],[4,6]] => [2,3,3]
[[1,3,7,8],[2,4],[5,6]] => [3,5]
[[1,2,7,8],[3,4],[5,6]] => [2,2,4]
[[1,4,6,8],[2,5],[3,7]] => [4,2,2]
[[1,3,6,8],[2,5],[4,7]] => [3,3,2]
[[1,2,6,8],[3,5],[4,7]] => [2,4,2]
[[1,3,6,8],[2,4],[5,7]] => [3,3,2]
[[1,2,6,8],[3,4],[5,7]] => [2,2,2,2]
[[1,4,5,8],[2,6],[3,7]] => [5,3]
[[1,3,5,8],[2,6],[4,7]] => [3,2,3]
[[1,2,5,8],[3,6],[4,7]] => [2,3,3]
[[1,3,4,8],[2,6],[5,7]] => [4,2,2]
[[1,2,4,8],[3,6],[5,7]] => [2,2,2,2]
[[1,2,3,8],[4,6],[5,7]] => [3,3,2]
[[1,3,5,8],[2,4],[6,7]] => [3,2,3]
[[1,2,5,8],[3,4],[6,7]] => [2,3,3]
[[1,3,4,8],[2,5],[6,7]] => [4,4]
[[1,2,4,8],[3,5],[6,7]] => [2,2,4]
[[1,2,3,8],[4,5],[6,7]] => [3,2,3]
[[1,4,6,7],[2,5],[3,8]] => [4,3,1]
[[1,3,6,7],[2,5],[4,8]] => [3,4,1]
[[1,2,6,7],[3,5],[4,8]] => [2,5,1]
[[1,3,6,7],[2,4],[5,8]] => [3,4,1]
[[1,2,6,7],[3,4],[5,8]] => [2,2,3,1]
[[1,4,5,7],[2,6],[3,8]] => [5,2,1]
[[1,3,5,7],[2,6],[4,8]] => [3,2,2,1]
[[1,2,5,7],[3,6],[4,8]] => [2,3,2,1]
[[1,3,4,7],[2,6],[5,8]] => [4,3,1]
[[1,2,4,7],[3,6],[5,8]] => [2,2,3,1]
[[1,2,3,7],[4,6],[5,8]] => [3,4,1]
[[1,3,5,7],[2,4],[6,8]] => [3,2,2,1]
[[1,2,5,7],[3,4],[6,8]] => [2,3,2,1]
[[1,3,4,7],[2,5],[6,8]] => [4,3,1]
[[1,2,4,7],[3,5],[6,8]] => [2,2,3,1]
[[1,2,3,7],[4,5],[6,8]] => [3,2,2,1]
[[1,4,5,6],[2,7],[3,8]] => [6,2]
[[1,3,5,6],[2,7],[4,8]] => [3,3,2]
[[1,2,5,6],[3,7],[4,8]] => [2,4,2]
[[1,3,4,6],[2,7],[5,8]] => [4,2,2]
[[1,2,4,6],[3,7],[5,8]] => [2,2,2,2]
[[1,2,3,6],[4,7],[5,8]] => [3,3,2]
[[1,3,4,5],[2,7],[6,8]] => [5,2,1]
[[1,2,4,5],[3,7],[6,8]] => [2,3,2,1]
[[1,2,3,5],[4,7],[6,8]] => [3,2,2,1]
[[1,2,3,4],[5,7],[6,8]] => [4,3,1]
[[1,3,5,6],[2,4],[7,8]] => [3,3,2]
[[1,2,5,6],[3,4],[7,8]] => [2,4,2]
[[1,3,4,6],[2,5],[7,8]] => [4,2,2]
[[1,2,4,6],[3,5],[7,8]] => [2,2,2,2]
[[1,2,3,6],[4,5],[7,8]] => [3,3,2]
[[1,3,4,5],[2,6],[7,8]] => [5,3]
[[1,2,4,5],[3,6],[7,8]] => [2,3,3]
[[1,2,3,5],[4,6],[7,8]] => [3,2,3]
[[1,2,3,4],[5,6],[7,8]] => [4,2,2]
[[1,5,7,8],[2,6],[3],[4]] => [5,3]
[[1,4,7,8],[2,6],[3],[5]] => [4,4]
[[1,3,7,8],[2,6],[4],[5]] => [3,5]
[[1,2,7,8],[3,6],[4],[5]] => [2,6]
[[1,4,7,8],[2,5],[3],[6]] => [4,4]
[[1,3,7,8],[2,5],[4],[6]] => [3,2,3]
[[1,2,7,8],[3,5],[4],[6]] => [2,3,3]
[[1,3,7,8],[2,4],[5],[6]] => [3,5]
[[1,2,7,8],[3,4],[5],[6]] => [2,2,4]
[[1,5,6,8],[2,7],[3],[4]] => [6,2]
[[1,4,6,8],[2,7],[3],[5]] => [4,2,2]
[[1,3,6,8],[2,7],[4],[5]] => [3,3,2]
[[1,2,6,8],[3,7],[4],[5]] => [2,4,2]
[[1,4,5,8],[2,7],[3],[6]] => [5,3]
[[1,3,5,8],[2,7],[4],[6]] => [3,2,3]
[[1,2,5,8],[3,7],[4],[6]] => [2,3,3]
[[1,3,4,8],[2,7],[5],[6]] => [4,4]
[[1,2,4,8],[3,7],[5],[6]] => [2,2,4]
[[1,2,3,8],[4,7],[5],[6]] => [3,5]
[[1,4,6,8],[2,5],[3],[7]] => [4,2,2]
[[1,3,6,8],[2,5],[4],[7]] => [3,3,2]
[[1,2,6,8],[3,5],[4],[7]] => [2,4,2]
[[1,3,6,8],[2,4],[5],[7]] => [3,3,2]
[[1,2,6,8],[3,4],[5],[7]] => [2,2,2,2]
[[1,4,5,8],[2,6],[3],[7]] => [5,3]
[[1,3,5,8],[2,6],[4],[7]] => [3,2,3]
[[1,2,5,8],[3,6],[4],[7]] => [2,3,3]
[[1,3,4,8],[2,6],[5],[7]] => [4,2,2]
[[1,2,4,8],[3,6],[5],[7]] => [2,2,2,2]
[[1,2,3,8],[4,6],[5],[7]] => [3,3,2]
[[1,3,5,8],[2,4],[6],[7]] => [3,2,3]
[[1,2,5,8],[3,4],[6],[7]] => [2,3,3]
[[1,3,4,8],[2,5],[6],[7]] => [4,4]
[[1,2,4,8],[3,5],[6],[7]] => [2,2,4]
[[1,2,3,8],[4,5],[6],[7]] => [3,2,3]
[[1,5,6,7],[2,8],[3],[4]] => [7,1]
[[1,4,6,7],[2,8],[3],[5]] => [4,3,1]
[[1,3,6,7],[2,8],[4],[5]] => [3,4,1]
[[1,2,6,7],[3,8],[4],[5]] => [2,5,1]
[[1,4,5,7],[2,8],[3],[6]] => [5,2,1]
[[1,3,5,7],[2,8],[4],[6]] => [3,2,2,1]
[[1,2,5,7],[3,8],[4],[6]] => [2,3,2,1]
[[1,3,4,7],[2,8],[5],[6]] => [4,3,1]
[[1,2,4,7],[3,8],[5],[6]] => [2,2,3,1]
[[1,2,3,7],[4,8],[5],[6]] => [3,4,1]
[[1,4,5,6],[2,8],[3],[7]] => [6,2]
[[1,3,5,6],[2,8],[4],[7]] => [3,3,2]
[[1,2,5,6],[3,8],[4],[7]] => [2,4,2]
[[1,3,4,6],[2,8],[5],[7]] => [4,2,2]
[[1,2,4,6],[3,8],[5],[7]] => [2,2,2,2]
[[1,2,3,6],[4,8],[5],[7]] => [3,3,2]
[[1,3,4,5],[2,8],[6],[7]] => [5,3]
[[1,2,4,5],[3,8],[6],[7]] => [2,3,3]
[[1,2,3,5],[4,8],[6],[7]] => [3,2,3]
[[1,2,3,4],[5,8],[6],[7]] => [4,4]
[[1,4,6,7],[2,5],[3],[8]] => [4,3,1]
[[1,3,6,7],[2,5],[4],[8]] => [3,4,1]
[[1,2,6,7],[3,5],[4],[8]] => [2,5,1]
[[1,3,6,7],[2,4],[5],[8]] => [3,4,1]
[[1,2,6,7],[3,4],[5],[8]] => [2,2,3,1]
[[1,4,5,7],[2,6],[3],[8]] => [5,2,1]
[[1,3,5,7],[2,6],[4],[8]] => [3,2,2,1]
[[1,2,5,7],[3,6],[4],[8]] => [2,3,2,1]
[[1,3,4,7],[2,6],[5],[8]] => [4,3,1]
[[1,2,4,7],[3,6],[5],[8]] => [2,2,3,1]
[[1,2,3,7],[4,6],[5],[8]] => [3,4,1]
[[1,3,5,7],[2,4],[6],[8]] => [3,2,2,1]
[[1,2,5,7],[3,4],[6],[8]] => [2,3,2,1]
[[1,3,4,7],[2,5],[6],[8]] => [4,3,1]
[[1,2,4,7],[3,5],[6],[8]] => [2,2,3,1]
[[1,2,3,7],[4,5],[6],[8]] => [3,2,2,1]
[[1,4,5,6],[2,7],[3],[8]] => [6,2]
[[1,3,5,6],[2,7],[4],[8]] => [3,3,2]
[[1,2,5,6],[3,7],[4],[8]] => [2,4,2]
[[1,3,4,6],[2,7],[5],[8]] => [4,2,2]
[[1,2,4,6],[3,7],[5],[8]] => [2,2,2,2]
[[1,2,3,6],[4,7],[5],[8]] => [3,3,2]
[[1,3,4,5],[2,7],[6],[8]] => [5,2,1]
[[1,2,4,5],[3,7],[6],[8]] => [2,3,2,1]
[[1,2,3,5],[4,7],[6],[8]] => [3,2,2,1]
[[1,2,3,4],[5,7],[6],[8]] => [4,3,1]
[[1,3,5,6],[2,4],[7],[8]] => [3,3,2]
[[1,2,5,6],[3,4],[7],[8]] => [2,4,2]
[[1,3,4,6],[2,5],[7],[8]] => [4,2,2]
[[1,2,4,6],[3,5],[7],[8]] => [2,2,2,2]
[[1,2,3,6],[4,5],[7],[8]] => [3,3,2]
[[1,3,4,5],[2,6],[7],[8]] => [5,3]
[[1,2,4,5],[3,6],[7],[8]] => [2,3,3]
[[1,2,3,5],[4,6],[7],[8]] => [3,2,3]
[[1,2,3,4],[5,6],[7],[8]] => [4,2,2]
[[1,6,7,8],[2],[3],[4],[5]] => [8]
[[1,5,7,8],[2],[3],[4],[6]] => [5,3]
[[1,4,7,8],[2],[3],[5],[6]] => [4,4]
[[1,3,7,8],[2],[4],[5],[6]] => [3,5]
[[1,2,7,8],[3],[4],[5],[6]] => [2,6]
[[1,5,6,8],[2],[3],[4],[7]] => [6,2]
[[1,4,6,8],[2],[3],[5],[7]] => [4,2,2]
[[1,3,6,8],[2],[4],[5],[7]] => [3,3,2]
[[1,2,6,8],[3],[4],[5],[7]] => [2,4,2]
[[1,4,5,8],[2],[3],[6],[7]] => [5,3]
[[1,3,5,8],[2],[4],[6],[7]] => [3,2,3]
[[1,2,5,8],[3],[4],[6],[7]] => [2,3,3]
[[1,3,4,8],[2],[5],[6],[7]] => [4,4]
[[1,2,4,8],[3],[5],[6],[7]] => [2,2,4]
[[1,2,3,8],[4],[5],[6],[7]] => [3,5]
[[1,5,6,7],[2],[3],[4],[8]] => [7,1]
[[1,4,6,7],[2],[3],[5],[8]] => [4,3,1]
[[1,3,6,7],[2],[4],[5],[8]] => [3,4,1]
[[1,2,6,7],[3],[4],[5],[8]] => [2,5,1]
[[1,4,5,7],[2],[3],[6],[8]] => [5,2,1]
[[1,3,5,7],[2],[4],[6],[8]] => [3,2,2,1]
[[1,2,5,7],[3],[4],[6],[8]] => [2,3,2,1]
[[1,3,4,7],[2],[5],[6],[8]] => [4,3,1]
[[1,2,4,7],[3],[5],[6],[8]] => [2,2,3,1]
[[1,2,3,7],[4],[5],[6],[8]] => [3,4,1]
[[1,4,5,6],[2],[3],[7],[8]] => [6,2]
[[1,3,5,6],[2],[4],[7],[8]] => [3,3,2]
[[1,2,5,6],[3],[4],[7],[8]] => [2,4,2]
[[1,3,4,6],[2],[5],[7],[8]] => [4,2,2]
[[1,2,4,6],[3],[5],[7],[8]] => [2,2,2,2]
[[1,2,3,6],[4],[5],[7],[8]] => [3,3,2]
[[1,3,4,5],[2],[6],[7],[8]] => [5,3]
[[1,2,4,5],[3],[6],[7],[8]] => [2,3,3]
[[1,2,3,5],[4],[6],[7],[8]] => [3,2,3]
[[1,2,3,4],[5],[6],[7],[8]] => [4,4]
[[1,4,7],[2,5,8],[3,6]] => [4,3,1]
[[1,3,7],[2,5,8],[4,6]] => [3,2,2,1]
[[1,2,7],[3,5,8],[4,6]] => [2,3,2,1]
[[1,3,7],[2,4,8],[5,6]] => [3,4,1]
[[1,2,7],[3,4,8],[5,6]] => [2,2,3,1]
[[1,4,6],[2,5,8],[3,7]] => [4,2,2]
[[1,3,6],[2,5,8],[4,7]] => [3,3,2]
[[1,2,6],[3,5,8],[4,7]] => [2,4,2]
[[1,3,6],[2,4,8],[5,7]] => [3,3,2]
[[1,2,6],[3,4,8],[5,7]] => [2,2,2,2]
[[1,4,5],[2,6,8],[3,7]] => [5,3]
[[1,3,5],[2,6,8],[4,7]] => [3,2,3]
[[1,2,5],[3,6,8],[4,7]] => [2,3,3]
[[1,3,4],[2,6,8],[5,7]] => [4,2,2]
[[1,2,4],[3,6,8],[5,7]] => [2,2,2,2]
[[1,2,3],[4,6,8],[5,7]] => [3,3,2]
[[1,3,5],[2,4,8],[6,7]] => [3,2,3]
[[1,2,5],[3,4,8],[6,7]] => [2,3,3]
[[1,3,4],[2,5,8],[6,7]] => [4,4]
[[1,2,4],[3,5,8],[6,7]] => [2,2,4]
[[1,2,3],[4,5,8],[6,7]] => [3,2,3]
[[1,4,6],[2,5,7],[3,8]] => [4,2,2]
[[1,3,6],[2,5,7],[4,8]] => [3,3,2]
[[1,2,6],[3,5,7],[4,8]] => [2,4,2]
[[1,3,6],[2,4,7],[5,8]] => [3,3,2]
[[1,2,6],[3,4,7],[5,8]] => [2,2,2,2]
[[1,4,5],[2,6,7],[3,8]] => [5,2,1]
[[1,3,5],[2,6,7],[4,8]] => [3,2,2,1]
[[1,2,5],[3,6,7],[4,8]] => [2,3,2,1]
[[1,3,4],[2,6,7],[5,8]] => [4,3,1]
[[1,2,4],[3,6,7],[5,8]] => [2,2,3,1]
[[1,2,3],[4,6,7],[5,8]] => [3,4,1]
[[1,3,5],[2,4,7],[6,8]] => [3,2,2,1]
[[1,2,5],[3,4,7],[6,8]] => [2,3,2,1]
[[1,3,4],[2,5,7],[6,8]] => [4,3,1]
[[1,2,4],[3,5,7],[6,8]] => [2,2,3,1]
[[1,2,3],[4,5,7],[6,8]] => [3,2,2,1]
[[1,3,5],[2,4,6],[7,8]] => [3,2,3]
[[1,2,5],[3,4,6],[7,8]] => [2,3,3]
[[1,3,4],[2,5,6],[7,8]] => [4,2,2]
[[1,2,4],[3,5,6],[7,8]] => [2,2,2,2]
[[1,2,3],[4,5,6],[7,8]] => [3,3,2]
[[1,5,7],[2,6,8],[3],[4]] => [5,2,1]
[[1,4,7],[2,6,8],[3],[5]] => [4,3,1]
[[1,3,7],[2,6,8],[4],[5]] => [3,4,1]
[[1,2,7],[3,6,8],[4],[5]] => [2,5,1]
[[1,4,7],[2,5,8],[3],[6]] => [4,3,1]
[[1,3,7],[2,5,8],[4],[6]] => [3,2,2,1]
[[1,2,7],[3,5,8],[4],[6]] => [2,3,2,1]
[[1,3,7],[2,4,8],[5],[6]] => [3,4,1]
[[1,2,7],[3,4,8],[5],[6]] => [2,2,3,1]
[[1,5,6],[2,7,8],[3],[4]] => [6,2]
[[1,4,6],[2,7,8],[3],[5]] => [4,2,2]
[[1,3,6],[2,7,8],[4],[5]] => [3,3,2]
[[1,2,6],[3,7,8],[4],[5]] => [2,4,2]
[[1,4,5],[2,7,8],[3],[6]] => [5,3]
[[1,3,5],[2,7,8],[4],[6]] => [3,2,3]
[[1,2,5],[3,7,8],[4],[6]] => [2,3,3]
[[1,3,4],[2,7,8],[5],[6]] => [4,4]
[[1,2,4],[3,7,8],[5],[6]] => [2,2,4]
[[1,2,3],[4,7,8],[5],[6]] => [3,5]
[[1,4,6],[2,5,8],[3],[7]] => [4,2,2]
[[1,3,6],[2,5,8],[4],[7]] => [3,3,2]
[[1,2,6],[3,5,8],[4],[7]] => [2,4,2]
[[1,3,6],[2,4,8],[5],[7]] => [3,3,2]
[[1,2,6],[3,4,8],[5],[7]] => [2,2,2,2]
[[1,4,5],[2,6,8],[3],[7]] => [5,3]
[[1,3,5],[2,6,8],[4],[7]] => [3,2,3]
[[1,2,5],[3,6,8],[4],[7]] => [2,3,3]
[[1,3,4],[2,6,8],[5],[7]] => [4,2,2]
[[1,2,4],[3,6,8],[5],[7]] => [2,2,2,2]
[[1,2,3],[4,6,8],[5],[7]] => [3,3,2]
[[1,3,5],[2,4,8],[6],[7]] => [3,2,3]
[[1,2,5],[3,4,8],[6],[7]] => [2,3,3]
[[1,3,4],[2,5,8],[6],[7]] => [4,4]
[[1,2,4],[3,5,8],[6],[7]] => [2,2,4]
[[1,2,3],[4,5,8],[6],[7]] => [3,2,3]
[[1,4,6],[2,5,7],[3],[8]] => [4,2,2]
[[1,3,6],[2,5,7],[4],[8]] => [3,3,2]
[[1,2,6],[3,5,7],[4],[8]] => [2,4,2]
[[1,3,6],[2,4,7],[5],[8]] => [3,3,2]
[[1,2,6],[3,4,7],[5],[8]] => [2,2,2,2]
[[1,4,5],[2,6,7],[3],[8]] => [5,2,1]
[[1,3,5],[2,6,7],[4],[8]] => [3,2,2,1]
[[1,2,5],[3,6,7],[4],[8]] => [2,3,2,1]
[[1,3,4],[2,6,7],[5],[8]] => [4,3,1]
[[1,2,4],[3,6,7],[5],[8]] => [2,2,3,1]
[[1,2,3],[4,6,7],[5],[8]] => [3,4,1]
[[1,3,5],[2,4,7],[6],[8]] => [3,2,2,1]
[[1,2,5],[3,4,7],[6],[8]] => [2,3,2,1]
[[1,3,4],[2,5,7],[6],[8]] => [4,3,1]
[[1,2,4],[3,5,7],[6],[8]] => [2,2,3,1]
[[1,2,3],[4,5,7],[6],[8]] => [3,2,2,1]
[[1,3,5],[2,4,6],[7],[8]] => [3,2,3]
[[1,2,5],[3,4,6],[7],[8]] => [2,3,3]
[[1,3,4],[2,5,6],[7],[8]] => [4,2,2]
[[1,2,4],[3,5,6],[7],[8]] => [2,2,2,2]
[[1,2,3],[4,5,6],[7],[8]] => [3,3,2]
[[1,5,8],[2,6],[3,7],[4]] => [5,3]
[[1,4,8],[2,6],[3,7],[5]] => [4,2,2]
[[1,3,8],[2,6],[4,7],[5]] => [3,3,2]
[[1,2,8],[3,6],[4,7],[5]] => [2,4,2]
[[1,4,8],[2,5],[3,7],[6]] => [4,4]
[[1,3,8],[2,5],[4,7],[6]] => [3,2,3]
[[1,2,8],[3,5],[4,7],[6]] => [2,3,3]
[[1,3,8],[2,4],[5,7],[6]] => [3,5]
[[1,2,8],[3,4],[5,7],[6]] => [2,2,4]
[[1,4,8],[2,5],[3,6],[7]] => [4,4]
[[1,3,8],[2,5],[4,6],[7]] => [3,2,3]
[[1,2,8],[3,5],[4,6],[7]] => [2,3,3]
[[1,3,8],[2,4],[5,6],[7]] => [3,3,2]
[[1,2,8],[3,4],[5,6],[7]] => [2,2,2,2]
[[1,5,7],[2,6],[3,8],[4]] => [5,2,1]
[[1,4,7],[2,6],[3,8],[5]] => [4,3,1]
[[1,3,7],[2,6],[4,8],[5]] => [3,4,1]
[[1,2,7],[3,6],[4,8],[5]] => [2,5,1]
[[1,4,7],[2,5],[3,8],[6]] => [4,3,1]
[[1,3,7],[2,5],[4,8],[6]] => [3,2,2,1]
[[1,2,7],[3,5],[4,8],[6]] => [2,3,2,1]
[[1,3,7],[2,4],[5,8],[6]] => [3,4,1]
[[1,2,7],[3,4],[5,8],[6]] => [2,2,3,1]
[[1,5,6],[2,7],[3,8],[4]] => [6,2]
[[1,4,6],[2,7],[3,8],[5]] => [4,2,2]
[[1,3,6],[2,7],[4,8],[5]] => [3,3,2]
[[1,2,6],[3,7],[4,8],[5]] => [2,4,2]
[[1,4,5],[2,7],[3,8],[6]] => [5,2,1]
[[1,3,5],[2,7],[4,8],[6]] => [3,2,2,1]
[[1,2,5],[3,7],[4,8],[6]] => [2,3,2,1]
[[1,3,4],[2,7],[5,8],[6]] => [4,3,1]
[[1,2,4],[3,7],[5,8],[6]] => [2,2,3,1]
[[1,2,3],[4,7],[5,8],[6]] => [3,4,1]
[[1,4,6],[2,5],[3,8],[7]] => [4,2,2]
[[1,3,6],[2,5],[4,8],[7]] => [3,3,2]
[[1,2,6],[3,5],[4,8],[7]] => [2,4,2]
[[1,3,6],[2,4],[5,8],[7]] => [3,3,2]
[[1,2,6],[3,4],[5,8],[7]] => [2,2,2,2]
[[1,4,5],[2,6],[3,8],[7]] => [5,3]
[[1,3,5],[2,6],[4,8],[7]] => [3,2,3]
[[1,2,5],[3,6],[4,8],[7]] => [2,3,3]
[[1,3,4],[2,6],[5,8],[7]] => [4,2,2]
[[1,2,4],[3,6],[5,8],[7]] => [2,2,2,2]
[[1,2,3],[4,6],[5,8],[7]] => [3,3,2]
[[1,3,5],[2,4],[6,8],[7]] => [3,2,3]
[[1,2,5],[3,4],[6,8],[7]] => [2,3,3]
[[1,3,4],[2,5],[6,8],[7]] => [4,4]
[[1,2,4],[3,5],[6,8],[7]] => [2,2,4]
[[1,2,3],[4,5],[6,8],[7]] => [3,2,3]
[[1,4,7],[2,5],[3,6],[8]] => [4,3,1]
[[1,3,7],[2,5],[4,6],[8]] => [3,2,2,1]
[[1,2,7],[3,5],[4,6],[8]] => [2,3,2,1]
[[1,3,7],[2,4],[5,6],[8]] => [3,4,1]
[[1,2,7],[3,4],[5,6],[8]] => [2,2,3,1]
[[1,4,6],[2,5],[3,7],[8]] => [4,2,2]
[[1,3,6],[2,5],[4,7],[8]] => [3,3,2]
[[1,2,6],[3,5],[4,7],[8]] => [2,4,2]
[[1,3,6],[2,4],[5,7],[8]] => [3,3,2]
[[1,2,6],[3,4],[5,7],[8]] => [2,2,2,2]
[[1,4,5],[2,6],[3,7],[8]] => [5,3]
[[1,3,5],[2,6],[4,7],[8]] => [3,2,3]
[[1,2,5],[3,6],[4,7],[8]] => [2,3,3]
[[1,3,4],[2,6],[5,7],[8]] => [4,2,2]
[[1,2,4],[3,6],[5,7],[8]] => [2,2,2,2]
[[1,2,3],[4,6],[5,7],[8]] => [3,3,2]
[[1,3,5],[2,4],[6,7],[8]] => [3,2,2,1]
[[1,2,5],[3,4],[6,7],[8]] => [2,3,2,1]
[[1,3,4],[2,5],[6,7],[8]] => [4,3,1]
[[1,2,4],[3,5],[6,7],[8]] => [2,2,3,1]
[[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1]
[[1,6,8],[2,7],[3],[4],[5]] => [6,2]
[[1,5,8],[2,7],[3],[4],[6]] => [5,3]
[[1,4,8],[2,7],[3],[5],[6]] => [4,4]
[[1,3,8],[2,7],[4],[5],[6]] => [3,5]
[[1,2,8],[3,7],[4],[5],[6]] => [2,6]
[[1,5,8],[2,6],[3],[4],[7]] => [5,3]
[[1,4,8],[2,6],[3],[5],[7]] => [4,2,2]
[[1,3,8],[2,6],[4],[5],[7]] => [3,3,2]
[[1,2,8],[3,6],[4],[5],[7]] => [2,4,2]
[[1,4,8],[2,5],[3],[6],[7]] => [4,4]
[[1,3,8],[2,5],[4],[6],[7]] => [3,2,3]
[[1,2,8],[3,5],[4],[6],[7]] => [2,3,3]
[[1,3,8],[2,4],[5],[6],[7]] => [3,5]
[[1,2,8],[3,4],[5],[6],[7]] => [2,2,4]
[[1,6,7],[2,8],[3],[4],[5]] => [7,1]
[[1,5,7],[2,8],[3],[4],[6]] => [5,2,1]
[[1,4,7],[2,8],[3],[5],[6]] => [4,3,1]
[[1,3,7],[2,8],[4],[5],[6]] => [3,4,1]
[[1,2,7],[3,8],[4],[5],[6]] => [2,5,1]
[[1,5,6],[2,8],[3],[4],[7]] => [6,2]
[[1,4,6],[2,8],[3],[5],[7]] => [4,2,2]
[[1,3,6],[2,8],[4],[5],[7]] => [3,3,2]
[[1,2,6],[3,8],[4],[5],[7]] => [2,4,2]
[[1,4,5],[2,8],[3],[6],[7]] => [5,3]
[[1,3,5],[2,8],[4],[6],[7]] => [3,2,3]
[[1,2,5],[3,8],[4],[6],[7]] => [2,3,3]
[[1,3,4],[2,8],[5],[6],[7]] => [4,4]
[[1,2,4],[3,8],[5],[6],[7]] => [2,2,4]
[[1,2,3],[4,8],[5],[6],[7]] => [3,5]
[[1,5,7],[2,6],[3],[4],[8]] => [5,2,1]
[[1,4,7],[2,6],[3],[5],[8]] => [4,3,1]
[[1,3,7],[2,6],[4],[5],[8]] => [3,4,1]
[[1,2,7],[3,6],[4],[5],[8]] => [2,5,1]
[[1,4,7],[2,5],[3],[6],[8]] => [4,3,1]
[[1,3,7],[2,5],[4],[6],[8]] => [3,2,2,1]
[[1,2,7],[3,5],[4],[6],[8]] => [2,3,2,1]
[[1,3,7],[2,4],[5],[6],[8]] => [3,4,1]
[[1,2,7],[3,4],[5],[6],[8]] => [2,2,3,1]
[[1,5,6],[2,7],[3],[4],[8]] => [6,2]
[[1,4,6],[2,7],[3],[5],[8]] => [4,2,2]
[[1,3,6],[2,7],[4],[5],[8]] => [3,3,2]
[[1,2,6],[3,7],[4],[5],[8]] => [2,4,2]
[[1,4,5],[2,7],[3],[6],[8]] => [5,2,1]
[[1,3,5],[2,7],[4],[6],[8]] => [3,2,2,1]
[[1,2,5],[3,7],[4],[6],[8]] => [2,3,2,1]
[[1,3,4],[2,7],[5],[6],[8]] => [4,3,1]
[[1,2,4],[3,7],[5],[6],[8]] => [2,2,3,1]
[[1,2,3],[4,7],[5],[6],[8]] => [3,4,1]
[[1,4,6],[2,5],[3],[7],[8]] => [4,2,2]
[[1,3,6],[2,5],[4],[7],[8]] => [3,3,2]
[[1,2,6],[3,5],[4],[7],[8]] => [2,4,2]
[[1,3,6],[2,4],[5],[7],[8]] => [3,3,2]
[[1,2,6],[3,4],[5],[7],[8]] => [2,2,2,2]
[[1,4,5],[2,6],[3],[7],[8]] => [5,3]
[[1,3,5],[2,6],[4],[7],[8]] => [3,2,3]
[[1,2,5],[3,6],[4],[7],[8]] => [2,3,3]
[[1,3,4],[2,6],[5],[7],[8]] => [4,2,2]
[[1,2,4],[3,6],[5],[7],[8]] => [2,2,2,2]
[[1,2,3],[4,6],[5],[7],[8]] => [3,3,2]
[[1,3,5],[2,4],[6],[7],[8]] => [3,2,3]
[[1,2,5],[3,4],[6],[7],[8]] => [2,3,3]
[[1,3,4],[2,5],[6],[7],[8]] => [4,4]
[[1,2,4],[3,5],[6],[7],[8]] => [2,2,4]
[[1,2,3],[4,5],[6],[7],[8]] => [3,2,3]
[[1,7,8],[2],[3],[4],[5],[6]] => [8]
[[1,6,8],[2],[3],[4],[5],[7]] => [6,2]
[[1,5,8],[2],[3],[4],[6],[7]] => [5,3]
[[1,4,8],[2],[3],[5],[6],[7]] => [4,4]
[[1,3,8],[2],[4],[5],[6],[7]] => [3,5]
[[1,2,8],[3],[4],[5],[6],[7]] => [2,6]
[[1,6,7],[2],[3],[4],[5],[8]] => [7,1]
[[1,5,7],[2],[3],[4],[6],[8]] => [5,2,1]
[[1,4,7],[2],[3],[5],[6],[8]] => [4,3,1]
[[1,3,7],[2],[4],[5],[6],[8]] => [3,4,1]
[[1,2,7],[3],[4],[5],[6],[8]] => [2,5,1]
[[1,5,6],[2],[3],[4],[7],[8]] => [6,2]
[[1,4,6],[2],[3],[5],[7],[8]] => [4,2,2]
[[1,3,6],[2],[4],[5],[7],[8]] => [3,3,2]
[[1,2,6],[3],[4],[5],[7],[8]] => [2,4,2]
[[1,4,5],[2],[3],[6],[7],[8]] => [5,3]
[[1,3,5],[2],[4],[6],[7],[8]] => [3,2,3]
[[1,2,5],[3],[4],[6],[7],[8]] => [2,3,3]
[[1,3,4],[2],[5],[6],[7],[8]] => [4,4]
[[1,2,4],[3],[5],[6],[7],[8]] => [2,2,4]
[[1,2,3],[4],[5],[6],[7],[8]] => [3,5]
[[1,5],[2,6],[3,7],[4,8]] => [5,3]
[[1,4],[2,6],[3,7],[5,8]] => [4,2,2]
[[1,3],[2,6],[4,7],[5,8]] => [3,3,2]
[[1,2],[3,6],[4,7],[5,8]] => [2,4,2]
[[1,4],[2,5],[3,7],[6,8]] => [4,3,1]
[[1,3],[2,5],[4,7],[6,8]] => [3,2,2,1]
[[1,2],[3,5],[4,7],[6,8]] => [2,3,2,1]
[[1,3],[2,4],[5,7],[6,8]] => [3,4,1]
[[1,2],[3,4],[5,7],[6,8]] => [2,2,3,1]
[[1,4],[2,5],[3,6],[7,8]] => [4,4]
[[1,3],[2,5],[4,6],[7,8]] => [3,2,3]
[[1,2],[3,5],[4,6],[7,8]] => [2,3,3]
[[1,3],[2,4],[5,6],[7,8]] => [3,3,2]
[[1,2],[3,4],[5,6],[7,8]] => [2,2,2,2]
[[1,6],[2,7],[3,8],[4],[5]] => [6,2]
[[1,5],[2,7],[3,8],[4],[6]] => [5,2,1]
[[1,4],[2,7],[3,8],[5],[6]] => [4,3,1]
[[1,3],[2,7],[4,8],[5],[6]] => [3,4,1]
[[1,2],[3,7],[4,8],[5],[6]] => [2,5,1]
[[1,5],[2,6],[3,8],[4],[7]] => [5,3]
[[1,4],[2,6],[3,8],[5],[7]] => [4,2,2]
[[1,3],[2,6],[4,8],[5],[7]] => [3,3,2]
[[1,2],[3,6],[4,8],[5],[7]] => [2,4,2]
[[1,4],[2,5],[3,8],[6],[7]] => [4,4]
[[1,3],[2,5],[4,8],[6],[7]] => [3,2,3]
[[1,2],[3,5],[4,8],[6],[7]] => [2,3,3]
[[1,3],[2,4],[5,8],[6],[7]] => [3,5]
[[1,2],[3,4],[5,8],[6],[7]] => [2,2,4]
[[1,5],[2,6],[3,7],[4],[8]] => [5,3]
[[1,4],[2,6],[3,7],[5],[8]] => [4,2,2]
[[1,3],[2,6],[4,7],[5],[8]] => [3,3,2]
[[1,2],[3,6],[4,7],[5],[8]] => [2,4,2]
[[1,4],[2,5],[3,7],[6],[8]] => [4,3,1]
[[1,3],[2,5],[4,7],[6],[8]] => [3,2,2,1]
[[1,2],[3,5],[4,7],[6],[8]] => [2,3,2,1]
[[1,3],[2,4],[5,7],[6],[8]] => [3,4,1]
[[1,2],[3,4],[5,7],[6],[8]] => [2,2,3,1]
[[1,4],[2,5],[3,6],[7],[8]] => [4,4]
[[1,3],[2,5],[4,6],[7],[8]] => [3,2,3]
[[1,2],[3,5],[4,6],[7],[8]] => [2,3,3]
[[1,3],[2,4],[5,6],[7],[8]] => [3,3,2]
[[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,2]
[[1,7],[2,8],[3],[4],[5],[6]] => [7,1]
[[1,6],[2,8],[3],[4],[5],[7]] => [6,2]
[[1,5],[2,8],[3],[4],[6],[7]] => [5,3]
[[1,4],[2,8],[3],[5],[6],[7]] => [4,4]
[[1,3],[2,8],[4],[5],[6],[7]] => [3,5]
[[1,2],[3,8],[4],[5],[6],[7]] => [2,6]
[[1,6],[2,7],[3],[4],[5],[8]] => [6,2]
[[1,5],[2,7],[3],[4],[6],[8]] => [5,2,1]
[[1,4],[2,7],[3],[5],[6],[8]] => [4,3,1]
[[1,3],[2,7],[4],[5],[6],[8]] => [3,4,1]
[[1,2],[3,7],[4],[5],[6],[8]] => [2,5,1]
[[1,5],[2,6],[3],[4],[7],[8]] => [5,3]
[[1,4],[2,6],[3],[5],[7],[8]] => [4,2,2]
[[1,3],[2,6],[4],[5],[7],[8]] => [3,3,2]
[[1,2],[3,6],[4],[5],[7],[8]] => [2,4,2]
[[1,4],[2,5],[3],[6],[7],[8]] => [4,4]
[[1,3],[2,5],[4],[6],[7],[8]] => [3,2,3]
[[1,2],[3,5],[4],[6],[7],[8]] => [2,3,3]
[[1,3],[2,4],[5],[6],[7],[8]] => [3,5]
[[1,2],[3,4],[5],[6],[7],[8]] => [2,2,4]
[[1,8],[2],[3],[4],[5],[6],[7]] => [8]
[[1,7],[2],[3],[4],[5],[6],[8]] => [7,1]
[[1,6],[2],[3],[4],[5],[7],[8]] => [6,2]
[[1,5],[2],[3],[4],[6],[7],[8]] => [5,3]
[[1,4],[2],[3],[5],[6],[7],[8]] => [4,4]
[[1,3],[2],[4],[5],[6],[7],[8]] => [3,5]
[[1,2],[3],[4],[5],[6],[7],[8]] => [2,6]
[[1],[2],[3],[4],[5],[6],[7],[8]] => [8]
[[1,3,5,7,9],[2,4,6,8,10]] => [3,2,2,2,1]
[[1,3,5,7,8],[2,4,6,9,10]] => [3,2,3,2]
[[1,3,5,6,9],[2,4,7,8,10]] => [3,3,3,1]
[[1,3,5,6,8],[2,4,7,9,10]] => [3,3,2,2]
[[1,3,5,6,7],[2,4,8,9,10]] => [3,4,3]
[[1,3,4,7,9],[2,5,6,8,10]] => [4,3,2,1]
[[1,3,4,7,8],[2,5,6,9,10]] => [4,4,2]
[[1,3,4,6,9],[2,5,7,8,10]] => [4,2,3,1]
[[1,3,4,6,8],[2,5,7,9,10]] => [4,2,2,2]
[[1,3,4,6,7],[2,5,8,9,10]] => [4,3,3]
[[1,3,4,5,9],[2,6,7,8,10]] => [5,4,1]
[[1,3,4,5,8],[2,6,7,9,10]] => [5,3,2]
[[1,3,4,5,7],[2,6,8,9,10]] => [5,2,3]
[[1,3,4,5,6],[2,7,8,9,10]] => [6,4]
[[1,2,5,7,9],[3,4,6,8,10]] => [2,3,2,2,1]
[[1,2,5,7,8],[3,4,6,9,10]] => [2,3,3,2]
[[1,2,5,6,9],[3,4,7,8,10]] => [2,4,3,1]
[[1,2,5,6,8],[3,4,7,9,10]] => [2,4,2,2]
[[1,2,5,6,7],[3,4,8,9,10]] => [2,5,3]
[[1,2,4,7,9],[3,5,6,8,10]] => [2,2,3,2,1]
[[1,2,4,7,8],[3,5,6,9,10]] => [2,2,4,2]
[[1,2,4,6,9],[3,5,7,8,10]] => [2,2,2,3,1]
[[1,2,4,6,8],[3,5,7,9,10]] => [2,2,2,2,2]
[[1,2,4,6,7],[3,5,8,9,10]] => [2,2,3,3]
[[1,2,4,5,9],[3,6,7,8,10]] => [2,3,4,1]
[[1,2,4,5,8],[3,6,7,9,10]] => [2,3,3,2]
[[1,2,4,5,7],[3,6,8,9,10]] => [2,3,2,3]
[[1,2,4,5,6],[3,7,8,9,10]] => [2,4,4]
[[1,2,3,7,9],[4,5,6,8,10]] => [3,4,2,1]
[[1,2,3,7,8],[4,5,6,9,10]] => [3,5,2]
[[1,2,3,6,9],[4,5,7,8,10]] => [3,3,3,1]
[[1,2,3,6,8],[4,5,7,9,10]] => [3,3,2,2]
[[1,2,3,6,7],[4,5,8,9,10]] => [3,4,3]
[[1,2,3,5,9],[4,6,7,8,10]] => [3,2,4,1]
[[1,2,3,5,8],[4,6,7,9,10]] => [3,2,3,2]
[[1,2,3,5,7],[4,6,8,9,10]] => [3,2,2,3]
[[1,2,3,5,6],[4,7,8,9,10]] => [3,3,4]
[[1,2,3,4,9],[5,6,7,8,10]] => [4,5,1]
[[1,2,3,4,8],[5,6,7,9,10]] => [4,4,2]
[[1,2,3,4,7],[5,6,8,9,10]] => [4,3,3]
[[1,2,3,4,6],[5,7,8,9,10]] => [4,2,4]
[[1,2,3,4,5],[6,7,8,9,10]] => [5,5]
[[1,3,5,7,9,11],[2,4,6,8,10,12]] => [3,2,2,2,2,1]
[[1,3,5,7,9,10],[2,4,6,8,11,12]] => [3,2,2,3,2]
[[1,3,5,7,8,11],[2,4,6,9,10,12]] => [3,2,3,3,1]
[[1,3,5,7,8,10],[2,4,6,9,11,12]] => [3,2,3,2,2]
[[1,3,5,7,8,9],[2,4,6,10,11,12]] => [3,2,4,3]
[[1,3,5,6,9,11],[2,4,7,8,10,12]] => [3,3,3,2,1]
[[1,3,5,6,9,10],[2,4,7,8,11,12]] => [3,3,4,2]
[[1,3,5,6,8,11],[2,4,7,9,10,12]] => [3,3,2,3,1]
[[1,3,5,6,8,10],[2,4,7,9,11,12]] => [3,3,2,2,2]
[[1,3,5,6,8,9],[2,4,7,10,11,12]] => [3,3,3,3]
[[1,3,5,6,7,11],[2,4,8,9,10,12]] => [3,4,4,1]
[[1,3,5,6,7,10],[2,4,8,9,11,12]] => [3,4,3,2]
[[1,3,5,6,7,9],[2,4,8,10,11,12]] => [3,4,2,3]
[[1,3,5,6,7,8],[2,4,9,10,11,12]] => [3,5,4]
[[1,3,4,7,9,11],[2,5,6,8,10,12]] => [4,3,2,2,1]
[[1,3,4,7,9,10],[2,5,6,8,11,12]] => [4,3,3,2]
[[1,3,4,7,8,11],[2,5,6,9,10,12]] => [4,4,3,1]
[[1,3,4,7,8,10],[2,5,6,9,11,12]] => [4,4,2,2]
[[1,3,4,7,8,9],[2,5,6,10,11,12]] => [4,5,3]
[[1,3,4,6,9,11],[2,5,7,8,10,12]] => [4,2,3,2,1]
[[1,3,4,6,9,10],[2,5,7,8,11,12]] => [4,2,4,2]
[[1,3,4,6,8,11],[2,5,7,9,10,12]] => [4,2,2,3,1]
[[1,3,4,6,8,10],[2,5,7,9,11,12]] => [4,2,2,2,2]
[[1,3,4,6,8,9],[2,5,7,10,11,12]] => [4,2,3,3]
[[1,3,4,6,7,11],[2,5,8,9,10,12]] => [4,3,4,1]
[[1,3,4,6,7,10],[2,5,8,9,11,12]] => [4,3,3,2]
[[1,3,4,6,7,9],[2,5,8,10,11,12]] => [4,3,2,3]
[[1,3,4,6,7,8],[2,5,9,10,11,12]] => [4,4,4]
[[1,3,4,5,9,11],[2,6,7,8,10,12]] => [5,4,2,1]
[[1,3,4,5,9,10],[2,6,7,8,11,12]] => [5,5,2]
[[1,3,4,5,8,11],[2,6,7,9,10,12]] => [5,3,3,1]
[[1,3,4,5,8,10],[2,6,7,9,11,12]] => [5,3,2,2]
[[1,3,4,5,8,9],[2,6,7,10,11,12]] => [5,4,3]
[[1,3,4,5,7,11],[2,6,8,9,10,12]] => [5,2,4,1]
[[1,3,4,5,7,10],[2,6,8,9,11,12]] => [5,2,3,2]
[[1,3,4,5,7,9],[2,6,8,10,11,12]] => [5,2,2,3]
[[1,3,4,5,7,8],[2,6,9,10,11,12]] => [5,3,4]
[[1,3,4,5,6,11],[2,7,8,9,10,12]] => [6,5,1]
[[1,3,4,5,6,10],[2,7,8,9,11,12]] => [6,4,2]
[[1,3,4,5,6,9],[2,7,8,10,11,12]] => [6,3,3]
[[1,3,4,5,6,8],[2,7,9,10,11,12]] => [6,2,4]
[[1,3,4,5,6,7],[2,8,9,10,11,12]] => [7,5]
[[1,2,5,7,9,11],[3,4,6,8,10,12]] => [2,3,2,2,2,1]
-----------------------------------------------------------------------------
Created: Jun 12, 2023 at 07:45 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Jun 12, 2023 at 07:45 by Martin Rubey