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------------------------------------------------------------------------
Map identifier: Mp00082

------------------------------------------------------------------------
Map name: to Gelfand-Tsetlin pattern

------------------------------------------------------------------------
Domain: Standard tableaux

------------------------------------------------------------------------
Codomain: Gelfand-Tsetlin patterns

------------------------------------------------------------------------
Description: Sends a tableau to its corresponding [[GelfandTsetlinPatterns|Gelfand-Tsetlin pattern]].

To obtain this Gelfand-Tsetlin pattern, fill in the first row of the pattern with the shape of the tableau.
Then remove the maximal entry from the tableau to obtain a smaller tableau, and repeat the process until the tableau is empty.

------------------------------------------------------------------------
References: 

------------------------------------------------------------------------
Code:

def mapping(T):
    return T.to_Gelfand_Tsetlin_pattern()

------------------------------------------------------------------------
Map images:

[[1]]                             => [[1]]
[[1,2]]                           => [[2,0],[1]]
[[1],[2]]                         => [[1,1],[1]]
[[1,2,3]]                         => [[3,0,0],[2,0],[1]]
[[1,3],[2]]                       => [[2,1,0],[1,1],[1]]
[[1,2],[3]]                       => [[2,1,0],[2,0],[1]]
[[1],[2],[3]]                     => [[1,1,1],[1,1],[1]]
[[1,2,3,4]]                       => [[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,4],[2]]                     => [[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3]]                     => [[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4]]                     => [[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3],[2,4]]                     => [[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2],[3,4]]                     => [[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4],[2],[3]]                   => [[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2],[4]]                   => [[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3],[4]]                   => [[2,1,1,0],[2,1,0],[2,0],[1]]
[[1],[2],[3],[4]]                 => [[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,2,3,4,5]]                     => [[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5],[2]]                   => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5],[3]]                   => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5],[4]]                   => [[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4],[5]]                   => [[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,5],[2,4]]                   => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,4]]                   => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,5]]                   => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,5]]                   => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,5]]                   => [[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,5],[2],[3]]                 => [[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2],[4]]                 => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3],[4]]                 => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2],[5]]                 => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3],[5]]                 => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4],[5]]                 => [[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4],[2,5],[3]]                 => [[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,5],[4]]                 => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,5],[4]]                 => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3],[2,4],[5]]                 => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2],[3,4],[5]]                 => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,5],[2],[3],[4]]               => [[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4],[2],[3],[5]]               => [[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2],[4],[5]]               => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3],[4],[5]]               => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1],[2],[3],[4],[5]]             => [[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,2,3,4,5,6]]                   => [[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,6],[2]]                 => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,6],[3]]                 => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,6],[4]]                 => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,6],[5]]                 => [[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,5],[6]]                 => [[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,6],[2,4]]                 => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,6],[3,4]]                 => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,6],[2,5]]                 => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6],[3,5]]                 => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6],[4,5]]                 => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5],[2,6]]                 => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5],[3,6]]                 => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5],[4,6]]                 => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4],[5,6]]                 => [[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,4,5,6],[2],[3]]               => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,6],[2],[4]]               => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,6],[3],[4]]               => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,6],[2],[5]]               => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6],[3],[5]]               => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6],[4],[5]]               => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5],[2],[6]]               => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5],[3],[6]]               => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5],[4],[6]]               => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4],[5],[6]]               => [[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,5],[2,4,6]]                 => [[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,4,6]]                 => [[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,5,6]]                 => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,5,6]]                 => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,5,6]]                 => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,6],[2,5],[3]]               => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6],[2,5],[4]]               => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,5],[4]]               => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,6],[2,4],[5]]               => [[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,4],[5]]               => [[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2,6],[3]]               => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2,6],[4]]               => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,6],[4]]               => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,6],[5]]               => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,6],[5]]               => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,6],[5]]               => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5],[2,4],[6]]               => [[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,4],[6]]               => [[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,5],[6]]               => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,5],[6]]               => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,5],[6]]               => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,5,6],[2],[3],[4]]             => [[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,6],[2],[3],[5]]             => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6],[2],[4],[5]]             => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3],[4],[5]]             => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2],[3],[6]]             => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2],[4],[6]]             => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3],[4],[6]]             => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2],[5],[6]]             => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3],[5],[6]]             => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4],[5],[6]]             => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4],[2,5],[3,6]]               => [[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,5],[4,6]]               => [[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,5],[4,6]]               => [[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3],[2,4],[5,6]]               => [[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2],[3,4],[5,6]]               => [[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,5],[2,6],[3],[4]]             => [[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4],[2,6],[3],[5]]             => [[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,6],[4],[5]]             => [[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,6],[4],[5]]             => [[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4],[2,5],[3],[6]]             => [[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,5],[4],[6]]             => [[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,5],[4],[6]]             => [[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3],[2,4],[5],[6]]             => [[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2],[3,4],[5],[6]]             => [[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,6],[2],[3],[4],[5]]           => [[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,5],[2],[3],[4],[6]]           => [[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4],[2],[3],[5],[6]]           => [[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2],[4],[5],[6]]           => [[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3],[4],[5],[6]]           => [[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1],[2],[3],[4],[5],[6]]         => [[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,2,3,4,5,6,7]]                 => [[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,6,7],[2]]               => [[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,6,7],[3]]               => [[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,6,7],[4]]               => [[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,6,7],[5]]               => [[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,5,7],[6]]               => [[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,5,6],[7]]               => [[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,6,7],[2,4]]               => [[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,6,7],[3,4]]               => [[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,6,7],[2,5]]               => [[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6,7],[3,5]]               => [[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6,7],[4,5]]               => [[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,7],[2,6]]               => [[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,7],[3,6]]               => [[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,7],[4,6]]               => [[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,7],[5,6]]               => [[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,6],[2,7]]               => [[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,6],[3,7]]               => [[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,6],[4,7]]               => [[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,6],[5,7]]               => [[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,5],[6,7]]               => [[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,4,5,6,7],[2],[3]]             => [[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,6,7],[2],[4]]             => [[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,6,7],[3],[4]]             => [[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,6,7],[2],[5]]             => [[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6,7],[3],[5]]             => [[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6,7],[4],[5]]             => [[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,7],[2],[6]]             => [[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,7],[3],[6]]             => [[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,7],[4],[6]]             => [[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,7],[5],[6]]             => [[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,6],[2],[7]]             => [[5,1,1,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,6],[3],[7]]             => [[5,1,1,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,6],[4],[7]]             => [[5,1,1,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,6],[5],[7]]             => [[5,1,1,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,5],[6],[7]]             => [[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,7],[2,4,6]]               => [[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,7],[3,4,6]]               => [[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,7],[2,5,6]]               => [[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,7],[3,5,6]]               => [[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,7],[4,5,6]]               => [[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,6],[2,4,7]]               => [[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,6],[3,4,7]]               => [[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,6],[2,5,7]]               => [[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6],[3,5,7]]               => [[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6],[4,5,7]]               => [[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5],[2,6,7]]               => [[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5],[3,6,7]]               => [[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5],[4,6,7]]               => [[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4],[5,6,7]]               => [[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,4,6,7],[2,5],[3]]             => [[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6,7],[2,5],[4]]             => [[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6,7],[3,5],[4]]             => [[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,6,7],[2,4],[5]]             => [[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,6,7],[3,4],[5]]             => [[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5,7],[2,6],[3]]             => [[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,7],[2,6],[4]]             => [[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,7],[3,6],[4]]             => [[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,7],[2,6],[5]]             => [[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,7],[3,6],[5]]             => [[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,7],[4,6],[5]]             => [[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,7],[2,4],[6]]             => [[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,7],[3,4],[6]]             => [[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,7],[2,5],[6]]             => [[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,7],[3,5],[6]]             => [[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,7],[4,5],[6]]             => [[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,5,6],[2,7],[3]]             => [[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,6],[2,7],[4]]             => [[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,6],[3,7],[4]]             => [[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,6],[2,7],[5]]             => [[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6],[3,7],[5]]             => [[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6],[4,7],[5]]             => [[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5],[2,7],[6]]             => [[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5],[3,7],[6]]             => [[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5],[4,7],[6]]             => [[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4],[5,7],[6]]             => [[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,6],[2,4],[7]]             => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,6],[3,4],[7]]             => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,6],[2,5],[7]]             => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6],[3,5],[7]]             => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6],[4,5],[7]]             => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5],[2,6],[7]]             => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5],[3,6],[7]]             => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5],[4,6],[7]]             => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4],[5,6],[7]]             => [[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,5,6,7],[2],[3],[4]]           => [[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,6,7],[2],[3],[5]]           => [[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6,7],[2],[4],[5]]           => [[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6,7],[3],[4],[5]]           => [[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,5,7],[2],[3],[6]]           => [[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,7],[2],[4],[6]]           => [[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,7],[3],[4],[6]]           => [[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,7],[2],[5],[6]]           => [[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,7],[3],[5],[6]]           => [[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,7],[4],[5],[6]]           => [[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,5,6],[2],[3],[7]]           => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,6],[2],[4],[7]]           => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,6],[3],[4],[7]]           => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,6],[2],[5],[7]]           => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6],[3],[5],[7]]           => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6],[4],[5],[7]]           => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5],[2],[6],[7]]           => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5],[3],[6],[7]]           => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5],[4],[6],[7]]           => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4],[5],[6],[7]]           => [[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,4,6],[2,5,7],[3]]             => [[3,3,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6],[2,5,7],[4]]             => [[3,3,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,5,7],[4]]             => [[3,3,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,6],[2,4,7],[5]]             => [[3,3,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,4,7],[5]]             => [[3,3,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2,6,7],[3]]             => [[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2,6,7],[4]]             => [[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,6,7],[4]]             => [[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,6,7],[5]]             => [[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,6,7],[5]]             => [[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,6,7],[5]]             => [[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5],[2,4,7],[6]]             => [[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,4,7],[6]]             => [[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,5,7],[6]]             => [[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,5,7],[6]]             => [[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,5,7],[6]]             => [[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5],[2,4,6],[7]]             => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,4,6],[7]]             => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,5,6],[7]]             => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,5,6],[7]]             => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,5,6],[7]]             => [[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,7],[2,5],[3,6]]             => [[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,7],[2,5],[4,6]]             => [[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3,5],[4,6]]             => [[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,7],[2,4],[5,6]]             => [[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3,4],[5,6]]             => [[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,6],[2,5],[3,7]]             => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6],[2,5],[4,7]]             => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,5],[4,7]]             => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,6],[2,4],[5,7]]             => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,4],[5,7]]             => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2,6],[3,7]]             => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2,6],[4,7]]             => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,6],[4,7]]             => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,6],[5,7]]             => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,6],[5,7]]             => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,6],[5,7]]             => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5],[2,4],[6,7]]             => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,4],[6,7]]             => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,5],[6,7]]             => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,5],[6,7]]             => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,5],[6,7]]             => [[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,5,7],[2,6],[3],[4]]           => [[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,7],[2,6],[3],[5]]           => [[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,7],[2,6],[4],[5]]           => [[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3,6],[4],[5]]           => [[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,7],[2,5],[3],[6]]           => [[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,7],[2,5],[4],[6]]           => [[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3,5],[4],[6]]           => [[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,7],[2,4],[5],[6]]           => [[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3,4],[5],[6]]           => [[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,5,6],[2,7],[3],[4]]           => [[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,6],[2,7],[3],[5]]           => [[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6],[2,7],[4],[5]]           => [[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,7],[4],[5]]           => [[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2,7],[3],[6]]           => [[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2,7],[4],[6]]           => [[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,7],[4],[6]]           => [[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,7],[5],[6]]           => [[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,7],[5],[6]]           => [[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,7],[5],[6]]           => [[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,6],[2,5],[3],[7]]           => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6],[2,5],[4],[7]]           => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,5],[4],[7]]           => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,6],[2,4],[5],[7]]           => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,4],[5],[7]]           => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2,6],[3],[7]]           => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2,6],[4],[7]]           => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,6],[4],[7]]           => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,6],[5],[7]]           => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,6],[5],[7]]           => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,6],[5],[7]]           => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5],[2,4],[6],[7]]           => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,4],[6],[7]]           => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,5],[6],[7]]           => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,5],[6],[7]]           => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,5],[6],[7]]           => [[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,6,7],[2],[3],[4],[5]]         => [[3,1,1,1,1,0,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,5,7],[2],[3],[4],[6]]         => [[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,7],[2],[3],[5],[6]]         => [[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,7],[2],[4],[5],[6]]         => [[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3],[4],[5],[6]]         => [[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,5,6],[2],[3],[4],[7]]         => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,6],[2],[3],[5],[7]]         => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6],[2],[4],[5],[7]]         => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3],[4],[5],[7]]         => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2],[3],[6],[7]]         => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2],[4],[6],[7]]         => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3],[4],[6],[7]]         => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2],[5],[6],[7]]         => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3],[5],[6],[7]]         => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4],[5],[6],[7]]         => [[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,5],[2,6],[3,7],[4]]           => [[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4],[2,6],[3,7],[5]]           => [[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,6],[4,7],[5]]           => [[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,6],[4,7],[5]]           => [[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4],[2,5],[3,7],[6]]           => [[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,5],[4,7],[6]]           => [[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,5],[4,7],[6]]           => [[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3],[2,4],[5,7],[6]]           => [[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2],[3,4],[5,7],[6]]           => [[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4],[2,5],[3,6],[7]]           => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,5],[4,6],[7]]           => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,5],[4,6],[7]]           => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3],[2,4],[5,6],[7]]           => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2],[3,4],[5,6],[7]]           => [[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,6],[2,7],[3],[4],[5]]         => [[2,2,1,1,1,0,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,5],[2,7],[3],[4],[6]]         => [[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4],[2,7],[3],[5],[6]]         => [[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,7],[4],[5],[6]]         => [[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,7],[4],[5],[6]]         => [[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,5],[2,6],[3],[4],[7]]         => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4],[2,6],[3],[5],[7]]         => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,6],[4],[5],[7]]         => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,6],[4],[5],[7]]         => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4],[2,5],[3],[6],[7]]         => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,5],[4],[6],[7]]         => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,5],[4],[6],[7]]         => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3],[2,4],[5],[6],[7]]         => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2],[3,4],[5],[6],[7]]         => [[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,7],[2],[3],[4],[5],[6]]       => [[2,1,1,1,1,1,0],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,6],[2],[3],[4],[5],[7]]       => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,5],[2],[3],[4],[6],[7]]       => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4],[2],[3],[5],[6],[7]]       => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2],[4],[5],[6],[7]]       => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3],[4],[5],[6],[7]]       => [[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1],[2],[3],[4],[5],[6],[7]]     => [[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,2,3,4,5,6,7,8]]               => [[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,6,7,8],[2]]             => [[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,6,7,8],[3]]             => [[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,6,7,8],[4]]             => [[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,6,7,8],[5]]             => [[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,5,7,8],[6]]             => [[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,5,6,8],[7]]             => [[7,1,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,5,6,7],[8]]             => [[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,6,7,8],[2,4]]             => [[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,6,7,8],[3,4]]             => [[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,6,7,8],[2,5]]             => [[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6,7,8],[3,5]]             => [[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6,7,8],[4,5]]             => [[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,7,8],[2,6]]             => [[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,7,8],[3,6]]             => [[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,7,8],[4,6]]             => [[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,7,8],[5,6]]             => [[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,6,8],[2,7]]             => [[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,6,8],[3,7]]             => [[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,6,8],[4,7]]             => [[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,6,8],[5,7]]             => [[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,5,8],[6,7]]             => [[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,6,7],[2,8]]             => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,6,7],[3,8]]             => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,6,7],[4,8]]             => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,6,7],[5,8]]             => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,5,7],[6,8]]             => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,5,6],[7,8]]             => [[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,4,5,6,7,8],[2],[3]]           => [[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,6,7,8],[2],[4]]           => [[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,6,7,8],[3],[4]]           => [[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,6,7,8],[2],[5]]           => [[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6,7,8],[3],[5]]           => [[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6,7,8],[4],[5]]           => [[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,7,8],[2],[6]]           => [[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,7,8],[3],[6]]           => [[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,7,8],[4],[6]]           => [[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,7,8],[5],[6]]           => [[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,6,8],[2],[7]]           => [[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,6,8],[3],[7]]           => [[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,6,8],[4],[7]]           => [[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,6,8],[5],[7]]           => [[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,5,8],[6],[7]]           => [[6,1,1,0,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,6,7],[2],[8]]           => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,6,7],[3],[8]]           => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,6,7],[4],[8]]           => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,6,7],[5],[8]]           => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,5,7],[6],[8]]           => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,5,6],[7],[8]]           => [[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,7,8],[2,4,6]]             => [[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,7,8],[3,4,6]]             => [[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,7,8],[2,5,6]]             => [[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,7,8],[3,5,6]]             => [[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,7,8],[4,5,6]]             => [[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,6,8],[2,4,7]]             => [[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,6,8],[3,4,7]]             => [[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,6,8],[2,5,7]]             => [[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6,8],[3,5,7]]             => [[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6,8],[4,5,7]]             => [[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,8],[2,6,7]]             => [[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,8],[3,6,7]]             => [[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,8],[4,6,7]]             => [[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,8],[5,6,7]]             => [[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,6,7],[2,4,8]]             => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,6,7],[3,4,8]]             => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,6,7],[2,5,8]]             => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6,7],[3,5,8]]             => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6,7],[4,5,8]]             => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,7],[2,6,8]]             => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,7],[3,6,8]]             => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,7],[4,6,8]]             => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,7],[5,6,8]]             => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,6],[2,7,8]]             => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,6],[3,7,8]]             => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,6],[4,7,8]]             => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,6],[5,7,8]]             => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,5],[6,7,8]]             => [[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,4,6,7,8],[2,5],[3]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6,7,8],[2,5],[4]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6,7,8],[3,5],[4]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,6,7,8],[2,4],[5]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,6,7,8],[3,4],[5]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5,7,8],[2,6],[3]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,7,8],[2,6],[4]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,7,8],[3,6],[4]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,7,8],[2,6],[5]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,7,8],[3,6],[5]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,7,8],[4,6],[5]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,7,8],[2,4],[6]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,7,8],[3,4],[6]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,7,8],[2,5],[6]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,7,8],[3,5],[6]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,7,8],[4,5],[6]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,5,6,8],[2,7],[3]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,6,8],[2,7],[4]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,6,8],[3,7],[4]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,6,8],[2,7],[5]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6,8],[3,7],[5]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6,8],[4,7],[5]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,8],[2,7],[6]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,8],[3,7],[6]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,8],[4,7],[6]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,8],[5,7],[6]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,6,8],[2,4],[7]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,6,8],[3,4],[7]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,6,8],[2,5],[7]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6,8],[3,5],[7]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6,8],[4,5],[7]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,8],[2,6],[7]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,8],[3,6],[7]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,8],[4,6],[7]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,8],[5,6],[7]]           => [[5,2,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,4,5,6,7],[2,8],[3]]           => [[5,2,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,6,7],[2,8],[4]]           => [[5,2,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,6,7],[3,8],[4]]           => [[5,2,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,6,7],[2,8],[5]]           => [[5,2,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6,7],[3,8],[5]]           => [[5,2,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6,7],[4,8],[5]]           => [[5,2,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,7],[2,8],[6]]           => [[5,2,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,7],[3,8],[6]]           => [[5,2,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,7],[4,8],[6]]           => [[5,2,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,7],[5,8],[6]]           => [[5,2,1,0,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,6],[2,8],[7]]           => [[5,2,1,0,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,6],[3,8],[7]]           => [[5,2,1,0,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,6],[4,8],[7]]           => [[5,2,1,0,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,6],[5,8],[7]]           => [[5,2,1,0,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,5],[6,8],[7]]           => [[5,2,1,0,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,6,7],[2,4],[8]]           => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,6,7],[3,4],[8]]           => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,6,7],[2,5],[8]]           => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6,7],[3,5],[8]]           => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6,7],[4,5],[8]]           => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,7],[2,6],[8]]           => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,7],[3,6],[8]]           => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,7],[4,6],[8]]           => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,7],[5,6],[8]]           => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,6],[2,7],[8]]           => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,6],[3,7],[8]]           => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,6],[4,7],[8]]           => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,6],[5,7],[8]]           => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,5],[6,7],[8]]           => [[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,5,6,7,8],[2],[3],[4]]         => [[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,6,7,8],[2],[3],[5]]         => [[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6,7,8],[2],[4],[5]]         => [[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6,7,8],[3],[4],[5]]         => [[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,5,7,8],[2],[3],[6]]         => [[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,7,8],[2],[4],[6]]         => [[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,7,8],[3],[4],[6]]         => [[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,7,8],[2],[5],[6]]         => [[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,7,8],[3],[5],[6]]         => [[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,7,8],[4],[5],[6]]         => [[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,5,6,8],[2],[3],[7]]         => [[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,6,8],[2],[4],[7]]         => [[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,6,8],[3],[4],[7]]         => [[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,6,8],[2],[5],[7]]         => [[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6,8],[3],[5],[7]]         => [[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6,8],[4],[5],[7]]         => [[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,8],[2],[6],[7]]         => [[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,8],[3],[6],[7]]         => [[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,8],[4],[6],[7]]         => [[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,8],[5],[6],[7]]         => [[5,1,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,4,5,6,7],[2],[3],[8]]         => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,6,7],[2],[4],[8]]         => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,6,7],[3],[4],[8]]         => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,6,7],[2],[5],[8]]         => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6,7],[3],[5],[8]]         => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6,7],[4],[5],[8]]         => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,7],[2],[6],[8]]         => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,7],[3],[6],[8]]         => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,7],[4],[6],[8]]         => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,7],[5],[6],[8]]         => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,6],[2],[7],[8]]         => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5,6],[3],[7],[8]]         => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5,6],[4],[7],[8]]         => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,6],[5],[7],[8]]         => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,5],[6],[7],[8]]         => [[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,7],[2,4,6,8]]             => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,7],[3,4,6,8]]             => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,7],[2,5,6,8]]             => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,7],[3,5,6,8]]             => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,7],[4,5,6,8]]             => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,6],[2,4,7,8]]             => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,6],[3,4,7,8]]             => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,6],[2,5,7,8]]             => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6],[3,5,7,8]]             => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6],[4,5,7,8]]             => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5],[2,6,7,8]]             => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5],[3,6,7,8]]             => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5],[4,6,7,8]]             => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4],[5,6,7,8]]             => [[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,4,6,8],[2,5,7],[3]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6,8],[2,5,7],[4]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6,8],[3,5,7],[4]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,6,8],[2,4,7],[5]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,6,8],[3,4,7],[5]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5,8],[2,6,7],[3]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,8],[2,6,7],[4]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,8],[3,6,7],[4]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,8],[2,6,7],[5]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,8],[3,6,7],[5]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,8],[4,6,7],[5]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,8],[2,4,7],[6]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,8],[3,4,7],[6]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,8],[2,5,7],[6]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,8],[3,5,7],[6]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,8],[4,5,7],[6]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,8],[2,4,6],[7]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,8],[3,4,6],[7]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,8],[2,5,6],[7]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,8],[3,5,6],[7]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,8],[4,5,6],[7]]           => [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,6,7],[2,5,8],[3]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6,7],[2,5,8],[4]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6,7],[3,5,8],[4]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,6,7],[2,4,8],[5]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,6,7],[3,4,8],[5]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5,7],[2,6,8],[3]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,7],[2,6,8],[4]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,7],[3,6,8],[4]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,7],[2,6,8],[5]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,7],[3,6,8],[5]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,7],[4,6,8],[5]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,7],[2,4,8],[6]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,7],[3,4,8],[6]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,7],[2,5,8],[6]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,7],[3,5,8],[6]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,7],[4,5,8],[6]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,5,6],[2,7,8],[3]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,6],[2,7,8],[4]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,6],[3,7,8],[4]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,6],[2,7,8],[5]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6],[3,7,8],[5]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6],[4,7,8],[5]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5],[2,7,8],[6]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5],[3,7,8],[6]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5],[4,7,8],[6]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4],[5,7,8],[6]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,6],[2,4,8],[7]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,6],[3,4,8],[7]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,6],[2,5,8],[7]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6],[3,5,8],[7]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6],[4,5,8],[7]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5],[2,6,8],[7]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5],[3,6,8],[7]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5],[4,6,8],[7]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4],[5,6,8],[7]]           => [[4,3,1,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,7],[2,4,6],[8]]           => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,7],[3,4,6],[8]]           => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,7],[2,5,6],[8]]           => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,7],[3,5,6],[8]]           => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,7],[4,5,6],[8]]           => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,6],[2,4,7],[8]]           => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,6],[3,4,7],[8]]           => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,6],[2,5,7],[8]]           => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6],[3,5,7],[8]]           => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6],[4,5,7],[8]]           => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5],[2,6,7],[8]]           => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5],[3,6,7],[8]]           => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5],[4,6,7],[8]]           => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4],[5,6,7],[8]]           => [[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,4,7,8],[2,5],[3,6]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,7,8],[2,5],[4,6]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,7,8],[3,5],[4,6]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,7,8],[2,4],[5,6]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,7,8],[3,4],[5,6]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,6,8],[2,5],[3,7]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6,8],[2,5],[4,7]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6,8],[3,5],[4,7]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,6,8],[2,4],[5,7]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,6,8],[3,4],[5,7]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5,8],[2,6],[3,7]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,8],[2,6],[4,7]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,8],[3,6],[4,7]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,8],[2,6],[5,7]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,8],[3,6],[5,7]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,8],[4,6],[5,7]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,8],[2,4],[6,7]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,8],[3,4],[6,7]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,8],[2,5],[6,7]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,8],[3,5],[6,7]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,8],[4,5],[6,7]]           => [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,6,7],[2,5],[3,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6,7],[2,5],[4,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6,7],[3,5],[4,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,6,7],[2,4],[5,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,6,7],[3,4],[5,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5,7],[2,6],[3,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,7],[2,6],[4,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,7],[3,6],[4,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,7],[2,6],[5,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,7],[3,6],[5,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,7],[4,6],[5,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,7],[2,4],[6,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,7],[3,4],[6,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,7],[2,5],[6,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,7],[3,5],[6,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,7],[4,5],[6,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,5,6],[2,7],[3,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,6],[2,7],[4,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,6],[3,7],[4,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,6],[2,7],[5,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6],[3,7],[5,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6],[4,7],[5,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5],[2,7],[6,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5],[3,7],[6,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5],[4,7],[6,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4],[5,7],[6,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,6],[2,4],[7,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,6],[3,4],[7,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,6],[2,5],[7,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6],[3,5],[7,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6],[4,5],[7,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5],[2,6],[7,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5],[3,6],[7,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5],[4,6],[7,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4],[5,6],[7,8]]           => [[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,5,7,8],[2,6],[3],[4]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,7,8],[2,6],[3],[5]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,7,8],[2,6],[4],[5]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,7,8],[3,6],[4],[5]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,7,8],[2,5],[3],[6]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,7,8],[2,5],[4],[6]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,7,8],[3,5],[4],[6]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,7,8],[2,4],[5],[6]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,7,8],[3,4],[5],[6]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,5,6,8],[2,7],[3],[4]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,6,8],[2,7],[3],[5]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6,8],[2,7],[4],[5]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6,8],[3,7],[4],[5]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,5,8],[2,7],[3],[6]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,8],[2,7],[4],[6]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,8],[3,7],[4],[6]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,8],[2,7],[5],[6]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,8],[3,7],[5],[6]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,8],[4,7],[5],[6]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,6,8],[2,5],[3],[7]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6,8],[2,5],[4],[7]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6,8],[3,5],[4],[7]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,6,8],[2,4],[5],[7]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,6,8],[3,4],[5],[7]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5,8],[2,6],[3],[7]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,8],[2,6],[4],[7]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,8],[3,6],[4],[7]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,8],[2,6],[5],[7]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,8],[3,6],[5],[7]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,8],[4,6],[5],[7]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,8],[2,4],[6],[7]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,8],[3,4],[6],[7]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,8],[2,5],[6],[7]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,8],[3,5],[6],[7]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,8],[4,5],[6],[7]]         => [[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,5,6,7],[2,8],[3],[4]]         => [[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,6,7],[2,8],[3],[5]]         => [[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6,7],[2,8],[4],[5]]         => [[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6,7],[3,8],[4],[5]]         => [[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,5,7],[2,8],[3],[6]]         => [[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,7],[2,8],[4],[6]]         => [[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,7],[3,8],[4],[6]]         => [[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,7],[2,8],[5],[6]]         => [[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,7],[3,8],[5],[6]]         => [[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,7],[4,8],[5],[6]]         => [[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,5,6],[2,8],[3],[7]]         => [[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,6],[2,8],[4],[7]]         => [[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,6],[3,8],[4],[7]]         => [[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,6],[2,8],[5],[7]]         => [[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6],[3,8],[5],[7]]         => [[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6],[4,8],[5],[7]]         => [[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5],[2,8],[6],[7]]         => [[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5],[3,8],[6],[7]]         => [[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5],[4,8],[6],[7]]         => [[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4],[5,8],[6],[7]]         => [[4,2,1,1,0,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,4,6,7],[2,5],[3],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6,7],[2,5],[4],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6,7],[3,5],[4],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,6,7],[2,4],[5],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,6,7],[3,4],[5],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5,7],[2,6],[3],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,7],[2,6],[4],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,7],[3,6],[4],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,7],[2,6],[5],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,7],[3,6],[5],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,7],[4,6],[5],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,7],[2,4],[6],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,7],[3,4],[6],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,7],[2,5],[6],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,7],[3,5],[6],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,7],[4,5],[6],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,5,6],[2,7],[3],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,6],[2,7],[4],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,6],[3,7],[4],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,6],[2,7],[5],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6],[3,7],[5],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6],[4,7],[5],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5],[2,7],[6],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5],[3,7],[6],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5],[4,7],[6],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4],[5,7],[6],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,6],[2,4],[7],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,6],[3,4],[7],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4,6],[2,5],[7],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6],[3,5],[7],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6],[4,5],[7],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5],[2,6],[7],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5],[3,6],[7],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5],[4,6],[7],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4],[5,6],[7],[8]]         => [[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,6,7,8],[2],[3],[4],[5]]       => [[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,5,7,8],[2],[3],[4],[6]]       => [[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,7,8],[2],[3],[5],[6]]       => [[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,7,8],[2],[4],[5],[6]]       => [[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,7,8],[3],[4],[5],[6]]       => [[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,5,6,8],[2],[3],[4],[7]]       => [[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,6,8],[2],[3],[5],[7]]       => [[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6,8],[2],[4],[5],[7]]       => [[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6,8],[3],[4],[5],[7]]       => [[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,5,8],[2],[3],[6],[7]]       => [[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,8],[2],[4],[6],[7]]       => [[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,8],[3],[4],[6],[7]]       => [[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,8],[2],[5],[6],[7]]       => [[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,8],[3],[5],[6],[7]]       => [[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,8],[4],[5],[6],[7]]       => [[4,1,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,5,6,7],[2],[3],[4],[8]]       => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,6,7],[2],[3],[5],[8]]       => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6,7],[2],[4],[5],[8]]       => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6,7],[3],[4],[5],[8]]       => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,5,7],[2],[3],[6],[8]]       => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,7],[2],[4],[6],[8]]       => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,7],[3],[4],[6],[8]]       => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,7],[2],[5],[6],[8]]       => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,7],[3],[5],[6],[8]]       => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,7],[4],[5],[6],[8]]       => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,5,6],[2],[3],[7],[8]]       => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5,6],[2],[4],[7],[8]]       => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5,6],[3],[4],[7],[8]]       => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,6],[2],[5],[7],[8]]       => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,6],[3],[5],[7],[8]]       => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6],[4],[5],[7],[8]]       => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5],[2],[6],[7],[8]]       => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5],[3],[6],[7],[8]]       => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,5],[4],[6],[7],[8]]       => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4],[5],[6],[7],[8]]       => [[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,4,7],[2,5,8],[3,6]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,7],[2,5,8],[4,6]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3,5,8],[4,6]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,7],[2,4,8],[5,6]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3,4,8],[5,6]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,6],[2,5,8],[3,7]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6],[2,5,8],[4,7]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,5,8],[4,7]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,6],[2,4,8],[5,7]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,4,8],[5,7]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2,6,8],[3,7]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2,6,8],[4,7]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,6,8],[4,7]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,6,8],[5,7]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,6,8],[5,7]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,6,8],[5,7]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5],[2,4,8],[6,7]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,4,8],[6,7]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,5,8],[6,7]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,5,8],[6,7]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,5,8],[6,7]]           => [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,6],[2,5,7],[3,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6],[2,5,7],[4,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,5,7],[4,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,6],[2,4,7],[5,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,4,7],[5,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2,6,7],[3,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2,6,7],[4,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,6,7],[4,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,6,7],[5,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,6,7],[5,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,6,7],[5,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5],[2,4,7],[6,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,4,7],[6,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,5,7],[6,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,5,7],[6,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,5,7],[6,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5],[2,4,6],[7,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,4,6],[7,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,5,6],[7,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,5,6],[7,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,5,6],[7,8]]           => [[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,5,7],[2,6,8],[3],[4]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,7],[2,6,8],[3],[5]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,7],[2,6,8],[4],[5]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3,6,8],[4],[5]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,7],[2,5,8],[3],[6]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,7],[2,5,8],[4],[6]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3,5,8],[4],[6]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,7],[2,4,8],[5],[6]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3,4,8],[5],[6]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,5,6],[2,7,8],[3],[4]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,6],[2,7,8],[3],[5]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6],[2,7,8],[4],[5]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,7,8],[4],[5]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2,7,8],[3],[6]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2,7,8],[4],[6]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,7,8],[4],[6]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,7,8],[5],[6]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,7,8],[5],[6]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,7,8],[5],[6]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,6],[2,5,8],[3],[7]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6],[2,5,8],[4],[7]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,5,8],[4],[7]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,6],[2,4,8],[5],[7]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,4,8],[5],[7]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2,6,8],[3],[7]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2,6,8],[4],[7]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,6,8],[4],[7]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,6,8],[5],[7]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,6,8],[5],[7]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,6,8],[5],[7]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5],[2,4,8],[6],[7]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,4,8],[6],[7]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,5,8],[6],[7]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,5,8],[6],[7]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,5,8],[6],[7]]         => [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,6],[2,5,7],[3],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6],[2,5,7],[4],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,5,7],[4],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,6],[2,4,7],[5],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,4,7],[5],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2,6,7],[3],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2,6,7],[4],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,6,7],[4],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,6,7],[5],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,6,7],[5],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,6,7],[5],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5],[2,4,7],[6],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,4,7],[6],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,5,7],[6],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,5,7],[6],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,5,7],[6],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5],[2,4,6],[7],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,4,6],[7],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,5,6],[7],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,5,6],[7],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,5,6],[7],[8]]         => [[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,5,8],[2,6],[3,7],[4]]         => [[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,8],[2,6],[3,7],[5]]         => [[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,8],[2,6],[4,7],[5]]         => [[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,8],[3,6],[4,7],[5]]         => [[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,8],[2,5],[3,7],[6]]         => [[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,8],[2,5],[4,7],[6]]         => [[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,8],[3,5],[4,7],[6]]         => [[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,8],[2,4],[5,7],[6]]         => [[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,8],[3,4],[5,7],[6]]         => [[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,8],[2,5],[3,6],[7]]         => [[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,8],[2,5],[4,6],[7]]         => [[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,8],[3,5],[4,6],[7]]         => [[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,8],[2,4],[5,6],[7]]         => [[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,8],[3,4],[5,6],[7]]         => [[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,5,7],[2,6],[3,8],[4]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,7],[2,6],[3,8],[5]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,7],[2,6],[4,8],[5]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3,6],[4,8],[5]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,7],[2,5],[3,8],[6]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,7],[2,5],[4,8],[6]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3,5],[4,8],[6]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,7],[2,4],[5,8],[6]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3,4],[5,8],[6]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,5,6],[2,7],[3,8],[4]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,6],[2,7],[3,8],[5]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6],[2,7],[4,8],[5]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,7],[4,8],[5]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2,7],[3,8],[6]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2,7],[4,8],[6]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,7],[4,8],[6]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,7],[5,8],[6]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,7],[5,8],[6]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,7],[5,8],[6]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,6],[2,5],[3,8],[7]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6],[2,5],[4,8],[7]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,5],[4,8],[7]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,6],[2,4],[5,8],[7]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,4],[5,8],[7]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2,6],[3,8],[7]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2,6],[4,8],[7]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,6],[4,8],[7]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,6],[5,8],[7]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,6],[5,8],[7]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,6],[5,8],[7]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5],[2,4],[6,8],[7]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,4],[6,8],[7]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,5],[6,8],[7]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,5],[6,8],[7]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,5],[6,8],[7]]         => [[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,7],[2,5],[3,6],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,7],[2,5],[4,6],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3,5],[4,6],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,7],[2,4],[5,6],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3,4],[5,6],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,6],[2,5],[3,7],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6],[2,5],[4,7],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,5],[4,7],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,6],[2,4],[5,7],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,4],[5,7],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2,6],[3,7],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2,6],[4,7],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,6],[4,7],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,6],[5,7],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,6],[5,7],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,6],[5,7],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5],[2,4],[6,7],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,4],[6,7],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,5],[6,7],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,5],[6,7],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,5],[6,7],[8]]         => [[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,6,8],[2,7],[3],[4],[5]]       => [[3,2,1,1,1,0,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,5,8],[2,7],[3],[4],[6]]       => [[3,2,1,1,1,0,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,8],[2,7],[3],[5],[6]]       => [[3,2,1,1,1,0,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,8],[2,7],[4],[5],[6]]       => [[3,2,1,1,1,0,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,8],[3,7],[4],[5],[6]]       => [[3,2,1,1,1,0,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,5,8],[2,6],[3],[4],[7]]       => [[3,2,1,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,8],[2,6],[3],[5],[7]]       => [[3,2,1,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,8],[2,6],[4],[5],[7]]       => [[3,2,1,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,8],[3,6],[4],[5],[7]]       => [[3,2,1,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,8],[2,5],[3],[6],[7]]       => [[3,2,1,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,8],[2,5],[4],[6],[7]]       => [[3,2,1,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,8],[3,5],[4],[6],[7]]       => [[3,2,1,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,8],[2,4],[5],[6],[7]]       => [[3,2,1,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,8],[3,4],[5],[6],[7]]       => [[3,2,1,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,6,7],[2,8],[3],[4],[5]]       => [[3,2,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,5,7],[2,8],[3],[4],[6]]       => [[3,2,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,7],[2,8],[3],[5],[6]]       => [[3,2,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,7],[2,8],[4],[5],[6]]       => [[3,2,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3,8],[4],[5],[6]]       => [[3,2,1,1,1,0,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,5,6],[2,8],[3],[4],[7]]       => [[3,2,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,6],[2,8],[3],[5],[7]]       => [[3,2,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6],[2,8],[4],[5],[7]]       => [[3,2,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,8],[4],[5],[7]]       => [[3,2,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2,8],[3],[6],[7]]       => [[3,2,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2,8],[4],[6],[7]]       => [[3,2,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,8],[4],[6],[7]]       => [[3,2,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,8],[5],[6],[7]]       => [[3,2,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,8],[5],[6],[7]]       => [[3,2,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,8],[5],[6],[7]]       => [[3,2,1,1,1,0,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,5,7],[2,6],[3],[4],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,7],[2,6],[3],[5],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,7],[2,6],[4],[5],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3,6],[4],[5],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,7],[2,5],[3],[6],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,7],[2,5],[4],[6],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3,5],[4],[6],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,7],[2,4],[5],[6],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3,4],[5],[6],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,5,6],[2,7],[3],[4],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,6],[2,7],[3],[5],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6],[2,7],[4],[5],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,7],[4],[5],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2,7],[3],[6],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2,7],[4],[6],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,7],[4],[6],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,7],[5],[6],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,7],[5],[6],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,7],[5],[6],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,6],[2,5],[3],[7],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6],[2,5],[4],[7],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,5],[4],[7],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,6],[2,4],[5],[7],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3,4],[5],[7],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2,6],[3],[7],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2,6],[4],[7],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,6],[4],[7],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,6],[5],[7],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,6],[5],[7],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,6],[5],[7],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5],[2,4],[6],[7],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,4],[6],[7],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2,5],[6],[7],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,5],[6],[7],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,5],[6],[7],[8]]       => [[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,7,8],[2],[3],[4],[5],[6]]     => [[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,6,8],[2],[3],[4],[5],[7]]     => [[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,5,8],[2],[3],[4],[6],[7]]     => [[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,8],[2],[3],[5],[6],[7]]     => [[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,8],[2],[4],[5],[6],[7]]     => [[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,8],[3],[4],[5],[6],[7]]     => [[3,1,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,6,7],[2],[3],[4],[5],[8]]     => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,5,7],[2],[3],[4],[6],[8]]     => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,7],[2],[3],[5],[6],[8]]     => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,7],[2],[4],[5],[6],[8]]     => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,7],[3],[4],[5],[6],[8]]     => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,5,6],[2],[3],[4],[7],[8]]     => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4,6],[2],[3],[5],[7],[8]]     => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,6],[2],[4],[5],[7],[8]]     => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,6],[3],[4],[5],[7],[8]]     => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2],[3],[6],[7],[8]]     => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2],[4],[6],[7],[8]]     => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3],[4],[6],[7],[8]]     => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2],[5],[6],[7],[8]]     => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3],[5],[6],[7],[8]]     => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4],[5],[6],[7],[8]]     => [[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,5],[2,6],[3,7],[4,8]]         => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4],[2,6],[3,7],[5,8]]         => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,6],[4,7],[5,8]]         => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,6],[4,7],[5,8]]         => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4],[2,5],[3,7],[6,8]]         => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,5],[4,7],[6,8]]         => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,5],[4,7],[6,8]]         => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3],[2,4],[5,7],[6,8]]         => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2],[3,4],[5,7],[6,8]]         => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4],[2,5],[3,6],[7,8]]         => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,5],[4,6],[7,8]]         => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,5],[4,6],[7,8]]         => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3],[2,4],[5,6],[7,8]]         => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2],[3,4],[5,6],[7,8]]         => [[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,6],[2,7],[3,8],[4],[5]]       => [[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,5],[2,7],[3,8],[4],[6]]       => [[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4],[2,7],[3,8],[5],[6]]       => [[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,7],[4,8],[5],[6]]       => [[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,7],[4,8],[5],[6]]       => [[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,5],[2,6],[3,8],[4],[7]]       => [[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4],[2,6],[3,8],[5],[7]]       => [[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,6],[4,8],[5],[7]]       => [[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,6],[4,8],[5],[7]]       => [[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4],[2,5],[3,8],[6],[7]]       => [[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,5],[4,8],[6],[7]]       => [[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,5],[4,8],[6],[7]]       => [[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3],[2,4],[5,8],[6],[7]]       => [[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2],[3,4],[5,8],[6],[7]]       => [[2,2,2,1,1,0,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,5],[2,6],[3,7],[4],[8]]       => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4],[2,6],[3,7],[5],[8]]       => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,6],[4,7],[5],[8]]       => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,6],[4,7],[5],[8]]       => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4],[2,5],[3,7],[6],[8]]       => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,5],[4,7],[6],[8]]       => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,5],[4,7],[6],[8]]       => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3],[2,4],[5,7],[6],[8]]       => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2],[3,4],[5,7],[6],[8]]       => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4],[2,5],[3,6],[7],[8]]       => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,5],[4,6],[7],[8]]       => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,5],[4,6],[7],[8]]       => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3],[2,4],[5,6],[7],[8]]       => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2],[3,4],[5,6],[7],[8]]       => [[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,7],[2,8],[3],[4],[5],[6]]     => [[2,2,1,1,1,1,0,0],[2,1,1,1,1,1,0],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,6],[2,8],[3],[4],[5],[7]]     => [[2,2,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,5],[2,8],[3],[4],[6],[7]]     => [[2,2,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4],[2,8],[3],[5],[6],[7]]     => [[2,2,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,8],[4],[5],[6],[7]]     => [[2,2,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,8],[4],[5],[6],[7]]     => [[2,2,1,1,1,1,0,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,6],[2,7],[3],[4],[5],[8]]     => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,5],[2,7],[3],[4],[6],[8]]     => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4],[2,7],[3],[5],[6],[8]]     => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,7],[4],[5],[6],[8]]     => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,7],[4],[5],[6],[8]]     => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,5],[2,6],[3],[4],[7],[8]]     => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4],[2,6],[3],[5],[7],[8]]     => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,6],[4],[5],[7],[8]]     => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,6],[4],[5],[7],[8]]     => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4],[2,5],[3],[6],[7],[8]]     => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,5],[4],[6],[7],[8]]     => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3,5],[4],[6],[7],[8]]     => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3],[2,4],[5],[6],[7],[8]]     => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2],[3,4],[5],[6],[7],[8]]     => [[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,8],[2],[3],[4],[5],[6],[7]]   => [[2,1,1,1,1,1,1,0],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,7],[2],[3],[4],[5],[6],[8]]   => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,6],[2],[3],[4],[5],[7],[8]]   => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,5],[2],[3],[4],[6],[7],[8]]   => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4],[2],[3],[5],[6],[7],[8]]   => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2],[4],[5],[6],[7],[8]]   => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3],[4],[5],[6],[7],[8]]   => [[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1],[2],[3],[4],[5],[6],[7],[8]] => [[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1],[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,3,5,7,9],[2,4,6,8,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3,5,7,8],[2,4,6,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3,5,6,9],[2,4,7,8,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3,5,6,8],[2,4,7,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3,5,6,7],[2,4,8,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,7,9],[2,5,6,8,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,7,8],[2,5,6,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,6,9],[2,5,7,8,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,6,8],[2,5,7,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,6,7],[2,5,8,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,5,9],[2,6,7,8,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,5,8],[2,6,7,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,5,7],[2,6,8,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,5,6],[2,7,8,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,7,9],[3,4,6,8,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,2,5,7,8],[3,4,6,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,2,5,6,9],[3,4,7,8,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,2,5,6,8],[3,4,7,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,2,5,6,7],[3,4,8,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,2,4,7,9],[3,5,6,8,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,4,7,8],[3,5,6,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,4,6,9],[3,5,7,8,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,4,6,8],[3,5,7,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,4,6,7],[3,5,8,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,4,5,9],[3,6,7,8,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,4,5,8],[3,6,7,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,4,5,7],[3,6,8,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,4,5,6],[3,7,8,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,7,9],[4,5,6,8,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,7,8],[4,5,6,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,6,9],[4,5,7,8,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,6,8],[4,5,7,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,6,7],[4,5,8,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,5,9],[4,6,7,8,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,5,8],[4,6,7,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,5,7],[4,6,8,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,5,6],[4,7,8,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,9],[5,6,7,8,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,8],[5,6,7,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,7],[5,6,8,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,6],[5,7,8,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,5],[6,7,8,9,10]]        => [[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,7,9,11],[2,4,6,8,10,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3,5,7,9,10],[2,4,6,8,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3,5,7,8,11],[2,4,6,9,10,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3,5,7,8,10],[2,4,6,9,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3,5,7,8,9],[2,4,6,10,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3,5,6,9,11],[2,4,7,8,10,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3,5,6,9,10],[2,4,7,8,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3,5,6,8,11],[2,4,7,9,10,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3,5,6,8,10],[2,4,7,9,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3,5,6,8,9],[2,4,7,10,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3,5,6,7,11],[2,4,8,9,10,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3,5,6,7,10],[2,4,8,9,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3,5,6,7,9],[2,4,8,10,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3,5,6,7,8],[2,4,9,10,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,7,9,11],[2,5,6,8,10,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,7,9,10],[2,5,6,8,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,7,8,11],[2,5,6,9,10,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,7,8,10],[2,5,6,9,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,7,8,9],[2,5,6,10,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,6,9,11],[2,5,7,8,10,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,6,9,10],[2,5,7,8,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,6,8,11],[2,5,7,9,10,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,6,8,10],[2,5,7,9,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,6,8,9],[2,5,7,10,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,6,7,11],[2,5,8,9,10,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,6,7,10],[2,5,8,9,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,6,7,9],[2,5,8,10,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,6,7,8],[2,5,9,10,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,5,9,11],[2,6,7,8,10,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,5,9,10],[2,6,7,8,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,5,8,11],[2,6,7,9,10,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,5,8,10],[2,6,7,9,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,5,8,9],[2,6,7,10,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,5,7,11],[2,6,8,9,10,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,5,7,10],[2,6,8,9,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,5,7,9],[2,6,8,10,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,5,7,8],[2,6,9,10,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,5,6,11],[2,7,8,9,10,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,5,6,10],[2,7,8,9,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,5,6,9],[2,7,8,10,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,5,6,8],[2,7,9,10,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4,5,6,7],[2,8,9,10,11,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,5,7,9,11],[3,4,6,8,10,12]]  => [[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]

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Created: Jan 26, 2020 at 12:32 by FindStatCrew

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Last Updated: Jan 26, 2020 at 12:32 by Martin Rubey