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Map identifier: Mp00258

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Map name: Standard tableau associated to a set partition

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Domain: Set partitions

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Codomain: Standard tableaux

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Description: Sends a set partition to the associated standard tableau.

The $j$th column of the standard tableau associated to a set partition is the set of $j$th smallest elements of its blocks arranged in increassing order.

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References: [1]   Prasad, A., Ram, S. Set partitions, tableaux, and subspace profiles under regular split semisimple matrices [[arXiv:2112.00479]]

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Code:

def mapping(x):
    """
    Return the standard tableau associated to a set partition.
    
    EXAMPLE::

    sage: mapping([[1, 2], [3, 6, 7], [4, 5]])
    [[1, 2, 7], [3, 5], [4, 6]]
    """
    A = [sorted(a) for a in x]
    m = max(len(a) for a in A)
    if m==1:
        return Tableau(sorted(a for a in A))
    else:
        last_row = sorted(a[-1] for a in A if len(a)==m)
        l = len(last_row)
        AA = [a[:m-1] for a in A]
        TT = mapping(AA)
        T = []
        for i,r in enumerate(TT):
            if i<l:
                r = r + (last_row[i],)
            T.append(r)
    return Tableau(T)

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

{{1}}                         => [[1]]
{{1,2}}                       => [[1,2]]
{{1},{2}}                     => [[1],[2]]
{{1,2,3}}                     => [[1,2,3]]
{{1,2},{3}}                   => [[1,2],[3]]
{{1,3},{2}}                   => [[1,3],[2]]
{{1},{2,3}}                   => [[1,3],[2]]
{{1},{2},{3}}                 => [[1],[2],[3]]
{{1,2,3,4}}                   => [[1,2,3,4]]
{{1,2,3},{4}}                 => [[1,2,3],[4]]
{{1,2,4},{3}}                 => [[1,2,4],[3]]
{{1,2},{3,4}}                 => [[1,2],[3,4]]
{{1,2},{3},{4}}               => [[1,2],[3],[4]]
{{1,3,4},{2}}                 => [[1,3,4],[2]]
{{1,3},{2,4}}                 => [[1,3],[2,4]]
{{1,3},{2},{4}}               => [[1,3],[2],[4]]
{{1,4},{2,3}}                 => [[1,3],[2,4]]
{{1},{2,3,4}}                 => [[1,3,4],[2]]
{{1},{2,3},{4}}               => [[1,3],[2],[4]]
{{1,4},{2},{3}}               => [[1,4],[2],[3]]
{{1},{2,4},{3}}               => [[1,4],[2],[3]]
{{1},{2},{3,4}}               => [[1,4],[2],[3]]
{{1},{2},{3},{4}}             => [[1],[2],[3],[4]]
{{1,2,3,4,5}}                 => [[1,2,3,4,5]]
{{1,2,3,4},{5}}               => [[1,2,3,4],[5]]
{{1,2,3,5},{4}}               => [[1,2,3,5],[4]]
{{1,2,3},{4,5}}               => [[1,2,3],[4,5]]
{{1,2,3},{4},{5}}             => [[1,2,3],[4],[5]]
{{1,2,4,5},{3}}               => [[1,2,4,5],[3]]
{{1,2,4},{3,5}}               => [[1,2,4],[3,5]]
{{1,2,4},{3},{5}}             => [[1,2,4],[3],[5]]
{{1,2,5},{3,4}}               => [[1,2,5],[3,4]]
{{1,2},{3,4,5}}               => [[1,2,5],[3,4]]
{{1,2},{3,4},{5}}             => [[1,2],[3,4],[5]]
{{1,2,5},{3},{4}}             => [[1,2,5],[3],[4]]
{{1,2},{3,5},{4}}             => [[1,2],[3,5],[4]]
{{1,2},{3},{4,5}}             => [[1,2],[3,5],[4]]
{{1,2},{3},{4},{5}}           => [[1,2],[3],[4],[5]]
{{1,3,4,5},{2}}               => [[1,3,4,5],[2]]
{{1,3,4},{2,5}}               => [[1,3,4],[2,5]]
{{1,3,4},{2},{5}}             => [[1,3,4],[2],[5]]
{{1,3,5},{2,4}}               => [[1,3,5],[2,4]]
{{1,3},{2,4,5}}               => [[1,3,5],[2,4]]
{{1,3},{2,4},{5}}             => [[1,3],[2,4],[5]]
{{1,3,5},{2},{4}}             => [[1,3,5],[2],[4]]
{{1,3},{2,5},{4}}             => [[1,3],[2,5],[4]]
{{1,3},{2},{4,5}}             => [[1,3],[2,5],[4]]
{{1,3},{2},{4},{5}}           => [[1,3],[2],[4],[5]]
{{1,4,5},{2,3}}               => [[1,3,5],[2,4]]
{{1,4},{2,3,5}}               => [[1,3,5],[2,4]]
{{1,4},{2,3},{5}}             => [[1,3],[2,4],[5]]
{{1,5},{2,3,4}}               => [[1,3,4],[2,5]]
{{1},{2,3,4,5}}               => [[1,3,4,5],[2]]
{{1},{2,3,4},{5}}             => [[1,3,4],[2],[5]]
{{1,5},{2,3},{4}}             => [[1,3],[2,5],[4]]
{{1},{2,3,5},{4}}             => [[1,3,5],[2],[4]]
{{1},{2,3},{4,5}}             => [[1,3],[2,5],[4]]
{{1},{2,3},{4},{5}}           => [[1,3],[2],[4],[5]]
{{1,4,5},{2},{3}}             => [[1,4,5],[2],[3]]
{{1,4},{2,5},{3}}             => [[1,4],[2,5],[3]]
{{1,4},{2},{3,5}}             => [[1,4],[2,5],[3]]
{{1,4},{2},{3},{5}}           => [[1,4],[2],[3],[5]]
{{1,5},{2,4},{3}}             => [[1,4],[2,5],[3]]
{{1},{2,4,5},{3}}             => [[1,4,5],[2],[3]]
{{1},{2,4},{3,5}}             => [[1,4],[2,5],[3]]
{{1},{2,4},{3},{5}}           => [[1,4],[2],[3],[5]]
{{1,5},{2},{3,4}}             => [[1,4],[2,5],[3]]
{{1},{2,5},{3,4}}             => [[1,4],[2,5],[3]]
{{1},{2},{3,4,5}}             => [[1,4,5],[2],[3]]
{{1},{2},{3,4},{5}}           => [[1,4],[2],[3],[5]]
{{1,5},{2},{3},{4}}           => [[1,5],[2],[3],[4]]
{{1},{2,5},{3},{4}}           => [[1,5],[2],[3],[4]]
{{1},{2},{3,5},{4}}           => [[1,5],[2],[3],[4]]
{{1},{2},{3},{4,5}}           => [[1,5],[2],[3],[4]]
{{1},{2},{3},{4},{5}}         => [[1],[2],[3],[4],[5]]
{{1,2,3,4,5,6}}               => [[1,2,3,4,5,6]]
{{1,2,3,4,5},{6}}             => [[1,2,3,4,5],[6]]
{{1,2,3,4,6},{5}}             => [[1,2,3,4,6],[5]]
{{1,2,3,4},{5,6}}             => [[1,2,3,4],[5,6]]
{{1,2,3,4},{5},{6}}           => [[1,2,3,4],[5],[6]]
{{1,2,3,5,6},{4}}             => [[1,2,3,5,6],[4]]
{{1,2,3,5},{4,6}}             => [[1,2,3,5],[4,6]]
{{1,2,3,5},{4},{6}}           => [[1,2,3,5],[4],[6]]
{{1,2,3,6},{4,5}}             => [[1,2,3,6],[4,5]]
{{1,2,3},{4,5,6}}             => [[1,2,3],[4,5,6]]
{{1,2,3},{4,5},{6}}           => [[1,2,3],[4,5],[6]]
{{1,2,3,6},{4},{5}}           => [[1,2,3,6],[4],[5]]
{{1,2,3},{4,6},{5}}           => [[1,2,3],[4,6],[5]]
{{1,2,3},{4},{5,6}}           => [[1,2,3],[4,6],[5]]
{{1,2,3},{4},{5},{6}}         => [[1,2,3],[4],[5],[6]]
{{1,2,4,5,6},{3}}             => [[1,2,4,5,6],[3]]
{{1,2,4,5},{3,6}}             => [[1,2,4,5],[3,6]]
{{1,2,4,5},{3},{6}}           => [[1,2,4,5],[3],[6]]
{{1,2,4,6},{3,5}}             => [[1,2,4,6],[3,5]]
{{1,2,4},{3,5,6}}             => [[1,2,4],[3,5,6]]
{{1,2,4},{3,5},{6}}           => [[1,2,4],[3,5],[6]]
{{1,2,4,6},{3},{5}}           => [[1,2,4,6],[3],[5]]
{{1,2,4},{3,6},{5}}           => [[1,2,4],[3,6],[5]]
{{1,2,4},{3},{5,6}}           => [[1,2,4],[3,6],[5]]
{{1,2,4},{3},{5},{6}}         => [[1,2,4],[3],[5],[6]]
{{1,2,5,6},{3,4}}             => [[1,2,5,6],[3,4]]
{{1,2,5},{3,4,6}}             => [[1,2,5],[3,4,6]]
{{1,2,5},{3,4},{6}}           => [[1,2,5],[3,4],[6]]
{{1,2,6},{3,4,5}}             => [[1,2,5],[3,4,6]]
{{1,2},{3,4,5,6}}             => [[1,2,5,6],[3,4]]
{{1,2},{3,4,5},{6}}           => [[1,2,5],[3,4],[6]]
{{1,2,6},{3,4},{5}}           => [[1,2,6],[3,4],[5]]
{{1,2},{3,4,6},{5}}           => [[1,2,6],[3,4],[5]]
{{1,2},{3,4},{5,6}}           => [[1,2],[3,4],[5,6]]
{{1,2},{3,4},{5},{6}}         => [[1,2],[3,4],[5],[6]]
{{1,2,5,6},{3},{4}}           => [[1,2,5,6],[3],[4]]
{{1,2,5},{3,6},{4}}           => [[1,2,5],[3,6],[4]]
{{1,2,5},{3},{4,6}}           => [[1,2,5],[3,6],[4]]
{{1,2,5},{3},{4},{6}}         => [[1,2,5],[3],[4],[6]]
{{1,2,6},{3,5},{4}}           => [[1,2,6],[3,5],[4]]
{{1,2},{3,5,6},{4}}           => [[1,2,6],[3,5],[4]]
{{1,2},{3,5},{4,6}}           => [[1,2],[3,5],[4,6]]
{{1,2},{3,5},{4},{6}}         => [[1,2],[3,5],[4],[6]]
{{1,2,6},{3},{4,5}}           => [[1,2,6],[3,5],[4]]
{{1,2},{3,6},{4,5}}           => [[1,2],[3,5],[4,6]]
{{1,2},{3},{4,5,6}}           => [[1,2,6],[3,5],[4]]
{{1,2},{3},{4,5},{6}}         => [[1,2],[3,5],[4],[6]]
{{1,2,6},{3},{4},{5}}         => [[1,2,6],[3],[4],[5]]
{{1,2},{3,6},{4},{5}}         => [[1,2],[3,6],[4],[5]]
{{1,2},{3},{4,6},{5}}         => [[1,2],[3,6],[4],[5]]
{{1,2},{3},{4},{5,6}}         => [[1,2],[3,6],[4],[5]]
{{1,2},{3},{4},{5},{6}}       => [[1,2],[3],[4],[5],[6]]
{{1,3,4,5,6},{2}}             => [[1,3,4,5,6],[2]]
{{1,3,4,5},{2,6}}             => [[1,3,4,5],[2,6]]
{{1,3,4,5},{2},{6}}           => [[1,3,4,5],[2],[6]]
{{1,3,4,6},{2,5}}             => [[1,3,4,6],[2,5]]
{{1,3,4},{2,5,6}}             => [[1,3,4],[2,5,6]]
{{1,3,4},{2,5},{6}}           => [[1,3,4],[2,5],[6]]
{{1,3,4,6},{2},{5}}           => [[1,3,4,6],[2],[5]]
{{1,3,4},{2,6},{5}}           => [[1,3,4],[2,6],[5]]
{{1,3,4},{2},{5,6}}           => [[1,3,4],[2,6],[5]]
{{1,3,4},{2},{5},{6}}         => [[1,3,4],[2],[5],[6]]
{{1,3,5,6},{2,4}}             => [[1,3,5,6],[2,4]]
{{1,3,5},{2,4,6}}             => [[1,3,5],[2,4,6]]
{{1,3,5},{2,4},{6}}           => [[1,3,5],[2,4],[6]]
{{1,3,6},{2,4,5}}             => [[1,3,5],[2,4,6]]
{{1,3},{2,4,5,6}}             => [[1,3,5,6],[2,4]]
{{1,3},{2,4,5},{6}}           => [[1,3,5],[2,4],[6]]
{{1,3,6},{2,4},{5}}           => [[1,3,6],[2,4],[5]]
{{1,3},{2,4,6},{5}}           => [[1,3,6],[2,4],[5]]
{{1,3},{2,4},{5,6}}           => [[1,3],[2,4],[5,6]]
{{1,3},{2,4},{5},{6}}         => [[1,3],[2,4],[5],[6]]
{{1,3,5,6},{2},{4}}           => [[1,3,5,6],[2],[4]]
{{1,3,5},{2,6},{4}}           => [[1,3,5],[2,6],[4]]
{{1,3,5},{2},{4,6}}           => [[1,3,5],[2,6],[4]]
{{1,3,5},{2},{4},{6}}         => [[1,3,5],[2],[4],[6]]
{{1,3,6},{2,5},{4}}           => [[1,3,6],[2,5],[4]]
{{1,3},{2,5,6},{4}}           => [[1,3,6],[2,5],[4]]
{{1,3},{2,5},{4,6}}           => [[1,3],[2,5],[4,6]]
{{1,3},{2,5},{4},{6}}         => [[1,3],[2,5],[4],[6]]
{{1,3,6},{2},{4,5}}           => [[1,3,6],[2,5],[4]]
{{1,3},{2,6},{4,5}}           => [[1,3],[2,5],[4,6]]
{{1,3},{2},{4,5,6}}           => [[1,3,6],[2,5],[4]]
{{1,3},{2},{4,5},{6}}         => [[1,3],[2,5],[4],[6]]
{{1,3,6},{2},{4},{5}}         => [[1,3,6],[2],[4],[5]]
{{1,3},{2,6},{4},{5}}         => [[1,3],[2,6],[4],[5]]
{{1,3},{2},{4,6},{5}}         => [[1,3],[2,6],[4],[5]]
{{1,3},{2},{4},{5,6}}         => [[1,3],[2,6],[4],[5]]
{{1,3},{2},{4},{5},{6}}       => [[1,3],[2],[4],[5],[6]]
{{1,4,5,6},{2,3}}             => [[1,3,5,6],[2,4]]
{{1,4,5},{2,3,6}}             => [[1,3,5],[2,4,6]]
{{1,4,5},{2,3},{6}}           => [[1,3,5],[2,4],[6]]
{{1,4,6},{2,3,5}}             => [[1,3,5],[2,4,6]]
{{1,4},{2,3,5,6}}             => [[1,3,5,6],[2,4]]
{{1,4},{2,3,5},{6}}           => [[1,3,5],[2,4],[6]]
{{1,4,6},{2,3},{5}}           => [[1,3,6],[2,4],[5]]
{{1,4},{2,3,6},{5}}           => [[1,3,6],[2,4],[5]]
{{1,4},{2,3},{5,6}}           => [[1,3],[2,4],[5,6]]
{{1,4},{2,3},{5},{6}}         => [[1,3],[2,4],[5],[6]]
{{1,5,6},{2,3,4}}             => [[1,3,4],[2,5,6]]
{{1,5},{2,3,4,6}}             => [[1,3,4,6],[2,5]]
{{1,5},{2,3,4},{6}}           => [[1,3,4],[2,5],[6]]
{{1,6},{2,3,4,5}}             => [[1,3,4,5],[2,6]]
{{1},{2,3,4,5,6}}             => [[1,3,4,5,6],[2]]
{{1},{2,3,4,5},{6}}           => [[1,3,4,5],[2],[6]]
{{1,6},{2,3,4},{5}}           => [[1,3,4],[2,6],[5]]
{{1},{2,3,4,6},{5}}           => [[1,3,4,6],[2],[5]]
{{1},{2,3,4},{5,6}}           => [[1,3,4],[2,6],[5]]
{{1},{2,3,4},{5},{6}}         => [[1,3,4],[2],[5],[6]]
{{1,5,6},{2,3},{4}}           => [[1,3,6],[2,5],[4]]
{{1,5},{2,3,6},{4}}           => [[1,3,6],[2,5],[4]]
{{1,5},{2,3},{4,6}}           => [[1,3],[2,5],[4,6]]
{{1,5},{2,3},{4},{6}}         => [[1,3],[2,5],[4],[6]]
{{1,6},{2,3,5},{4}}           => [[1,3,5],[2,6],[4]]
{{1},{2,3,5,6},{4}}           => [[1,3,5,6],[2],[4]]
{{1},{2,3,5},{4,6}}           => [[1,3,5],[2,6],[4]]
{{1},{2,3,5},{4},{6}}         => [[1,3,5],[2],[4],[6]]
{{1,6},{2,3},{4,5}}           => [[1,3],[2,5],[4,6]]
{{1},{2,3,6},{4,5}}           => [[1,3,6],[2,5],[4]]
{{1},{2,3},{4,5,6}}           => [[1,3,6],[2,5],[4]]
{{1},{2,3},{4,5},{6}}         => [[1,3],[2,5],[4],[6]]
{{1,6},{2,3},{4},{5}}         => [[1,3],[2,6],[4],[5]]
{{1},{2,3,6},{4},{5}}         => [[1,3,6],[2],[4],[5]]
{{1},{2,3},{4,6},{5}}         => [[1,3],[2,6],[4],[5]]
{{1},{2,3},{4},{5,6}}         => [[1,3],[2,6],[4],[5]]
{{1},{2,3},{4},{5},{6}}       => [[1,3],[2],[4],[5],[6]]
{{1,4,5,6},{2},{3}}           => [[1,4,5,6],[2],[3]]
{{1,4,5},{2,6},{3}}           => [[1,4,5],[2,6],[3]]
{{1,4,5},{2},{3,6}}           => [[1,4,5],[2,6],[3]]
{{1,4,5},{2},{3},{6}}         => [[1,4,5],[2],[3],[6]]
{{1,4,6},{2,5},{3}}           => [[1,4,6],[2,5],[3]]
{{1,4},{2,5,6},{3}}           => [[1,4,6],[2,5],[3]]
{{1,4},{2,5},{3,6}}           => [[1,4],[2,5],[3,6]]
{{1,4},{2,5},{3},{6}}         => [[1,4],[2,5],[3],[6]]
{{1,4,6},{2},{3,5}}           => [[1,4,6],[2,5],[3]]
{{1,4},{2,6},{3,5}}           => [[1,4],[2,5],[3,6]]
{{1,4},{2},{3,5,6}}           => [[1,4,6],[2,5],[3]]
{{1,4},{2},{3,5},{6}}         => [[1,4],[2,5],[3],[6]]
{{1,4,6},{2},{3},{5}}         => [[1,4,6],[2],[3],[5]]
{{1,4},{2,6},{3},{5}}         => [[1,4],[2,6],[3],[5]]
{{1,4},{2},{3,6},{5}}         => [[1,4],[2,6],[3],[5]]
{{1,4},{2},{3},{5,6}}         => [[1,4],[2,6],[3],[5]]
{{1,4},{2},{3},{5},{6}}       => [[1,4],[2],[3],[5],[6]]
{{1,5,6},{2,4},{3}}           => [[1,4,6],[2,5],[3]]
{{1,5},{2,4,6},{3}}           => [[1,4,6],[2,5],[3]]
{{1,5},{2,4},{3,6}}           => [[1,4],[2,5],[3,6]]
{{1,5},{2,4},{3},{6}}         => [[1,4],[2,5],[3],[6]]
{{1,6},{2,4,5},{3}}           => [[1,4,5],[2,6],[3]]
{{1},{2,4,5,6},{3}}           => [[1,4,5,6],[2],[3]]
{{1},{2,4,5},{3,6}}           => [[1,4,5],[2,6],[3]]
{{1},{2,4,5},{3},{6}}         => [[1,4,5],[2],[3],[6]]
{{1,6},{2,4},{3,5}}           => [[1,4],[2,5],[3,6]]
{{1},{2,4,6},{3,5}}           => [[1,4,6],[2,5],[3]]
{{1},{2,4},{3,5,6}}           => [[1,4,6],[2,5],[3]]
{{1},{2,4},{3,5},{6}}         => [[1,4],[2,5],[3],[6]]
{{1,6},{2,4},{3},{5}}         => [[1,4],[2,6],[3],[5]]
{{1},{2,4,6},{3},{5}}         => [[1,4,6],[2],[3],[5]]
{{1},{2,4},{3,6},{5}}         => [[1,4],[2,6],[3],[5]]
{{1},{2,4},{3},{5,6}}         => [[1,4],[2,6],[3],[5]]
{{1},{2,4},{3},{5},{6}}       => [[1,4],[2],[3],[5],[6]]
{{1,5,6},{2},{3,4}}           => [[1,4,6],[2,5],[3]]
{{1,5},{2,6},{3,4}}           => [[1,4],[2,5],[3,6]]
{{1,5},{2},{3,4,6}}           => [[1,4,6],[2,5],[3]]
{{1,5},{2},{3,4},{6}}         => [[1,4],[2,5],[3],[6]]
{{1,6},{2,5},{3,4}}           => [[1,4],[2,5],[3,6]]
{{1},{2,5,6},{3,4}}           => [[1,4,6],[2,5],[3]]
{{1},{2,5},{3,4,6}}           => [[1,4,6],[2,5],[3]]
{{1},{2,5},{3,4},{6}}         => [[1,4],[2,5],[3],[6]]
{{1,6},{2},{3,4,5}}           => [[1,4,5],[2,6],[3]]
{{1},{2,6},{3,4,5}}           => [[1,4,5],[2,6],[3]]
{{1},{2},{3,4,5,6}}           => [[1,4,5,6],[2],[3]]
{{1},{2},{3,4,5},{6}}         => [[1,4,5],[2],[3],[6]]
{{1,6},{2},{3,4},{5}}         => [[1,4],[2,6],[3],[5]]
{{1},{2,6},{3,4},{5}}         => [[1,4],[2,6],[3],[5]]
{{1},{2},{3,4,6},{5}}         => [[1,4,6],[2],[3],[5]]
{{1},{2},{3,4},{5,6}}         => [[1,4],[2,6],[3],[5]]
{{1},{2},{3,4},{5},{6}}       => [[1,4],[2],[3],[5],[6]]
{{1,5,6},{2},{3},{4}}         => [[1,5,6],[2],[3],[4]]
{{1,5},{2,6},{3},{4}}         => [[1,5],[2,6],[3],[4]]
{{1,5},{2},{3,6},{4}}         => [[1,5],[2,6],[3],[4]]
{{1,5},{2},{3},{4,6}}         => [[1,5],[2,6],[3],[4]]
{{1,5},{2},{3},{4},{6}}       => [[1,5],[2],[3],[4],[6]]
{{1,6},{2,5},{3},{4}}         => [[1,5],[2,6],[3],[4]]
{{1},{2,5,6},{3},{4}}         => [[1,5,6],[2],[3],[4]]
{{1},{2,5},{3,6},{4}}         => [[1,5],[2,6],[3],[4]]
{{1},{2,5},{3},{4,6}}         => [[1,5],[2,6],[3],[4]]
{{1},{2,5},{3},{4},{6}}       => [[1,5],[2],[3],[4],[6]]
{{1,6},{2},{3,5},{4}}         => [[1,5],[2,6],[3],[4]]
{{1},{2,6},{3,5},{4}}         => [[1,5],[2,6],[3],[4]]
{{1},{2},{3,5,6},{4}}         => [[1,5,6],[2],[3],[4]]
{{1},{2},{3,5},{4,6}}         => [[1,5],[2,6],[3],[4]]
{{1},{2},{3,5},{4},{6}}       => [[1,5],[2],[3],[4],[6]]
{{1,6},{2},{3},{4,5}}         => [[1,5],[2,6],[3],[4]]
{{1},{2,6},{3},{4,5}}         => [[1,5],[2,6],[3],[4]]
{{1},{2},{3,6},{4,5}}         => [[1,5],[2,6],[3],[4]]
{{1},{2},{3},{4,5,6}}         => [[1,5,6],[2],[3],[4]]
{{1},{2},{3},{4,5},{6}}       => [[1,5],[2],[3],[4],[6]]
{{1,6},{2},{3},{4},{5}}       => [[1,6],[2],[3],[4],[5]]
{{1},{2,6},{3},{4},{5}}       => [[1,6],[2],[3],[4],[5]]
{{1},{2},{3,6},{4},{5}}       => [[1,6],[2],[3],[4],[5]]
{{1},{2},{3},{4,6},{5}}       => [[1,6],[2],[3],[4],[5]]
{{1},{2},{3},{4},{5,6}}       => [[1,6],[2],[3],[4],[5]]
{{1},{2},{3},{4},{5},{6}}     => [[1],[2],[3],[4],[5],[6]]
{{1,2,3,4,5,6,7}}             => [[1,2,3,4,5,6,7]]
{{1,2,3,4,5,6},{7}}           => [[1,2,3,4,5,6],[7]]
{{1,2,3,4,5,7},{6}}           => [[1,2,3,4,5,7],[6]]
{{1,2,3,4,5},{6,7}}           => [[1,2,3,4,5],[6,7]]
{{1,2,3,4,5},{6},{7}}         => [[1,2,3,4,5],[6],[7]]
{{1,2,3,4,6,7},{5}}           => [[1,2,3,4,6,7],[5]]
{{1,2,3,4,6},{5,7}}           => [[1,2,3,4,6],[5,7]]
{{1,2,3,4,6},{5},{7}}         => [[1,2,3,4,6],[5],[7]]
{{1,2,3,4,7},{5,6}}           => [[1,2,3,4,7],[5,6]]
{{1,2,3,4},{5,6,7}}           => [[1,2,3,4],[5,6,7]]
{{1,2,3,4},{5,6},{7}}         => [[1,2,3,4],[5,6],[7]]
{{1,2,3,4,7},{5},{6}}         => [[1,2,3,4,7],[5],[6]]
{{1,2,3,4},{5,7},{6}}         => [[1,2,3,4],[5,7],[6]]
{{1,2,3,4},{5},{6,7}}         => [[1,2,3,4],[5,7],[6]]
{{1,2,3,4},{5},{6},{7}}       => [[1,2,3,4],[5],[6],[7]]
{{1,2,3,5,6,7},{4}}           => [[1,2,3,5,6,7],[4]]
{{1,2,3,5,6},{4,7}}           => [[1,2,3,5,6],[4,7]]
{{1,2,3,5,6},{4},{7}}         => [[1,2,3,5,6],[4],[7]]
{{1,2,3,5,7},{4,6}}           => [[1,2,3,5,7],[4,6]]
{{1,2,3,5},{4,6,7}}           => [[1,2,3,5],[4,6,7]]
{{1,2,3,5},{4,6},{7}}         => [[1,2,3,5],[4,6],[7]]
{{1,2,3,5,7},{4},{6}}         => [[1,2,3,5,7],[4],[6]]
{{1,2,3,5},{4,7},{6}}         => [[1,2,3,5],[4,7],[6]]
{{1,2,3,5},{4},{6,7}}         => [[1,2,3,5],[4,7],[6]]
{{1,2,3,5},{4},{6},{7}}       => [[1,2,3,5],[4],[6],[7]]
{{1,2,3,6,7},{4,5}}           => [[1,2,3,6,7],[4,5]]
{{1,2,3,6},{4,5,7}}           => [[1,2,3,6],[4,5,7]]
{{1,2,3,6},{4,5},{7}}         => [[1,2,3,6],[4,5],[7]]
{{1,2,3,7},{4,5,6}}           => [[1,2,3,7],[4,5,6]]
{{1,2,3},{4,5,6,7}}           => [[1,2,3,7],[4,5,6]]
{{1,2,3},{4,5,6},{7}}         => [[1,2,3],[4,5,6],[7]]
{{1,2,3,7},{4,5},{6}}         => [[1,2,3,7],[4,5],[6]]
{{1,2,3},{4,5,7},{6}}         => [[1,2,3],[4,5,7],[6]]
{{1,2,3},{4,5},{6,7}}         => [[1,2,3],[4,5],[6,7]]
{{1,2,3},{4,5},{6},{7}}       => [[1,2,3],[4,5],[6],[7]]
{{1,2,3,6,7},{4},{5}}         => [[1,2,3,6,7],[4],[5]]
{{1,2,3,6},{4,7},{5}}         => [[1,2,3,6],[4,7],[5]]
{{1,2,3,6},{4},{5,7}}         => [[1,2,3,6],[4,7],[5]]
{{1,2,3,6},{4},{5},{7}}       => [[1,2,3,6],[4],[5],[7]]
{{1,2,3,7},{4,6},{5}}         => [[1,2,3,7],[4,6],[5]]
{{1,2,3},{4,6,7},{5}}         => [[1,2,3],[4,6,7],[5]]
{{1,2,3},{4,6},{5,7}}         => [[1,2,3],[4,6],[5,7]]
{{1,2,3},{4,6},{5},{7}}       => [[1,2,3],[4,6],[5],[7]]
{{1,2,3,7},{4},{5,6}}         => [[1,2,3,7],[4,6],[5]]
{{1,2,3},{4,7},{5,6}}         => [[1,2,3],[4,6],[5,7]]
{{1,2,3},{4},{5,6,7}}         => [[1,2,3],[4,6,7],[5]]
{{1,2,3},{4},{5,6},{7}}       => [[1,2,3],[4,6],[5],[7]]
{{1,2,3,7},{4},{5},{6}}       => [[1,2,3,7],[4],[5],[6]]
{{1,2,3},{4,7},{5},{6}}       => [[1,2,3],[4,7],[5],[6]]
{{1,2,3},{4},{5,7},{6}}       => [[1,2,3],[4,7],[5],[6]]
{{1,2,3},{4},{5},{6,7}}       => [[1,2,3],[4,7],[5],[6]]
{{1,2,3},{4},{5},{6},{7}}     => [[1,2,3],[4],[5],[6],[7]]
{{1,2,4,5,6,7},{3}}           => [[1,2,4,5,6,7],[3]]
{{1,2,4,5,6},{3,7}}           => [[1,2,4,5,6],[3,7]]
{{1,2,4,5,6},{3},{7}}         => [[1,2,4,5,6],[3],[7]]
{{1,2,4,5,7},{3,6}}           => [[1,2,4,5,7],[3,6]]
{{1,2,4,5},{3,6,7}}           => [[1,2,4,5],[3,6,7]]
{{1,2,4,5},{3,6},{7}}         => [[1,2,4,5],[3,6],[7]]
{{1,2,4,5,7},{3},{6}}         => [[1,2,4,5,7],[3],[6]]
{{1,2,4,5},{3,7},{6}}         => [[1,2,4,5],[3,7],[6]]
{{1,2,4,5},{3},{6,7}}         => [[1,2,4,5],[3,7],[6]]
{{1,2,4,5},{3},{6},{7}}       => [[1,2,4,5],[3],[6],[7]]
{{1,2,4,6,7},{3,5}}           => [[1,2,4,6,7],[3,5]]
{{1,2,4,6},{3,5,7}}           => [[1,2,4,6],[3,5,7]]
{{1,2,4,6},{3,5},{7}}         => [[1,2,4,6],[3,5],[7]]
{{1,2,4,7},{3,5,6}}           => [[1,2,4,7],[3,5,6]]
{{1,2,4},{3,5,6,7}}           => [[1,2,4,7],[3,5,6]]
{{1,2,4},{3,5,6},{7}}         => [[1,2,4],[3,5,6],[7]]
{{1,2,4,7},{3,5},{6}}         => [[1,2,4,7],[3,5],[6]]
{{1,2,4},{3,5,7},{6}}         => [[1,2,4],[3,5,7],[6]]
{{1,2,4},{3,5},{6,7}}         => [[1,2,4],[3,5],[6,7]]
{{1,2,4},{3,5},{6},{7}}       => [[1,2,4],[3,5],[6],[7]]
{{1,2,4,6,7},{3},{5}}         => [[1,2,4,6,7],[3],[5]]
{{1,2,4,6},{3,7},{5}}         => [[1,2,4,6],[3,7],[5]]
{{1,2,4,6},{3},{5,7}}         => [[1,2,4,6],[3,7],[5]]
{{1,2,4,6},{3},{5},{7}}       => [[1,2,4,6],[3],[5],[7]]
{{1,2,4,7},{3,6},{5}}         => [[1,2,4,7],[3,6],[5]]
{{1,2,4},{3,6,7},{5}}         => [[1,2,4],[3,6,7],[5]]
{{1,2,4},{3,6},{5,7}}         => [[1,2,4],[3,6],[5,7]]
{{1,2,4},{3,6},{5},{7}}       => [[1,2,4],[3,6],[5],[7]]
{{1,2,4,7},{3},{5,6}}         => [[1,2,4,7],[3,6],[5]]
{{1,2,4},{3,7},{5,6}}         => [[1,2,4],[3,6],[5,7]]
{{1,2,4},{3},{5,6,7}}         => [[1,2,4],[3,6,7],[5]]
{{1,2,4},{3},{5,6},{7}}       => [[1,2,4],[3,6],[5],[7]]
{{1,2,4,7},{3},{5},{6}}       => [[1,2,4,7],[3],[5],[6]]
{{1,2,4},{3,7},{5},{6}}       => [[1,2,4],[3,7],[5],[6]]
{{1,2,4},{3},{5,7},{6}}       => [[1,2,4],[3,7],[5],[6]]
{{1,2,4},{3},{5},{6,7}}       => [[1,2,4],[3,7],[5],[6]]
{{1,2,4},{3},{5},{6},{7}}     => [[1,2,4],[3],[5],[6],[7]]
{{1,2,5,6,7},{3,4}}           => [[1,2,5,6,7],[3,4]]
{{1,2,5,6},{3,4,7}}           => [[1,2,5,6],[3,4,7]]
{{1,2,5,6},{3,4},{7}}         => [[1,2,5,6],[3,4],[7]]
{{1,2,5,7},{3,4,6}}           => [[1,2,5,7],[3,4,6]]
{{1,2,5},{3,4,6,7}}           => [[1,2,5,7],[3,4,6]]
{{1,2,5},{3,4,6},{7}}         => [[1,2,5],[3,4,6],[7]]
{{1,2,5,7},{3,4},{6}}         => [[1,2,5,7],[3,4],[6]]
{{1,2,5},{3,4,7},{6}}         => [[1,2,5],[3,4,7],[6]]
{{1,2,5},{3,4},{6,7}}         => [[1,2,5],[3,4],[6,7]]
{{1,2,5},{3,4},{6},{7}}       => [[1,2,5],[3,4],[6],[7]]
{{1,2,6,7},{3,4,5}}           => [[1,2,5,7],[3,4,6]]
{{1,2,6},{3,4,5,7}}           => [[1,2,5,7],[3,4,6]]
{{1,2,6},{3,4,5},{7}}         => [[1,2,5],[3,4,6],[7]]
{{1,2,7},{3,4,5,6}}           => [[1,2,5,6],[3,4,7]]
{{1,2},{3,4,5,6,7}}           => [[1,2,5,6,7],[3,4]]
{{1,2},{3,4,5,6},{7}}         => [[1,2,5,6],[3,4],[7]]
{{1,2,7},{3,4,5},{6}}         => [[1,2,5],[3,4,7],[6]]
{{1,2},{3,4,5,7},{6}}         => [[1,2,5,7],[3,4],[6]]
{{1,2},{3,4,5},{6,7}}         => [[1,2,5],[3,4],[6,7]]
{{1,2},{3,4,5},{6},{7}}       => [[1,2,5],[3,4],[6],[7]]
{{1,2,6,7},{3,4},{5}}         => [[1,2,6,7],[3,4],[5]]
{{1,2,6},{3,4,7},{5}}         => [[1,2,6],[3,4,7],[5]]
{{1,2,6},{3,4},{5,7}}         => [[1,2,6],[3,4],[5,7]]
{{1,2,6},{3,4},{5},{7}}       => [[1,2,6],[3,4],[5],[7]]
{{1,2,7},{3,4,6},{5}}         => [[1,2,6],[3,4,7],[5]]
{{1,2},{3,4,6,7},{5}}         => [[1,2,6,7],[3,4],[5]]
{{1,2},{3,4,6},{5,7}}         => [[1,2,6],[3,4],[5,7]]
{{1,2},{3,4,6},{5},{7}}       => [[1,2,6],[3,4],[5],[7]]
{{1,2,7},{3,4},{5,6}}         => [[1,2,7],[3,4],[5,6]]
{{1,2},{3,4,7},{5,6}}         => [[1,2,7],[3,4],[5,6]]
{{1,2},{3,4},{5,6,7}}         => [[1,2,7],[3,4],[5,6]]
{{1,2},{3,4},{5,6},{7}}       => [[1,2],[3,4],[5,6],[7]]
{{1,2,7},{3,4},{5},{6}}       => [[1,2,7],[3,4],[5],[6]]
{{1,2},{3,4,7},{5},{6}}       => [[1,2,7],[3,4],[5],[6]]
{{1,2},{3,4},{5,7},{6}}       => [[1,2],[3,4],[5,7],[6]]
{{1,2},{3,4},{5},{6,7}}       => [[1,2],[3,4],[5,7],[6]]
{{1,2},{3,4},{5},{6},{7}}     => [[1,2],[3,4],[5],[6],[7]]
{{1,2,5,6,7},{3},{4}}         => [[1,2,5,6,7],[3],[4]]
{{1,2,5,6},{3,7},{4}}         => [[1,2,5,6],[3,7],[4]]
{{1,2,5,6},{3},{4,7}}         => [[1,2,5,6],[3,7],[4]]
{{1,2,5,6},{3},{4},{7}}       => [[1,2,5,6],[3],[4],[7]]
{{1,2,5,7},{3,6},{4}}         => [[1,2,5,7],[3,6],[4]]
{{1,2,5},{3,6,7},{4}}         => [[1,2,5],[3,6,7],[4]]
{{1,2,5},{3,6},{4,7}}         => [[1,2,5],[3,6],[4,7]]
{{1,2,5},{3,6},{4},{7}}       => [[1,2,5],[3,6],[4],[7]]
{{1,2,5,7},{3},{4,6}}         => [[1,2,5,7],[3,6],[4]]
{{1,2,5},{3,7},{4,6}}         => [[1,2,5],[3,6],[4,7]]
{{1,2,5},{3},{4,6,7}}         => [[1,2,5],[3,6,7],[4]]
{{1,2,5},{3},{4,6},{7}}       => [[1,2,5],[3,6],[4],[7]]
{{1,2,5,7},{3},{4},{6}}       => [[1,2,5,7],[3],[4],[6]]
{{1,2,5},{3,7},{4},{6}}       => [[1,2,5],[3,7],[4],[6]]
{{1,2,5},{3},{4,7},{6}}       => [[1,2,5],[3,7],[4],[6]]
{{1,2,5},{3},{4},{6,7}}       => [[1,2,5],[3,7],[4],[6]]
{{1,2,5},{3},{4},{6},{7}}     => [[1,2,5],[3],[4],[6],[7]]
{{1,2,6,7},{3,5},{4}}         => [[1,2,6,7],[3,5],[4]]
{{1,2,6},{3,5,7},{4}}         => [[1,2,6],[3,5,7],[4]]
{{1,2,6},{3,5},{4,7}}         => [[1,2,6],[3,5],[4,7]]
{{1,2,6},{3,5},{4},{7}}       => [[1,2,6],[3,5],[4],[7]]
{{1,2,7},{3,5,6},{4}}         => [[1,2,6],[3,5,7],[4]]
{{1,2},{3,5,6,7},{4}}         => [[1,2,6,7],[3,5],[4]]
{{1,2},{3,5,6},{4,7}}         => [[1,2,6],[3,5],[4,7]]
{{1,2},{3,5,6},{4},{7}}       => [[1,2,6],[3,5],[4],[7]]
{{1,2,7},{3,5},{4,6}}         => [[1,2,7],[3,5],[4,6]]
{{1,2},{3,5,7},{4,6}}         => [[1,2,7],[3,5],[4,6]]
{{1,2},{3,5},{4,6,7}}         => [[1,2,7],[3,5],[4,6]]
{{1,2},{3,5},{4,6},{7}}       => [[1,2],[3,5],[4,6],[7]]
{{1,2,7},{3,5},{4},{6}}       => [[1,2,7],[3,5],[4],[6]]
{{1,2},{3,5,7},{4},{6}}       => [[1,2,7],[3,5],[4],[6]]
{{1,2},{3,5},{4,7},{6}}       => [[1,2],[3,5],[4,7],[6]]
{{1,2},{3,5},{4},{6,7}}       => [[1,2],[3,5],[4,7],[6]]
{{1,2},{3,5},{4},{6},{7}}     => [[1,2],[3,5],[4],[6],[7]]
{{1,2,6,7},{3},{4,5}}         => [[1,2,6,7],[3,5],[4]]
{{1,2,6},{3,7},{4,5}}         => [[1,2,6],[3,5],[4,7]]
{{1,2,6},{3},{4,5,7}}         => [[1,2,6],[3,5,7],[4]]
{{1,2,6},{3},{4,5},{7}}       => [[1,2,6],[3,5],[4],[7]]
{{1,2,7},{3,6},{4,5}}         => [[1,2,7],[3,5],[4,6]]
{{1,2},{3,6,7},{4,5}}         => [[1,2,7],[3,5],[4,6]]
{{1,2},{3,6},{4,5,7}}         => [[1,2,7],[3,5],[4,6]]
{{1,2},{3,6},{4,5},{7}}       => [[1,2],[3,5],[4,6],[7]]
{{1,2,7},{3},{4,5,6}}         => [[1,2,6],[3,5,7],[4]]
{{1,2},{3,7},{4,5,6}}         => [[1,2,6],[3,5],[4,7]]
{{1,2},{3},{4,5,6,7}}         => [[1,2,6,7],[3,5],[4]]
{{1,2},{3},{4,5,6},{7}}       => [[1,2,6],[3,5],[4],[7]]
{{1,2,7},{3},{4,5},{6}}       => [[1,2,7],[3,5],[4],[6]]
{{1,2},{3,7},{4,5},{6}}       => [[1,2],[3,5],[4,7],[6]]
{{1,2},{3},{4,5,7},{6}}       => [[1,2,7],[3,5],[4],[6]]
{{1,2},{3},{4,5},{6,7}}       => [[1,2],[3,5],[4,7],[6]]
{{1,2},{3},{4,5},{6},{7}}     => [[1,2],[3,5],[4],[6],[7]]
{{1,2,6,7},{3},{4},{5}}       => [[1,2,6,7],[3],[4],[5]]
{{1,2,6},{3,7},{4},{5}}       => [[1,2,6],[3,7],[4],[5]]
{{1,2,6},{3},{4,7},{5}}       => [[1,2,6],[3,7],[4],[5]]
{{1,2,6},{3},{4},{5,7}}       => [[1,2,6],[3,7],[4],[5]]
{{1,2,6},{3},{4},{5},{7}}     => [[1,2,6],[3],[4],[5],[7]]
{{1,2,7},{3,6},{4},{5}}       => [[1,2,7],[3,6],[4],[5]]
{{1,2},{3,6,7},{4},{5}}       => [[1,2,7],[3,6],[4],[5]]
{{1,2},{3,6},{4,7},{5}}       => [[1,2],[3,6],[4,7],[5]]
{{1,2},{3,6},{4},{5,7}}       => [[1,2],[3,6],[4,7],[5]]
{{1,2},{3,6},{4},{5},{7}}     => [[1,2],[3,6],[4],[5],[7]]
{{1,2,7},{3},{4,6},{5}}       => [[1,2,7],[3,6],[4],[5]]
{{1,2},{3,7},{4,6},{5}}       => [[1,2],[3,6],[4,7],[5]]
{{1,2},{3},{4,6,7},{5}}       => [[1,2,7],[3,6],[4],[5]]
{{1,2},{3},{4,6},{5,7}}       => [[1,2],[3,6],[4,7],[5]]
{{1,2},{3},{4,6},{5},{7}}     => [[1,2],[3,6],[4],[5],[7]]
{{1,2,7},{3},{4},{5,6}}       => [[1,2,7],[3,6],[4],[5]]
{{1,2},{3,7},{4},{5,6}}       => [[1,2],[3,6],[4,7],[5]]
{{1,2},{3},{4,7},{5,6}}       => [[1,2],[3,6],[4,7],[5]]
{{1,2},{3},{4},{5,6,7}}       => [[1,2,7],[3,6],[4],[5]]
{{1,2},{3},{4},{5,6},{7}}     => [[1,2],[3,6],[4],[5],[7]]
{{1,2,7},{3},{4},{5},{6}}     => [[1,2,7],[3],[4],[5],[6]]
{{1,2},{3,7},{4},{5},{6}}     => [[1,2],[3,7],[4],[5],[6]]
{{1,2},{3},{4,7},{5},{6}}     => [[1,2],[3,7],[4],[5],[6]]
{{1,2},{3},{4},{5,7},{6}}     => [[1,2],[3,7],[4],[5],[6]]
{{1,2},{3},{4},{5},{6,7}}     => [[1,2],[3,7],[4],[5],[6]]
{{1,2},{3},{4},{5},{6},{7}}   => [[1,2],[3],[4],[5],[6],[7]]
{{1,3,4,5,6,7},{2}}           => [[1,3,4,5,6,7],[2]]
{{1,3,4,5,6},{2,7}}           => [[1,3,4,5,6],[2,7]]
{{1,3,4,5,6},{2},{7}}         => [[1,3,4,5,6],[2],[7]]
{{1,3,4,5,7},{2,6}}           => [[1,3,4,5,7],[2,6]]
{{1,3,4,5},{2,6,7}}           => [[1,3,4,5],[2,6,7]]
{{1,3,4,5},{2,6},{7}}         => [[1,3,4,5],[2,6],[7]]
{{1,3,4,5,7},{2},{6}}         => [[1,3,4,5,7],[2],[6]]
{{1,3,4,5},{2,7},{6}}         => [[1,3,4,5],[2,7],[6]]
{{1,3,4,5},{2},{6,7}}         => [[1,3,4,5],[2,7],[6]]
{{1,3,4,5},{2},{6},{7}}       => [[1,3,4,5],[2],[6],[7]]
{{1,3,4,6,7},{2,5}}           => [[1,3,4,6,7],[2,5]]
{{1,3,4,6},{2,5,7}}           => [[1,3,4,6],[2,5,7]]
{{1,3,4,6},{2,5},{7}}         => [[1,3,4,6],[2,5],[7]]
{{1,3,4,7},{2,5,6}}           => [[1,3,4,7],[2,5,6]]
{{1,3,4},{2,5,6,7}}           => [[1,3,4,7],[2,5,6]]
{{1,3,4},{2,5,6},{7}}         => [[1,3,4],[2,5,6],[7]]
{{1,3,4,7},{2,5},{6}}         => [[1,3,4,7],[2,5],[6]]
{{1,3,4},{2,5,7},{6}}         => [[1,3,4],[2,5,7],[6]]
{{1,3,4},{2,5},{6,7}}         => [[1,3,4],[2,5],[6,7]]
{{1,3,4},{2,5},{6},{7}}       => [[1,3,4],[2,5],[6],[7]]
{{1,3,4,6,7},{2},{5}}         => [[1,3,4,6,7],[2],[5]]
{{1,3,4,6},{2,7},{5}}         => [[1,3,4,6],[2,7],[5]]
{{1,3,4,6},{2},{5,7}}         => [[1,3,4,6],[2,7],[5]]
{{1,3,4,6},{2},{5},{7}}       => [[1,3,4,6],[2],[5],[7]]
{{1,3,4,7},{2,6},{5}}         => [[1,3,4,7],[2,6],[5]]
{{1,3,4},{2,6,7},{5}}         => [[1,3,4],[2,6,7],[5]]
{{1,3,4},{2,6},{5,7}}         => [[1,3,4],[2,6],[5,7]]
{{1,3,4},{2,6},{5},{7}}       => [[1,3,4],[2,6],[5],[7]]
{{1,3,4,7},{2},{5,6}}         => [[1,3,4,7],[2,6],[5]]
{{1,3,4},{2,7},{5,6}}         => [[1,3,4],[2,6],[5,7]]
{{1,3,4},{2},{5,6,7}}         => [[1,3,4],[2,6,7],[5]]
{{1,3,4},{2},{5,6},{7}}       => [[1,3,4],[2,6],[5],[7]]
{{1,3,4,7},{2},{5},{6}}       => [[1,3,4,7],[2],[5],[6]]
{{1,3,4},{2,7},{5},{6}}       => [[1,3,4],[2,7],[5],[6]]
{{1,3,4},{2},{5,7},{6}}       => [[1,3,4],[2,7],[5],[6]]
{{1,3,4},{2},{5},{6,7}}       => [[1,3,4],[2,7],[5],[6]]
{{1,3,4},{2},{5},{6},{7}}     => [[1,3,4],[2],[5],[6],[7]]
{{1,3,5,6,7},{2,4}}           => [[1,3,5,6,7],[2,4]]
{{1,3,5,6},{2,4,7}}           => [[1,3,5,6],[2,4,7]]
{{1,3,5,6},{2,4},{7}}         => [[1,3,5,6],[2,4],[7]]
{{1,3,5,7},{2,4,6}}           => [[1,3,5,7],[2,4,6]]
{{1,3,5},{2,4,6,7}}           => [[1,3,5,7],[2,4,6]]
{{1,3,5},{2,4,6},{7}}         => [[1,3,5],[2,4,6],[7]]
{{1,3,5,7},{2,4},{6}}         => [[1,3,5,7],[2,4],[6]]
{{1,3,5},{2,4,7},{6}}         => [[1,3,5],[2,4,7],[6]]
{{1,3,5},{2,4},{6,7}}         => [[1,3,5],[2,4],[6,7]]
{{1,3,5},{2,4},{6},{7}}       => [[1,3,5],[2,4],[6],[7]]
{{1,3,6,7},{2,4,5}}           => [[1,3,5,7],[2,4,6]]
{{1,3,6},{2,4,5,7}}           => [[1,3,5,7],[2,4,6]]
{{1,3,6},{2,4,5},{7}}         => [[1,3,5],[2,4,6],[7]]
{{1,3,7},{2,4,5,6}}           => [[1,3,5,6],[2,4,7]]
{{1,3},{2,4,5,6,7}}           => [[1,3,5,6,7],[2,4]]
{{1,3},{2,4,5,6},{7}}         => [[1,3,5,6],[2,4],[7]]
{{1,3,7},{2,4,5},{6}}         => [[1,3,5],[2,4,7],[6]]
{{1,3},{2,4,5,7},{6}}         => [[1,3,5,7],[2,4],[6]]
{{1,3},{2,4,5},{6,7}}         => [[1,3,5],[2,4],[6,7]]
{{1,3},{2,4,5},{6},{7}}       => [[1,3,5],[2,4],[6],[7]]
{{1,3,6,7},{2,4},{5}}         => [[1,3,6,7],[2,4],[5]]
{{1,3,6},{2,4,7},{5}}         => [[1,3,6],[2,4,7],[5]]
{{1,3,6},{2,4},{5,7}}         => [[1,3,6],[2,4],[5,7]]
{{1,3,6},{2,4},{5},{7}}       => [[1,3,6],[2,4],[5],[7]]
{{1,3,7},{2,4,6},{5}}         => [[1,3,6],[2,4,7],[5]]
{{1,3},{2,4,6,7},{5}}         => [[1,3,6,7],[2,4],[5]]
{{1,3},{2,4,6},{5,7}}         => [[1,3,6],[2,4],[5,7]]
{{1,3},{2,4,6},{5},{7}}       => [[1,3,6],[2,4],[5],[7]]
{{1,3,7},{2,4},{5,6}}         => [[1,3,7],[2,4],[5,6]]
{{1,3},{2,4,7},{5,6}}         => [[1,3,7],[2,4],[5,6]]
{{1,3},{2,4},{5,6,7}}         => [[1,3,7],[2,4],[5,6]]
{{1,3},{2,4},{5,6},{7}}       => [[1,3],[2,4],[5,6],[7]]
{{1,3,7},{2,4},{5},{6}}       => [[1,3,7],[2,4],[5],[6]]
{{1,3},{2,4,7},{5},{6}}       => [[1,3,7],[2,4],[5],[6]]
{{1,3},{2,4},{5,7},{6}}       => [[1,3],[2,4],[5,7],[6]]
{{1,3},{2,4},{5},{6,7}}       => [[1,3],[2,4],[5,7],[6]]
{{1,3},{2,4},{5},{6},{7}}     => [[1,3],[2,4],[5],[6],[7]]
{{1,3,5,6,7},{2},{4}}         => [[1,3,5,6,7],[2],[4]]
{{1,3,5,6},{2,7},{4}}         => [[1,3,5,6],[2,7],[4]]
{{1,3,5,6},{2},{4,7}}         => [[1,3,5,6],[2,7],[4]]
{{1,3,5,6},{2},{4},{7}}       => [[1,3,5,6],[2],[4],[7]]
{{1,3,5,7},{2,6},{4}}         => [[1,3,5,7],[2,6],[4]]
{{1,3,5},{2,6,7},{4}}         => [[1,3,5],[2,6,7],[4]]
{{1,3,5},{2,6},{4,7}}         => [[1,3,5],[2,6],[4,7]]
{{1,3,5},{2,6},{4},{7}}       => [[1,3,5],[2,6],[4],[7]]
{{1,3,5,7},{2},{4,6}}         => [[1,3,5,7],[2,6],[4]]
{{1,3,5},{2,7},{4,6}}         => [[1,3,5],[2,6],[4,7]]
{{1,3,5},{2},{4,6,7}}         => [[1,3,5],[2,6,7],[4]]
{{1,3,5},{2},{4,6},{7}}       => [[1,3,5],[2,6],[4],[7]]
{{1,3,5,7},{2},{4},{6}}       => [[1,3,5,7],[2],[4],[6]]
{{1,3,5},{2,7},{4},{6}}       => [[1,3,5],[2,7],[4],[6]]
{{1,3,5},{2},{4,7},{6}}       => [[1,3,5],[2,7],[4],[6]]
{{1,3,5},{2},{4},{6,7}}       => [[1,3,5],[2,7],[4],[6]]
{{1,3,5},{2},{4},{6},{7}}     => [[1,3,5],[2],[4],[6],[7]]
{{1,3,6,7},{2,5},{4}}         => [[1,3,6,7],[2,5],[4]]
{{1,3,6},{2,5,7},{4}}         => [[1,3,6],[2,5,7],[4]]
{{1,3,6},{2,5},{4,7}}         => [[1,3,6],[2,5],[4,7]]
{{1,3,6},{2,5},{4},{7}}       => [[1,3,6],[2,5],[4],[7]]
{{1,3,7},{2,5,6},{4}}         => [[1,3,6],[2,5,7],[4]]
{{1,3},{2,5,6,7},{4}}         => [[1,3,6,7],[2,5],[4]]
{{1,3},{2,5,6},{4,7}}         => [[1,3,6],[2,5],[4,7]]
{{1,3},{2,5,6},{4},{7}}       => [[1,3,6],[2,5],[4],[7]]
{{1,3,7},{2,5},{4,6}}         => [[1,3,7],[2,5],[4,6]]
{{1,3},{2,5,7},{4,6}}         => [[1,3,7],[2,5],[4,6]]
{{1,3},{2,5},{4,6,7}}         => [[1,3,7],[2,5],[4,6]]
{{1,3},{2,5},{4,6},{7}}       => [[1,3],[2,5],[4,6],[7]]
{{1,3,7},{2,5},{4},{6}}       => [[1,3,7],[2,5],[4],[6]]
{{1,3},{2,5,7},{4},{6}}       => [[1,3,7],[2,5],[4],[6]]
{{1,3},{2,5},{4,7},{6}}       => [[1,3],[2,5],[4,7],[6]]
{{1,3},{2,5},{4},{6,7}}       => [[1,3],[2,5],[4,7],[6]]
{{1,3},{2,5},{4},{6},{7}}     => [[1,3],[2,5],[4],[6],[7]]
{{1,3,6,7},{2},{4,5}}         => [[1,3,6,7],[2,5],[4]]
{{1,3,6},{2,7},{4,5}}         => [[1,3,6],[2,5],[4,7]]
{{1,3,6},{2},{4,5,7}}         => [[1,3,6],[2,5,7],[4]]
{{1,3,6},{2},{4,5},{7}}       => [[1,3,6],[2,5],[4],[7]]
{{1,3,7},{2,6},{4,5}}         => [[1,3,7],[2,5],[4,6]]
{{1,3},{2,6,7},{4,5}}         => [[1,3,7],[2,5],[4,6]]
{{1,3},{2,6},{4,5,7}}         => [[1,3,7],[2,5],[4,6]]
{{1,3},{2,6},{4,5},{7}}       => [[1,3],[2,5],[4,6],[7]]
{{1,3,7},{2},{4,5,6}}         => [[1,3,6],[2,5,7],[4]]
{{1,3},{2,7},{4,5,6}}         => [[1,3,6],[2,5],[4,7]]
{{1,3},{2},{4,5,6,7}}         => [[1,3,6,7],[2,5],[4]]
{{1,3},{2},{4,5,6},{7}}       => [[1,3,6],[2,5],[4],[7]]
{{1,3,7},{2},{4,5},{6}}       => [[1,3,7],[2,5],[4],[6]]
{{1,3},{2,7},{4,5},{6}}       => [[1,3],[2,5],[4,7],[6]]
{{1,3},{2},{4,5,7},{6}}       => [[1,3,7],[2,5],[4],[6]]
{{1,3},{2},{4,5},{6,7}}       => [[1,3],[2,5],[4,7],[6]]
{{1,3},{2},{4,5},{6},{7}}     => [[1,3],[2,5],[4],[6],[7]]
{{1,3,6,7},{2},{4},{5}}       => [[1,3,6,7],[2],[4],[5]]
{{1,3,6},{2,7},{4},{5}}       => [[1,3,6],[2,7],[4],[5]]
{{1,3,6},{2},{4,7},{5}}       => [[1,3,6],[2,7],[4],[5]]
{{1,3,6},{2},{4},{5,7}}       => [[1,3,6],[2,7],[4],[5]]
{{1,3,6},{2},{4},{5},{7}}     => [[1,3,6],[2],[4],[5],[7]]
{{1,3,7},{2,6},{4},{5}}       => [[1,3,7],[2,6],[4],[5]]
{{1,3},{2,6,7},{4},{5}}       => [[1,3,7],[2,6],[4],[5]]
{{1,3},{2,6},{4,7},{5}}       => [[1,3],[2,6],[4,7],[5]]
{{1,3},{2,6},{4},{5,7}}       => [[1,3],[2,6],[4,7],[5]]
{{1,3},{2,6},{4},{5},{7}}     => [[1,3],[2,6],[4],[5],[7]]
{{1,3,7},{2},{4,6},{5}}       => [[1,3,7],[2,6],[4],[5]]
{{1,3},{2,7},{4,6},{5}}       => [[1,3],[2,6],[4,7],[5]]
{{1,3},{2},{4,6,7},{5}}       => [[1,3,7],[2,6],[4],[5]]
{{1,3},{2},{4,6},{5,7}}       => [[1,3],[2,6],[4,7],[5]]
{{1,3},{2},{4,6},{5},{7}}     => [[1,3],[2,6],[4],[5],[7]]
{{1,3,7},{2},{4},{5,6}}       => [[1,3,7],[2,6],[4],[5]]
{{1,3},{2,7},{4},{5,6}}       => [[1,3],[2,6],[4,7],[5]]
{{1,3},{2},{4,7},{5,6}}       => [[1,3],[2,6],[4,7],[5]]
{{1,3},{2},{4},{5,6,7}}       => [[1,3,7],[2,6],[4],[5]]
{{1,3},{2},{4},{5,6},{7}}     => [[1,3],[2,6],[4],[5],[7]]
{{1,3,7},{2},{4},{5},{6}}     => [[1,3,7],[2],[4],[5],[6]]
{{1,3},{2,7},{4},{5},{6}}     => [[1,3],[2,7],[4],[5],[6]]
{{1,3},{2},{4,7},{5},{6}}     => [[1,3],[2,7],[4],[5],[6]]
{{1,3},{2},{4},{5,7},{6}}     => [[1,3],[2,7],[4],[5],[6]]
{{1,3},{2},{4},{5},{6,7}}     => [[1,3],[2,7],[4],[5],[6]]
{{1,3},{2},{4},{5},{6},{7}}   => [[1,3],[2],[4],[5],[6],[7]]
{{1,4,5,6,7},{2,3}}           => [[1,3,5,6,7],[2,4]]
{{1,4,5,6},{2,3,7}}           => [[1,3,5,6],[2,4,7]]
{{1,4,5,6},{2,3},{7}}         => [[1,3,5,6],[2,4],[7]]
{{1,4,5,7},{2,3,6}}           => [[1,3,5,7],[2,4,6]]
{{1,4,5},{2,3,6,7}}           => [[1,3,5,7],[2,4,6]]
{{1,4,5},{2,3,6},{7}}         => [[1,3,5],[2,4,6],[7]]
{{1,4,5,7},{2,3},{6}}         => [[1,3,5,7],[2,4],[6]]
{{1,4,5},{2,3,7},{6}}         => [[1,3,5],[2,4,7],[6]]
{{1,4,5},{2,3},{6,7}}         => [[1,3,5],[2,4],[6,7]]
{{1,4,5},{2,3},{6},{7}}       => [[1,3,5],[2,4],[6],[7]]
{{1,4,6,7},{2,3,5}}           => [[1,3,5,7],[2,4,6]]
{{1,4,6},{2,3,5,7}}           => [[1,3,5,7],[2,4,6]]
{{1,4,6},{2,3,5},{7}}         => [[1,3,5],[2,4,6],[7]]
{{1,4,7},{2,3,5,6}}           => [[1,3,5,6],[2,4,7]]
{{1,4},{2,3,5,6,7}}           => [[1,3,5,6,7],[2,4]]
{{1,4},{2,3,5,6},{7}}         => [[1,3,5,6],[2,4],[7]]
{{1,4,7},{2,3,5},{6}}         => [[1,3,5],[2,4,7],[6]]
{{1,4},{2,3,5,7},{6}}         => [[1,3,5,7],[2,4],[6]]
{{1,4},{2,3,5},{6,7}}         => [[1,3,5],[2,4],[6,7]]
{{1,4},{2,3,5},{6},{7}}       => [[1,3,5],[2,4],[6],[7]]
{{1,4,6,7},{2,3},{5}}         => [[1,3,6,7],[2,4],[5]]
{{1,4,6},{2,3,7},{5}}         => [[1,3,6],[2,4,7],[5]]
{{1,4,6},{2,3},{5,7}}         => [[1,3,6],[2,4],[5,7]]
{{1,4,6},{2,3},{5},{7}}       => [[1,3,6],[2,4],[5],[7]]
{{1,4,7},{2,3,6},{5}}         => [[1,3,6],[2,4,7],[5]]
{{1,4},{2,3,6,7},{5}}         => [[1,3,6,7],[2,4],[5]]
{{1,4},{2,3,6},{5,7}}         => [[1,3,6],[2,4],[5,7]]
{{1,4},{2,3,6},{5},{7}}       => [[1,3,6],[2,4],[5],[7]]
{{1,4,7},{2,3},{5,6}}         => [[1,3,7],[2,4],[5,6]]
{{1,4},{2,3,7},{5,6}}         => [[1,3,7],[2,4],[5,6]]
{{1,4},{2,3},{5,6,7}}         => [[1,3,7],[2,4],[5,6]]
{{1,4},{2,3},{5,6},{7}}       => [[1,3],[2,4],[5,6],[7]]
{{1,4,7},{2,3},{5},{6}}       => [[1,3,7],[2,4],[5],[6]]
{{1,4},{2,3,7},{5},{6}}       => [[1,3,7],[2,4],[5],[6]]
{{1,4},{2,3},{5,7},{6}}       => [[1,3],[2,4],[5,7],[6]]
{{1,4},{2,3},{5},{6,7}}       => [[1,3],[2,4],[5,7],[6]]
{{1,4},{2,3},{5},{6},{7}}     => [[1,3],[2,4],[5],[6],[7]]
{{1,5,6,7},{2,3,4}}           => [[1,3,4,7],[2,5,6]]
{{1,5,6},{2,3,4,7}}           => [[1,3,4,7],[2,5,6]]
{{1,5,6},{2,3,4},{7}}         => [[1,3,4],[2,5,6],[7]]
{{1,5,7},{2,3,4,6}}           => [[1,3,4,6],[2,5,7]]
{{1,5},{2,3,4,6,7}}           => [[1,3,4,6,7],[2,5]]
{{1,5},{2,3,4,6},{7}}         => [[1,3,4,6],[2,5],[7]]
{{1,5,7},{2,3,4},{6}}         => [[1,3,4],[2,5,7],[6]]
{{1,5},{2,3,4,7},{6}}         => [[1,3,4,7],[2,5],[6]]
{{1,5},{2,3,4},{6,7}}         => [[1,3,4],[2,5],[6,7]]
{{1,5},{2,3,4},{6},{7}}       => [[1,3,4],[2,5],[6],[7]]
{{1,6,7},{2,3,4,5}}           => [[1,3,4,5],[2,6,7]]
{{1,6},{2,3,4,5,7}}           => [[1,3,4,5,7],[2,6]]
{{1,6},{2,3,4,5},{7}}         => [[1,3,4,5],[2,6],[7]]
{{1,7},{2,3,4,5,6}}           => [[1,3,4,5,6],[2,7]]
{{1},{2,3,4,5,6,7}}           => [[1,3,4,5,6,7],[2]]
{{1},{2,3,4,5,6},{7}}         => [[1,3,4,5,6],[2],[7]]
{{1,7},{2,3,4,5},{6}}         => [[1,3,4,5],[2,7],[6]]
{{1},{2,3,4,5,7},{6}}         => [[1,3,4,5,7],[2],[6]]
{{1},{2,3,4,5},{6,7}}         => [[1,3,4,5],[2,7],[6]]
{{1},{2,3,4,5},{6},{7}}       => [[1,3,4,5],[2],[6],[7]]
{{1,6,7},{2,3,4},{5}}         => [[1,3,4],[2,6,7],[5]]
{{1,6},{2,3,4,7},{5}}         => [[1,3,4,7],[2,6],[5]]
{{1,6},{2,3,4},{5,7}}         => [[1,3,4],[2,6],[5,7]]
{{1,6},{2,3,4},{5},{7}}       => [[1,3,4],[2,6],[5],[7]]
{{1,7},{2,3,4,6},{5}}         => [[1,3,4,6],[2,7],[5]]
{{1},{2,3,4,6,7},{5}}         => [[1,3,4,6,7],[2],[5]]
{{1},{2,3,4,6},{5,7}}         => [[1,3,4,6],[2,7],[5]]
{{1},{2,3,4,6},{5},{7}}       => [[1,3,4,6],[2],[5],[7]]
{{1,7},{2,3,4},{5,6}}         => [[1,3,4],[2,6],[5,7]]
{{1},{2,3,4,7},{5,6}}         => [[1,3,4,7],[2,6],[5]]
{{1},{2,3,4},{5,6,7}}         => [[1,3,4],[2,6,7],[5]]
{{1},{2,3,4},{5,6},{7}}       => [[1,3,4],[2,6],[5],[7]]
{{1,7},{2,3,4},{5},{6}}       => [[1,3,4],[2,7],[5],[6]]
{{1},{2,3,4,7},{5},{6}}       => [[1,3,4,7],[2],[5],[6]]
{{1},{2,3,4},{5,7},{6}}       => [[1,3,4],[2,7],[5],[6]]
{{1},{2,3,4},{5},{6,7}}       => [[1,3,4],[2,7],[5],[6]]
{{1},{2,3,4},{5},{6},{7}}     => [[1,3,4],[2],[5],[6],[7]]
{{1,5,6,7},{2,3},{4}}         => [[1,3,6,7],[2,5],[4]]
{{1,5,6},{2,3,7},{4}}         => [[1,3,6],[2,5,7],[4]]
{{1,5,6},{2,3},{4,7}}         => [[1,3,6],[2,5],[4,7]]
{{1,5,6},{2,3},{4},{7}}       => [[1,3,6],[2,5],[4],[7]]
{{1,5,7},{2,3,6},{4}}         => [[1,3,6],[2,5,7],[4]]
{{1,5},{2,3,6,7},{4}}         => [[1,3,6,7],[2,5],[4]]
{{1,5},{2,3,6},{4,7}}         => [[1,3,6],[2,5],[4,7]]
{{1,5},{2,3,6},{4},{7}}       => [[1,3,6],[2,5],[4],[7]]
{{1,5,7},{2,3},{4,6}}         => [[1,3,7],[2,5],[4,6]]
{{1,5},{2,3,7},{4,6}}         => [[1,3,7],[2,5],[4,6]]
{{1,5},{2,3},{4,6,7}}         => [[1,3,7],[2,5],[4,6]]
{{1,5},{2,3},{4,6},{7}}       => [[1,3],[2,5],[4,6],[7]]
{{1,5,7},{2,3},{4},{6}}       => [[1,3,7],[2,5],[4],[6]]
{{1,5},{2,3,7},{4},{6}}       => [[1,3,7],[2,5],[4],[6]]
{{1,5},{2,3},{4,7},{6}}       => [[1,3],[2,5],[4,7],[6]]
{{1,5},{2,3},{4},{6,7}}       => [[1,3],[2,5],[4,7],[6]]
{{1,5},{2,3},{4},{6},{7}}     => [[1,3],[2,5],[4],[6],[7]]
{{1,6,7},{2,3,5},{4}}         => [[1,3,5],[2,6,7],[4]]
{{1,6},{2,3,5,7},{4}}         => [[1,3,5,7],[2,6],[4]]
{{1,6},{2,3,5},{4,7}}         => [[1,3,5],[2,6],[4,7]]
{{1,6},{2,3,5},{4},{7}}       => [[1,3,5],[2,6],[4],[7]]
{{1,7},{2,3,5,6},{4}}         => [[1,3,5,6],[2,7],[4]]
{{1},{2,3,5,6,7},{4}}         => [[1,3,5,6,7],[2],[4]]
{{1},{2,3,5,6},{4,7}}         => [[1,3,5,6],[2,7],[4]]
{{1},{2,3,5,6},{4},{7}}       => [[1,3,5,6],[2],[4],[7]]
{{1,7},{2,3,5},{4,6}}         => [[1,3,5],[2,6],[4,7]]
{{1},{2,3,5,7},{4,6}}         => [[1,3,5,7],[2,6],[4]]
{{1},{2,3,5},{4,6,7}}         => [[1,3,5],[2,6,7],[4]]
{{1},{2,3,5},{4,6},{7}}       => [[1,3,5],[2,6],[4],[7]]
{{1,7},{2,3,5},{4},{6}}       => [[1,3,5],[2,7],[4],[6]]
{{1},{2,3,5,7},{4},{6}}       => [[1,3,5,7],[2],[4],[6]]
{{1},{2,3,5},{4,7},{6}}       => [[1,3,5],[2,7],[4],[6]]
{{1},{2,3,5},{4},{6,7}}       => [[1,3,5],[2,7],[4],[6]]
{{1},{2,3,5},{4},{6},{7}}     => [[1,3,5],[2],[4],[6],[7]]
{{1,6,7},{2,3},{4,5}}         => [[1,3,7],[2,5],[4,6]]
{{1,6},{2,3,7},{4,5}}         => [[1,3,7],[2,5],[4,6]]
{{1,6},{2,3},{4,5,7}}         => [[1,3,7],[2,5],[4,6]]
{{1,6},{2,3},{4,5},{7}}       => [[1,3],[2,5],[4,6],[7]]
{{1,7},{2,3,6},{4,5}}         => [[1,3,6],[2,5],[4,7]]
{{1},{2,3,6,7},{4,5}}         => [[1,3,6,7],[2,5],[4]]
{{1},{2,3,6},{4,5,7}}         => [[1,3,6],[2,5,7],[4]]
{{1},{2,3,6},{4,5},{7}}       => [[1,3,6],[2,5],[4],[7]]
{{1,7},{2,3},{4,5,6}}         => [[1,3,6],[2,5],[4,7]]
{{1},{2,3,7},{4,5,6}}         => [[1,3,6],[2,5,7],[4]]
{{1},{2,3},{4,5,6,7}}         => [[1,3,6,7],[2,5],[4]]
{{1},{2,3},{4,5,6},{7}}       => [[1,3,6],[2,5],[4],[7]]
{{1,7},{2,3},{4,5},{6}}       => [[1,3],[2,5],[4,7],[6]]
{{1},{2,3,7},{4,5},{6}}       => [[1,3,7],[2,5],[4],[6]]
{{1},{2,3},{4,5,7},{6}}       => [[1,3,7],[2,5],[4],[6]]
{{1},{2,3},{4,5},{6,7}}       => [[1,3],[2,5],[4,7],[6]]
{{1},{2,3},{4,5},{6},{7}}     => [[1,3],[2,5],[4],[6],[7]]
{{1,6,7},{2,3},{4},{5}}       => [[1,3,7],[2,6],[4],[5]]
{{1,6},{2,3,7},{4},{5}}       => [[1,3,7],[2,6],[4],[5]]
{{1,6},{2,3},{4,7},{5}}       => [[1,3],[2,6],[4,7],[5]]
{{1,6},{2,3},{4},{5,7}}       => [[1,3],[2,6],[4,7],[5]]
{{1,6},{2,3},{4},{5},{7}}     => [[1,3],[2,6],[4],[5],[7]]
{{1,7},{2,3,6},{4},{5}}       => [[1,3,6],[2,7],[4],[5]]
{{1},{2,3,6,7},{4},{5}}       => [[1,3,6,7],[2],[4],[5]]
{{1},{2,3,6},{4,7},{5}}       => [[1,3,6],[2,7],[4],[5]]
{{1},{2,3,6},{4},{5,7}}       => [[1,3,6],[2,7],[4],[5]]
{{1},{2,3,6},{4},{5},{7}}     => [[1,3,6],[2],[4],[5],[7]]
{{1,7},{2,3},{4,6},{5}}       => [[1,3],[2,6],[4,7],[5]]
{{1},{2,3,7},{4,6},{5}}       => [[1,3,7],[2,6],[4],[5]]
{{1},{2,3},{4,6,7},{5}}       => [[1,3,7],[2,6],[4],[5]]
{{1},{2,3},{4,6},{5,7}}       => [[1,3],[2,6],[4,7],[5]]
{{1},{2,3},{4,6},{5},{7}}     => [[1,3],[2,6],[4],[5],[7]]
{{1,7},{2,3},{4},{5,6}}       => [[1,3],[2,6],[4,7],[5]]
{{1},{2,3,7},{4},{5,6}}       => [[1,3,7],[2,6],[4],[5]]
{{1},{2,3},{4,7},{5,6}}       => [[1,3],[2,6],[4,7],[5]]
{{1},{2,3},{4},{5,6,7}}       => [[1,3,7],[2,6],[4],[5]]
{{1},{2,3},{4},{5,6},{7}}     => [[1,3],[2,6],[4],[5],[7]]
{{1,7},{2,3},{4},{5},{6}}     => [[1,3],[2,7],[4],[5],[6]]
{{1},{2,3,7},{4},{5},{6}}     => [[1,3,7],[2],[4],[5],[6]]
{{1},{2,3},{4,7},{5},{6}}     => [[1,3],[2,7],[4],[5],[6]]
{{1},{2,3},{4},{5,7},{6}}     => [[1,3],[2,7],[4],[5],[6]]
{{1},{2,3},{4},{5},{6,7}}     => [[1,3],[2,7],[4],[5],[6]]
{{1},{2,3},{4},{5},{6},{7}}   => [[1,3],[2],[4],[5],[6],[7]]
{{1,4,5,6,7},{2},{3}}         => [[1,4,5,6,7],[2],[3]]
{{1,4,5,6},{2,7},{3}}         => [[1,4,5,6],[2,7],[3]]
{{1,4,5,6},{2},{3,7}}         => [[1,4,5,6],[2,7],[3]]
{{1,4,5,6},{2},{3},{7}}       => [[1,4,5,6],[2],[3],[7]]
{{1,4,5,7},{2,6},{3}}         => [[1,4,5,7],[2,6],[3]]
{{1,4,5},{2,6,7},{3}}         => [[1,4,5],[2,6,7],[3]]
{{1,4,5},{2,6},{3,7}}         => [[1,4,5],[2,6],[3,7]]
{{1,4,5},{2,6},{3},{7}}       => [[1,4,5],[2,6],[3],[7]]
{{1,4,5,7},{2},{3,6}}         => [[1,4,5,7],[2,6],[3]]
{{1,4,5},{2,7},{3,6}}         => [[1,4,5],[2,6],[3,7]]
{{1,4,5},{2},{3,6,7}}         => [[1,4,5],[2,6,7],[3]]
{{1,4,5},{2},{3,6},{7}}       => [[1,4,5],[2,6],[3],[7]]
{{1,4,5,7},{2},{3},{6}}       => [[1,4,5,7],[2],[3],[6]]
{{1,4,5},{2,7},{3},{6}}       => [[1,4,5],[2,7],[3],[6]]
{{1,4,5},{2},{3,7},{6}}       => [[1,4,5],[2,7],[3],[6]]
{{1,4,5},{2},{3},{6,7}}       => [[1,4,5],[2,7],[3],[6]]
{{1,4,5},{2},{3},{6},{7}}     => [[1,4,5],[2],[3],[6],[7]]
{{1,4,6,7},{2,5},{3}}         => [[1,4,6,7],[2,5],[3]]
{{1,4,6},{2,5,7},{3}}         => [[1,4,6],[2,5,7],[3]]
{{1,4,6},{2,5},{3,7}}         => [[1,4,6],[2,5],[3,7]]
{{1,4,6},{2,5},{3},{7}}       => [[1,4,6],[2,5],[3],[7]]
{{1,4,7},{2,5,6},{3}}         => [[1,4,6],[2,5,7],[3]]
{{1,4},{2,5,6,7},{3}}         => [[1,4,6,7],[2,5],[3]]
{{1,4},{2,5,6},{3,7}}         => [[1,4,6],[2,5],[3,7]]
{{1,4},{2,5,6},{3},{7}}       => [[1,4,6],[2,5],[3],[7]]
{{1,4,7},{2,5},{3,6}}         => [[1,4,7],[2,5],[3,6]]
{{1,4},{2,5,7},{3,6}}         => [[1,4,7],[2,5],[3,6]]
{{1,4},{2,5},{3,6,7}}         => [[1,4,7],[2,5],[3,6]]
{{1,4},{2,5},{3,6},{7}}       => [[1,4],[2,5],[3,6],[7]]
{{1,4,7},{2,5},{3},{6}}       => [[1,4,7],[2,5],[3],[6]]
{{1,4},{2,5,7},{3},{6}}       => [[1,4,7],[2,5],[3],[6]]
{{1,4},{2,5},{3,7},{6}}       => [[1,4],[2,5],[3,7],[6]]
{{1,4},{2,5},{3},{6,7}}       => [[1,4],[2,5],[3,7],[6]]
{{1,4},{2,5},{3},{6},{7}}     => [[1,4],[2,5],[3],[6],[7]]
{{1,4,6,7},{2},{3,5}}         => [[1,4,6,7],[2,5],[3]]
{{1,4,6},{2,7},{3,5}}         => [[1,4,6],[2,5],[3,7]]
{{1,4,6},{2},{3,5,7}}         => [[1,4,6],[2,5,7],[3]]
{{1,4,6},{2},{3,5},{7}}       => [[1,4,6],[2,5],[3],[7]]
{{1,4,7},{2,6},{3,5}}         => [[1,4,7],[2,5],[3,6]]
{{1,4},{2,6,7},{3,5}}         => [[1,4,7],[2,5],[3,6]]
{{1,4},{2,6},{3,5,7}}         => [[1,4,7],[2,5],[3,6]]
{{1,4},{2,6},{3,5},{7}}       => [[1,4],[2,5],[3,6],[7]]
{{1,4,7},{2},{3,5,6}}         => [[1,4,6],[2,5,7],[3]]
{{1,4},{2,7},{3,5,6}}         => [[1,4,6],[2,5],[3,7]]
{{1,4},{2},{3,5,6,7}}         => [[1,4,6,7],[2,5],[3]]
{{1,4},{2},{3,5,6},{7}}       => [[1,4,6],[2,5],[3],[7]]
{{1,4,7},{2},{3,5},{6}}       => [[1,4,7],[2,5],[3],[6]]
{{1,4},{2,7},{3,5},{6}}       => [[1,4],[2,5],[3,7],[6]]
{{1,4},{2},{3,5,7},{6}}       => [[1,4,7],[2,5],[3],[6]]
{{1,4},{2},{3,5},{6,7}}       => [[1,4],[2,5],[3,7],[6]]
{{1,4},{2},{3,5},{6},{7}}     => [[1,4],[2,5],[3],[6],[7]]
{{1,4,6,7},{2},{3},{5}}       => [[1,4,6,7],[2],[3],[5]]
{{1,4,6},{2,7},{3},{5}}       => [[1,4,6],[2,7],[3],[5]]
{{1,4,6},{2},{3,7},{5}}       => [[1,4,6],[2,7],[3],[5]]
{{1,4,6},{2},{3},{5,7}}       => [[1,4,6],[2,7],[3],[5]]
{{1,4,6},{2},{3},{5},{7}}     => [[1,4,6],[2],[3],[5],[7]]
{{1,4,7},{2,6},{3},{5}}       => [[1,4,7],[2,6],[3],[5]]
{{1,4},{2,6,7},{3},{5}}       => [[1,4,7],[2,6],[3],[5]]
{{1,4},{2,6},{3,7},{5}}       => [[1,4],[2,6],[3,7],[5]]
{{1,4},{2,6},{3},{5,7}}       => [[1,4],[2,6],[3,7],[5]]
{{1,4},{2,6},{3},{5},{7}}     => [[1,4],[2,6],[3],[5],[7]]
{{1,4,7},{2},{3,6},{5}}       => [[1,4,7],[2,6],[3],[5]]
{{1,4},{2,7},{3,6},{5}}       => [[1,4],[2,6],[3,7],[5]]
{{1,4},{2},{3,6,7},{5}}       => [[1,4,7],[2,6],[3],[5]]
{{1,4},{2},{3,6},{5,7}}       => [[1,4],[2,6],[3,7],[5]]
{{1,4},{2},{3,6},{5},{7}}     => [[1,4],[2,6],[3],[5],[7]]
{{1,4,7},{2},{3},{5,6}}       => [[1,4,7],[2,6],[3],[5]]
{{1,4},{2,7},{3},{5,6}}       => [[1,4],[2,6],[3,7],[5]]
{{1,4},{2},{3,7},{5,6}}       => [[1,4],[2,6],[3,7],[5]]
{{1,4},{2},{3},{5,6,7}}       => [[1,4,7],[2,6],[3],[5]]
{{1,4},{2},{3},{5,6},{7}}     => [[1,4],[2,6],[3],[5],[7]]
{{1,4,7},{2},{3},{5},{6}}     => [[1,4,7],[2],[3],[5],[6]]
{{1,4},{2,7},{3},{5},{6}}     => [[1,4],[2,7],[3],[5],[6]]
{{1,4},{2},{3,7},{5},{6}}     => [[1,4],[2,7],[3],[5],[6]]
{{1,4},{2},{3},{5,7},{6}}     => [[1,4],[2,7],[3],[5],[6]]
{{1,4},{2},{3},{5},{6,7}}     => [[1,4],[2,7],[3],[5],[6]]
{{1,4},{2},{3},{5},{6},{7}}   => [[1,4],[2],[3],[5],[6],[7]]
{{1,5,6,7},{2,4},{3}}         => [[1,4,6,7],[2,5],[3]]
{{1,5,6},{2,4,7},{3}}         => [[1,4,6],[2,5,7],[3]]
{{1,5,6},{2,4},{3,7}}         => [[1,4,6],[2,5],[3,7]]
{{1,5,6},{2,4},{3},{7}}       => [[1,4,6],[2,5],[3],[7]]
{{1,5,7},{2,4,6},{3}}         => [[1,4,6],[2,5,7],[3]]
{{1,5},{2,4,6,7},{3}}         => [[1,4,6,7],[2,5],[3]]
{{1,5},{2,4,6},{3,7}}         => [[1,4,6],[2,5],[3,7]]
{{1,5},{2,4,6},{3},{7}}       => [[1,4,6],[2,5],[3],[7]]
{{1,5,7},{2,4},{3,6}}         => [[1,4,7],[2,5],[3,6]]
{{1,5},{2,4,7},{3,6}}         => [[1,4,7],[2,5],[3,6]]
{{1,5},{2,4},{3,6,7}}         => [[1,4,7],[2,5],[3,6]]
{{1,5},{2,4},{3,6},{7}}       => [[1,4],[2,5],[3,6],[7]]
{{1,5,7},{2,4},{3},{6}}       => [[1,4,7],[2,5],[3],[6]]
{{1,5},{2,4,7},{3},{6}}       => [[1,4,7],[2,5],[3],[6]]
{{1,5},{2,4},{3,7},{6}}       => [[1,4],[2,5],[3,7],[6]]
{{1,5},{2,4},{3},{6,7}}       => [[1,4],[2,5],[3,7],[6]]
{{1,5},{2,4},{3},{6},{7}}     => [[1,4],[2,5],[3],[6],[7]]
{{1,6,7},{2,4,5},{3}}         => [[1,4,5],[2,6,7],[3]]
{{1,6},{2,4,5,7},{3}}         => [[1,4,5,7],[2,6],[3]]
{{1,6},{2,4,5},{3,7}}         => [[1,4,5],[2,6],[3,7]]
{{1,6},{2,4,5},{3},{7}}       => [[1,4,5],[2,6],[3],[7]]
{{1,7},{2,4,5,6},{3}}         => [[1,4,5,6],[2,7],[3]]
{{1},{2,4,5,6,7},{3}}         => [[1,4,5,6,7],[2],[3]]
{{1},{2,4,5,6},{3,7}}         => [[1,4,5,6],[2,7],[3]]
{{1},{2,4,5,6},{3},{7}}       => [[1,4,5,6],[2],[3],[7]]
{{1,7},{2,4,5},{3,6}}         => [[1,4,5],[2,6],[3,7]]
{{1},{2,4,5,7},{3,6}}         => [[1,4,5,7],[2,6],[3]]
{{1},{2,4,5},{3,6,7}}         => [[1,4,5],[2,6,7],[3]]
{{1},{2,4,5},{3,6},{7}}       => [[1,4,5],[2,6],[3],[7]]
{{1,7},{2,4,5},{3},{6}}       => [[1,4,5],[2,7],[3],[6]]
{{1},{2,4,5,7},{3},{6}}       => [[1,4,5,7],[2],[3],[6]]
{{1},{2,4,5},{3,7},{6}}       => [[1,4,5],[2,7],[3],[6]]
{{1},{2,4,5},{3},{6,7}}       => [[1,4,5],[2,7],[3],[6]]
{{1},{2,4,5},{3},{6},{7}}     => [[1,4,5],[2],[3],[6],[7]]
{{1,6,7},{2,4},{3,5}}         => [[1,4,7],[2,5],[3,6]]
{{1,6},{2,4,7},{3,5}}         => [[1,4,7],[2,5],[3,6]]
{{1,6},{2,4},{3,5,7}}         => [[1,4,7],[2,5],[3,6]]
{{1,6},{2,4},{3,5},{7}}       => [[1,4],[2,5],[3,6],[7]]
{{1,7},{2,4,6},{3,5}}         => [[1,4,6],[2,5],[3,7]]
{{1},{2,4,6,7},{3,5}}         => [[1,4,6,7],[2,5],[3]]
{{1},{2,4,6},{3,5,7}}         => [[1,4,6],[2,5,7],[3]]
{{1},{2,4,6},{3,5},{7}}       => [[1,4,6],[2,5],[3],[7]]
{{1,7},{2,4},{3,5,6}}         => [[1,4,6],[2,5],[3,7]]
{{1},{2,4,7},{3,5,6}}         => [[1,4,6],[2,5,7],[3]]
{{1},{2,4},{3,5,6,7}}         => [[1,4,6,7],[2,5],[3]]
{{1},{2,4},{3,5,6},{7}}       => [[1,4,6],[2,5],[3],[7]]
{{1,7},{2,4},{3,5},{6}}       => [[1,4],[2,5],[3,7],[6]]
{{1},{2,4,7},{3,5},{6}}       => [[1,4,7],[2,5],[3],[6]]
{{1},{2,4},{3,5,7},{6}}       => [[1,4,7],[2,5],[3],[6]]
{{1},{2,4},{3,5},{6,7}}       => [[1,4],[2,5],[3,7],[6]]
{{1},{2,4},{3,5},{6},{7}}     => [[1,4],[2,5],[3],[6],[7]]
{{1,6,7},{2,4},{3},{5}}       => [[1,4,7],[2,6],[3],[5]]
{{1,6},{2,4,7},{3},{5}}       => [[1,4,7],[2,6],[3],[5]]
{{1,6},{2,4},{3,7},{5}}       => [[1,4],[2,6],[3,7],[5]]
{{1,6},{2,4},{3},{5,7}}       => [[1,4],[2,6],[3,7],[5]]
{{1,6},{2,4},{3},{5},{7}}     => [[1,4],[2,6],[3],[5],[7]]
{{1,7},{2,4,6},{3},{5}}       => [[1,4,6],[2,7],[3],[5]]
{{1},{2,4,6,7},{3},{5}}       => [[1,4,6,7],[2],[3],[5]]
{{1},{2,4,6},{3,7},{5}}       => [[1,4,6],[2,7],[3],[5]]
{{1},{2,4,6},{3},{5,7}}       => [[1,4,6],[2,7],[3],[5]]
{{1},{2,4,6},{3},{5},{7}}     => [[1,4,6],[2],[3],[5],[7]]
{{1,7},{2,4},{3,6},{5}}       => [[1,4],[2,6],[3,7],[5]]
{{1},{2,4,7},{3,6},{5}}       => [[1,4,7],[2,6],[3],[5]]
{{1},{2,4},{3,6,7},{5}}       => [[1,4,7],[2,6],[3],[5]]
{{1},{2,4},{3,6},{5,7}}       => [[1,4],[2,6],[3,7],[5]]
{{1},{2,4},{3,6},{5},{7}}     => [[1,4],[2,6],[3],[5],[7]]
{{1,7},{2,4},{3},{5,6}}       => [[1,4],[2,6],[3,7],[5]]
{{1},{2,4,7},{3},{5,6}}       => [[1,4,7],[2,6],[3],[5]]
{{1},{2,4},{3,7},{5,6}}       => [[1,4],[2,6],[3,7],[5]]
{{1},{2,4},{3},{5,6,7}}       => [[1,4,7],[2,6],[3],[5]]
{{1},{2,4},{3},{5,6},{7}}     => [[1,4],[2,6],[3],[5],[7]]
{{1,7},{2,4},{3},{5},{6}}     => [[1,4],[2,7],[3],[5],[6]]
{{1},{2,4,7},{3},{5},{6}}     => [[1,4,7],[2],[3],[5],[6]]
{{1},{2,4},{3,7},{5},{6}}     => [[1,4],[2,7],[3],[5],[6]]
{{1},{2,4},{3},{5,7},{6}}     => [[1,4],[2,7],[3],[5],[6]]
{{1},{2,4},{3},{5},{6,7}}     => [[1,4],[2,7],[3],[5],[6]]
{{1},{2,4},{3},{5},{6},{7}}   => [[1,4],[2],[3],[5],[6],[7]]
{{1,5,6,7},{2},{3,4}}         => [[1,4,6,7],[2,5],[3]]
{{1,5,6},{2,7},{3,4}}         => [[1,4,6],[2,5],[3,7]]
{{1,5,6},{2},{3,4,7}}         => [[1,4,6],[2,5,7],[3]]
{{1,5,6},{2},{3,4},{7}}       => [[1,4,6],[2,5],[3],[7]]
{{1,5,7},{2,6},{3,4}}         => [[1,4,7],[2,5],[3,6]]
{{1,5},{2,6,7},{3,4}}         => [[1,4,7],[2,5],[3,6]]
{{1,5},{2,6},{3,4,7}}         => [[1,4,7],[2,5],[3,6]]
{{1,5},{2,6},{3,4},{7}}       => [[1,4],[2,5],[3,6],[7]]
{{1,5,7},{2},{3,4,6}}         => [[1,4,6],[2,5,7],[3]]
{{1,5},{2,7},{3,4,6}}         => [[1,4,6],[2,5],[3,7]]
{{1,5},{2},{3,4,6,7}}         => [[1,4,6,7],[2,5],[3]]
{{1,5},{2},{3,4,6},{7}}       => [[1,4,6],[2,5],[3],[7]]
{{1,5,7},{2},{3,4},{6}}       => [[1,4,7],[2,5],[3],[6]]
{{1,5},{2,7},{3,4},{6}}       => [[1,4],[2,5],[3,7],[6]]
{{1,5},{2},{3,4,7},{6}}       => [[1,4,7],[2,5],[3],[6]]
{{1,5},{2},{3,4},{6,7}}       => [[1,4],[2,5],[3,7],[6]]
{{1,5},{2},{3,4},{6},{7}}     => [[1,4],[2,5],[3],[6],[7]]
{{1,6,7},{2,5},{3,4}}         => [[1,4,7],[2,5],[3,6]]
{{1,6},{2,5,7},{3,4}}         => [[1,4,7],[2,5],[3,6]]
{{1,6},{2,5},{3,4,7}}         => [[1,4,7],[2,5],[3,6]]
{{1,6},{2,5},{3,4},{7}}       => [[1,4],[2,5],[3,6],[7]]
{{1,7},{2,5,6},{3,4}}         => [[1,4,6],[2,5],[3,7]]
{{1},{2,5,6,7},{3,4}}         => [[1,4,6,7],[2,5],[3]]
{{1},{2,5,6},{3,4,7}}         => [[1,4,6],[2,5,7],[3]]
{{1},{2,5,6},{3,4},{7}}       => [[1,4,6],[2,5],[3],[7]]
{{1,7},{2,5},{3,4,6}}         => [[1,4,6],[2,5],[3,7]]
{{1},{2,5,7},{3,4,6}}         => [[1,4,6],[2,5,7],[3]]
{{1},{2,5},{3,4,6,7}}         => [[1,4,6,7],[2,5],[3]]
{{1},{2,5},{3,4,6},{7}}       => [[1,4,6],[2,5],[3],[7]]
{{1,7},{2,5},{3,4},{6}}       => [[1,4],[2,5],[3,7],[6]]
{{1},{2,5,7},{3,4},{6}}       => [[1,4,7],[2,5],[3],[6]]
{{1},{2,5},{3,4,7},{6}}       => [[1,4,7],[2,5],[3],[6]]
{{1},{2,5},{3,4},{6,7}}       => [[1,4],[2,5],[3,7],[6]]
{{1},{2,5},{3,4},{6},{7}}     => [[1,4],[2,5],[3],[6],[7]]
{{1,6,7},{2},{3,4,5}}         => [[1,4,5],[2,6,7],[3]]
{{1,6},{2,7},{3,4,5}}         => [[1,4,5],[2,6],[3,7]]
{{1,6},{2},{3,4,5,7}}         => [[1,4,5,7],[2,6],[3]]
{{1,6},{2},{3,4,5},{7}}       => [[1,4,5],[2,6],[3],[7]]
{{1,7},{2,6},{3,4,5}}         => [[1,4,5],[2,6],[3,7]]
{{1},{2,6,7},{3,4,5}}         => [[1,4,5],[2,6,7],[3]]
{{1},{2,6},{3,4,5,7}}         => [[1,4,5,7],[2,6],[3]]
{{1},{2,6},{3,4,5},{7}}       => [[1,4,5],[2,6],[3],[7]]
{{1,7},{2},{3,4,5,6}}         => [[1,4,5,6],[2,7],[3]]
{{1},{2,7},{3,4,5,6}}         => [[1,4,5,6],[2,7],[3]]
{{1},{2},{3,4,5,6,7}}         => [[1,4,5,6,7],[2],[3]]
{{1},{2},{3,4,5,6},{7}}       => [[1,4,5,6],[2],[3],[7]]
{{1,7},{2},{3,4,5},{6}}       => [[1,4,5],[2,7],[3],[6]]
{{1},{2,7},{3,4,5},{6}}       => [[1,4,5],[2,7],[3],[6]]
{{1},{2},{3,4,5,7},{6}}       => [[1,4,5,7],[2],[3],[6]]
{{1},{2},{3,4,5},{6,7}}       => [[1,4,5],[2,7],[3],[6]]
{{1},{2},{3,4,5},{6},{7}}     => [[1,4,5],[2],[3],[6],[7]]
{{1,6,7},{2},{3,4},{5}}       => [[1,4,7],[2,6],[3],[5]]
{{1,6},{2,7},{3,4},{5}}       => [[1,4],[2,6],[3,7],[5]]
{{1,6},{2},{3,4,7},{5}}       => [[1,4,7],[2,6],[3],[5]]
{{1,6},{2},{3,4},{5,7}}       => [[1,4],[2,6],[3,7],[5]]
{{1,6},{2},{3,4},{5},{7}}     => [[1,4],[2,6],[3],[5],[7]]
{{1,7},{2,6},{3,4},{5}}       => [[1,4],[2,6],[3,7],[5]]
{{1},{2,6,7},{3,4},{5}}       => [[1,4,7],[2,6],[3],[5]]
{{1},{2,6},{3,4,7},{5}}       => [[1,4,7],[2,6],[3],[5]]
{{1},{2,6},{3,4},{5,7}}       => [[1,4],[2,6],[3,7],[5]]
{{1},{2,6},{3,4},{5},{7}}     => [[1,4],[2,6],[3],[5],[7]]
{{1,7},{2},{3,4,6},{5}}       => [[1,4,6],[2,7],[3],[5]]
{{1},{2,7},{3,4,6},{5}}       => [[1,4,6],[2,7],[3],[5]]
{{1},{2},{3,4,6,7},{5}}       => [[1,4,6,7],[2],[3],[5]]
{{1},{2},{3,4,6},{5,7}}       => [[1,4,6],[2,7],[3],[5]]
{{1},{2},{3,4,6},{5},{7}}     => [[1,4,6],[2],[3],[5],[7]]
{{1,7},{2},{3,4},{5,6}}       => [[1,4],[2,6],[3,7],[5]]
{{1},{2,7},{3,4},{5,6}}       => [[1,4],[2,6],[3,7],[5]]
{{1},{2},{3,4,7},{5,6}}       => [[1,4,7],[2,6],[3],[5]]
{{1},{2},{3,4},{5,6,7}}       => [[1,4,7],[2,6],[3],[5]]
{{1},{2},{3,4},{5,6},{7}}     => [[1,4],[2,6],[3],[5],[7]]
{{1,7},{2},{3,4},{5},{6}}     => [[1,4],[2,7],[3],[5],[6]]
{{1},{2,7},{3,4},{5},{6}}     => [[1,4],[2,7],[3],[5],[6]]
{{1},{2},{3,4,7},{5},{6}}     => [[1,4,7],[2],[3],[5],[6]]
{{1},{2},{3,4},{5,7},{6}}     => [[1,4],[2,7],[3],[5],[6]]
{{1},{2},{3,4},{5},{6,7}}     => [[1,4],[2,7],[3],[5],[6]]
{{1},{2},{3,4},{5},{6},{7}}   => [[1,4],[2],[3],[5],[6],[7]]
{{1,5,6,7},{2},{3},{4}}       => [[1,5,6,7],[2],[3],[4]]
{{1,5,6},{2,7},{3},{4}}       => [[1,5,6],[2,7],[3],[4]]
{{1,5,6},{2},{3,7},{4}}       => [[1,5,6],[2,7],[3],[4]]
{{1,5,6},{2},{3},{4,7}}       => [[1,5,6],[2,7],[3],[4]]
{{1,5,6},{2},{3},{4},{7}}     => [[1,5,6],[2],[3],[4],[7]]
{{1,5,7},{2,6},{3},{4}}       => [[1,5,7],[2,6],[3],[4]]
{{1,5},{2,6,7},{3},{4}}       => [[1,5,7],[2,6],[3],[4]]
{{1,5},{2,6},{3,7},{4}}       => [[1,5],[2,6],[3,7],[4]]
{{1,5},{2,6},{3},{4,7}}       => [[1,5],[2,6],[3,7],[4]]
{{1,5},{2,6},{3},{4},{7}}     => [[1,5],[2,6],[3],[4],[7]]
{{1,5,7},{2},{3,6},{4}}       => [[1,5,7],[2,6],[3],[4]]
{{1,5},{2,7},{3,6},{4}}       => [[1,5],[2,6],[3,7],[4]]
{{1,5},{2},{3,6,7},{4}}       => [[1,5,7],[2,6],[3],[4]]
{{1,5},{2},{3,6},{4,7}}       => [[1,5],[2,6],[3,7],[4]]
{{1,5},{2},{3,6},{4},{7}}     => [[1,5],[2,6],[3],[4],[7]]
{{1,5,7},{2},{3},{4,6}}       => [[1,5,7],[2,6],[3],[4]]
{{1,5},{2,7},{3},{4,6}}       => [[1,5],[2,6],[3,7],[4]]
{{1,5},{2},{3,7},{4,6}}       => [[1,5],[2,6],[3,7],[4]]
{{1,5},{2},{3},{4,6,7}}       => [[1,5,7],[2,6],[3],[4]]
{{1,5},{2},{3},{4,6},{7}}     => [[1,5],[2,6],[3],[4],[7]]
{{1,5,7},{2},{3},{4},{6}}     => [[1,5,7],[2],[3],[4],[6]]
{{1,5},{2,7},{3},{4},{6}}     => [[1,5],[2,7],[3],[4],[6]]
{{1,5},{2},{3,7},{4},{6}}     => [[1,5],[2,7],[3],[4],[6]]
{{1,5},{2},{3},{4,7},{6}}     => [[1,5],[2,7],[3],[4],[6]]
{{1,5},{2},{3},{4},{6,7}}     => [[1,5],[2,7],[3],[4],[6]]
{{1,5},{2},{3},{4},{6},{7}}   => [[1,5],[2],[3],[4],[6],[7]]
{{1,6,7},{2,5},{3},{4}}       => [[1,5,7],[2,6],[3],[4]]
{{1,6},{2,5,7},{3},{4}}       => [[1,5,7],[2,6],[3],[4]]
{{1,6},{2,5},{3,7},{4}}       => [[1,5],[2,6],[3,7],[4]]
{{1,6},{2,5},{3},{4,7}}       => [[1,5],[2,6],[3,7],[4]]
{{1,6},{2,5},{3},{4},{7}}     => [[1,5],[2,6],[3],[4],[7]]
{{1,7},{2,5,6},{3},{4}}       => [[1,5,6],[2,7],[3],[4]]
{{1},{2,5,6,7},{3},{4}}       => [[1,5,6,7],[2],[3],[4]]
{{1},{2,5,6},{3,7},{4}}       => [[1,5,6],[2,7],[3],[4]]
{{1},{2,5,6},{3},{4,7}}       => [[1,5,6],[2,7],[3],[4]]
{{1},{2,5,6},{3},{4},{7}}     => [[1,5,6],[2],[3],[4],[7]]
{{1,7},{2,5},{3,6},{4}}       => [[1,5],[2,6],[3,7],[4]]
{{1},{2,5,7},{3,6},{4}}       => [[1,5,7],[2,6],[3],[4]]
{{1},{2,5},{3,6,7},{4}}       => [[1,5,7],[2,6],[3],[4]]
{{1},{2,5},{3,6},{4,7}}       => [[1,5],[2,6],[3,7],[4]]
{{1},{2,5},{3,6},{4},{7}}     => [[1,5],[2,6],[3],[4],[7]]
{{1,7},{2,5},{3},{4,6}}       => [[1,5],[2,6],[3,7],[4]]
{{1},{2,5,7},{3},{4,6}}       => [[1,5,7],[2,6],[3],[4]]
{{1},{2,5},{3,7},{4,6}}       => [[1,5],[2,6],[3,7],[4]]
{{1},{2,5},{3},{4,6,7}}       => [[1,5,7],[2,6],[3],[4]]
{{1},{2,5},{3},{4,6},{7}}     => [[1,5],[2,6],[3],[4],[7]]
{{1,7},{2,5},{3},{4},{6}}     => [[1,5],[2,7],[3],[4],[6]]
{{1},{2,5,7},{3},{4},{6}}     => [[1,5,7],[2],[3],[4],[6]]
{{1},{2,5},{3,7},{4},{6}}     => [[1,5],[2,7],[3],[4],[6]]
{{1},{2,5},{3},{4,7},{6}}     => [[1,5],[2,7],[3],[4],[6]]
{{1},{2,5},{3},{4},{6,7}}     => [[1,5],[2,7],[3],[4],[6]]
{{1},{2,5},{3},{4},{6},{7}}   => [[1,5],[2],[3],[4],[6],[7]]
{{1,6,7},{2},{3,5},{4}}       => [[1,5,7],[2,6],[3],[4]]
{{1,6},{2,7},{3,5},{4}}       => [[1,5],[2,6],[3,7],[4]]
{{1,6},{2},{3,5,7},{4}}       => [[1,5,7],[2,6],[3],[4]]
{{1,6},{2},{3,5},{4,7}}       => [[1,5],[2,6],[3,7],[4]]
{{1,6},{2},{3,5},{4},{7}}     => [[1,5],[2,6],[3],[4],[7]]
{{1,7},{2,6},{3,5},{4}}       => [[1,5],[2,6],[3,7],[4]]
{{1},{2,6,7},{3,5},{4}}       => [[1,5,7],[2,6],[3],[4]]
{{1},{2,6},{3,5,7},{4}}       => [[1,5,7],[2,6],[3],[4]]
{{1},{2,6},{3,5},{4,7}}       => [[1,5],[2,6],[3,7],[4]]
{{1},{2,6},{3,5},{4},{7}}     => [[1,5],[2,6],[3],[4],[7]]
{{1,7},{2},{3,5,6},{4}}       => [[1,5,6],[2,7],[3],[4]]
{{1},{2,7},{3,5,6},{4}}       => [[1,5,6],[2,7],[3],[4]]
{{1},{2},{3,5,6,7},{4}}       => [[1,5,6,7],[2],[3],[4]]
{{1},{2},{3,5,6},{4,7}}       => [[1,5,6],[2,7],[3],[4]]
{{1},{2},{3,5,6},{4},{7}}     => [[1,5,6],[2],[3],[4],[7]]
{{1,7},{2},{3,5},{4,6}}       => [[1,5],[2,6],[3,7],[4]]
{{1},{2,7},{3,5},{4,6}}       => [[1,5],[2,6],[3,7],[4]]
{{1},{2},{3,5,7},{4,6}}       => [[1,5,7],[2,6],[3],[4]]
{{1},{2},{3,5},{4,6,7}}       => [[1,5,7],[2,6],[3],[4]]
{{1},{2},{3,5},{4,6},{7}}     => [[1,5],[2,6],[3],[4],[7]]
{{1,7},{2},{3,5},{4},{6}}     => [[1,5],[2,7],[3],[4],[6]]
{{1},{2,7},{3,5},{4},{6}}     => [[1,5],[2,7],[3],[4],[6]]
{{1},{2},{3,5,7},{4},{6}}     => [[1,5,7],[2],[3],[4],[6]]
{{1},{2},{3,5},{4,7},{6}}     => [[1,5],[2,7],[3],[4],[6]]
{{1},{2},{3,5},{4},{6,7}}     => [[1,5],[2,7],[3],[4],[6]]
{{1},{2},{3,5},{4},{6},{7}}   => [[1,5],[2],[3],[4],[6],[7]]
{{1,6,7},{2},{3},{4,5}}       => [[1,5,7],[2,6],[3],[4]]
{{1,6},{2,7},{3},{4,5}}       => [[1,5],[2,6],[3,7],[4]]
{{1,6},{2},{3,7},{4,5}}       => [[1,5],[2,6],[3,7],[4]]
{{1,6},{2},{3},{4,5,7}}       => [[1,5,7],[2,6],[3],[4]]
{{1,6},{2},{3},{4,5},{7}}     => [[1,5],[2,6],[3],[4],[7]]
{{1,7},{2,6},{3},{4,5}}       => [[1,5],[2,6],[3,7],[4]]
{{1},{2,6,7},{3},{4,5}}       => [[1,5,7],[2,6],[3],[4]]
{{1},{2,6},{3,7},{4,5}}       => [[1,5],[2,6],[3,7],[4]]
{{1},{2,6},{3},{4,5,7}}       => [[1,5,7],[2,6],[3],[4]]
{{1},{2,6},{3},{4,5},{7}}     => [[1,5],[2,6],[3],[4],[7]]
{{1,7},{2},{3,6},{4,5}}       => [[1,5],[2,6],[3,7],[4]]
{{1},{2,7},{3,6},{4,5}}       => [[1,5],[2,6],[3,7],[4]]
{{1},{2},{3,6,7},{4,5}}       => [[1,5,7],[2,6],[3],[4]]
{{1},{2},{3,6},{4,5,7}}       => [[1,5,7],[2,6],[3],[4]]
{{1},{2},{3,6},{4,5},{7}}     => [[1,5],[2,6],[3],[4],[7]]
{{1,7},{2},{3},{4,5,6}}       => [[1,5,6],[2,7],[3],[4]]
{{1},{2,7},{3},{4,5,6}}       => [[1,5,6],[2,7],[3],[4]]
{{1},{2},{3,7},{4,5,6}}       => [[1,5,6],[2,7],[3],[4]]
{{1},{2},{3},{4,5,6,7}}       => [[1,5,6,7],[2],[3],[4]]
{{1},{2},{3},{4,5,6},{7}}     => [[1,5,6],[2],[3],[4],[7]]
{{1,7},{2},{3},{4,5},{6}}     => [[1,5],[2,7],[3],[4],[6]]
{{1},{2,7},{3},{4,5},{6}}     => [[1,5],[2,7],[3],[4],[6]]
{{1},{2},{3,7},{4,5},{6}}     => [[1,5],[2,7],[3],[4],[6]]
{{1},{2},{3},{4,5,7},{6}}     => [[1,5,7],[2],[3],[4],[6]]
{{1},{2},{3},{4,5},{6,7}}     => [[1,5],[2,7],[3],[4],[6]]
{{1},{2},{3},{4,5},{6},{7}}   => [[1,5],[2],[3],[4],[6],[7]]
{{1,6,7},{2},{3},{4},{5}}     => [[1,6,7],[2],[3],[4],[5]]
{{1,6},{2,7},{3},{4},{5}}     => [[1,6],[2,7],[3],[4],[5]]
{{1,6},{2},{3,7},{4},{5}}     => [[1,6],[2,7],[3],[4],[5]]
{{1,6},{2},{3},{4,7},{5}}     => [[1,6],[2,7],[3],[4],[5]]
{{1,6},{2},{3},{4},{5,7}}     => [[1,6],[2,7],[3],[4],[5]]
{{1,6},{2},{3},{4},{5},{7}}   => [[1,6],[2],[3],[4],[5],[7]]
{{1,7},{2,6},{3},{4},{5}}     => [[1,6],[2,7],[3],[4],[5]]
{{1},{2,6,7},{3},{4},{5}}     => [[1,6,7],[2],[3],[4],[5]]
{{1},{2,6},{3,7},{4},{5}}     => [[1,6],[2,7],[3],[4],[5]]
{{1},{2,6},{3},{4,7},{5}}     => [[1,6],[2,7],[3],[4],[5]]
{{1},{2,6},{3},{4},{5,7}}     => [[1,6],[2,7],[3],[4],[5]]
{{1},{2,6},{3},{4},{5},{7}}   => [[1,6],[2],[3],[4],[5],[7]]
{{1,7},{2},{3,6},{4},{5}}     => [[1,6],[2,7],[3],[4],[5]]
{{1},{2,7},{3,6},{4},{5}}     => [[1,6],[2,7],[3],[4],[5]]
{{1},{2},{3,6,7},{4},{5}}     => [[1,6,7],[2],[3],[4],[5]]
{{1},{2},{3,6},{4,7},{5}}     => [[1,6],[2,7],[3],[4],[5]]
{{1},{2},{3,6},{4},{5,7}}     => [[1,6],[2,7],[3],[4],[5]]
{{1},{2},{3,6},{4},{5},{7}}   => [[1,6],[2],[3],[4],[5],[7]]
{{1,7},{2},{3},{4,6},{5}}     => [[1,6],[2,7],[3],[4],[5]]
{{1},{2,7},{3},{4,6},{5}}     => [[1,6],[2,7],[3],[4],[5]]
{{1},{2},{3,7},{4,6},{5}}     => [[1,6],[2,7],[3],[4],[5]]
{{1},{2},{3},{4,6,7},{5}}     => [[1,6,7],[2],[3],[4],[5]]
{{1},{2},{3},{4,6},{5,7}}     => [[1,6],[2,7],[3],[4],[5]]
{{1},{2},{3},{4,6},{5},{7}}   => [[1,6],[2],[3],[4],[5],[7]]
{{1,7},{2},{3},{4},{5,6}}     => [[1,6],[2,7],[3],[4],[5]]
{{1},{2,7},{3},{4},{5,6}}     => [[1,6],[2,7],[3],[4],[5]]
{{1},{2},{3,7},{4},{5,6}}     => [[1,6],[2,7],[3],[4],[5]]
{{1},{2},{3},{4,7},{5,6}}     => [[1,6],[2,7],[3],[4],[5]]
{{1},{2},{3},{4},{5,6,7}}     => [[1,6,7],[2],[3],[4],[5]]
{{1},{2},{3},{4},{5,6},{7}}   => [[1,6],[2],[3],[4],[5],[7]]
{{1,7},{2},{3},{4},{5},{6}}   => [[1,7],[2],[3],[4],[5],[6]]
{{1},{2,7},{3},{4},{5},{6}}   => [[1,7],[2],[3],[4],[5],[6]]
{{1},{2},{3,7},{4},{5},{6}}   => [[1,7],[2],[3],[4],[5],[6]]
{{1},{2},{3},{4,7},{5},{6}}   => [[1,7],[2],[3],[4],[5],[6]]
{{1},{2},{3},{4},{5,7},{6}}   => [[1,7],[2],[3],[4],[5],[6]]
{{1},{2},{3},{4},{5},{6,7}}   => [[1,7],[2],[3],[4],[5],[6]]
{{1},{2},{3},{4},{5},{6},{7}} => [[1],[2],[3],[4],[5],[6],[7]]
{{1,2},{3,4},{5,6},{7,8}}     => [[1,2],[3,4],[5,6],[7,8]]
{{1,3},{2,4},{5,6},{7,8}}     => [[1,3],[2,4],[5,6],[7,8]]
{{1,4},{2,3},{5,6},{7,8}}     => [[1,3],[2,4],[5,6],[7,8]]
{{1,5},{2,3},{4,6},{7,8}}     => [[1,3],[2,5],[4,6],[7,8]]
{{1,6},{2,3},{4,5},{7,8}}     => [[1,3],[2,5],[4,6],[7,8]]
{{1,7},{2,3},{4,5},{6,8}}     => [[1,3],[2,5],[4,7],[6,8]]
{{1,8},{2,3},{4,5},{6,7}}     => [[1,3],[2,5],[4,7],[6,8]]
{{1,8},{2,4},{3,5},{6,7}}     => [[1,4],[2,5],[3,7],[6,8]]
{{1,7},{2,4},{3,5},{6,8}}     => [[1,4],[2,5],[3,7],[6,8]]
{{1,6},{2,4},{3,5},{7,8}}     => [[1,4],[2,5],[3,6],[7,8]]
{{1,5},{2,4},{3,6},{7,8}}     => [[1,4],[2,5],[3,6],[7,8]]
{{1,4},{2,5},{3,6},{7,8}}     => [[1,4],[2,5],[3,6],[7,8]]
{{1,3},{2,5},{4,6},{7,8}}     => [[1,3],[2,5],[4,6],[7,8]]
{{1,2},{3,5},{4,6},{7,8}}     => [[1,2],[3,5],[4,6],[7,8]]
{{1,2},{3,6},{4,5},{7,8}}     => [[1,2],[3,5],[4,6],[7,8]]
{{1,3},{2,6},{4,5},{7,8}}     => [[1,3],[2,5],[4,6],[7,8]]
{{1,4},{2,6},{3,5},{7,8}}     => [[1,4],[2,5],[3,6],[7,8]]
{{1,5},{2,6},{3,4},{7,8}}     => [[1,4],[2,5],[3,6],[7,8]]
{{1,6},{2,5},{3,4},{7,8}}     => [[1,4],[2,5],[3,6],[7,8]]
{{1,7},{2,5},{3,4},{6,8}}     => [[1,4],[2,5],[3,7],[6,8]]
{{1,8},{2,5},{3,4},{6,7}}     => [[1,4],[2,5],[3,7],[6,8]]
{{1,8},{2,6},{3,4},{5,7}}     => [[1,4],[2,6],[3,7],[5,8]]
{{1,7},{2,6},{3,4},{5,8}}     => [[1,4],[2,6],[3,7],[5,8]]
{{1,6},{2,7},{3,4},{5,8}}     => [[1,4],[2,6],[3,7],[5,8]]
{{1,5},{2,7},{3,4},{6,8}}     => [[1,4],[2,5],[3,7],[6,8]]
{{1,4},{2,7},{3,5},{6,8}}     => [[1,4],[2,5],[3,7],[6,8]]
{{1,3},{2,7},{4,5},{6,8}}     => [[1,3],[2,5],[4,7],[6,8]]
{{1,2},{3,7},{4,5},{6,8}}     => [[1,2],[3,5],[4,7],[6,8]]
{{1,2},{3,8},{4,5},{6,7}}     => [[1,2],[3,5],[4,7],[6,8]]
{{1,3},{2,8},{4,5},{6,7}}     => [[1,3],[2,5],[4,7],[6,8]]
{{1,4},{2,8},{3,5},{6,7}}     => [[1,4],[2,5],[3,7],[6,8]]
{{1,5},{2,8},{3,4},{6,7}}     => [[1,4],[2,5],[3,7],[6,8]]
{{1,6},{2,8},{3,4},{5,7}}     => [[1,4],[2,6],[3,7],[5,8]]
{{1,7},{2,8},{3,4},{5,6}}     => [[1,4],[2,6],[3,7],[5,8]]
{{1,8},{2,7},{3,4},{5,6}}     => [[1,4],[2,6],[3,7],[5,8]]
{{1,8},{2,7},{3,5},{4,6}}     => [[1,5],[2,6],[3,7],[4,8]]
{{1,7},{2,8},{3,5},{4,6}}     => [[1,5],[2,6],[3,7],[4,8]]
{{1,6},{2,8},{3,5},{4,7}}     => [[1,5],[2,6],[3,7],[4,8]]
{{1,5},{2,8},{3,6},{4,7}}     => [[1,5],[2,6],[3,7],[4,8]]
{{1,4},{2,8},{3,6},{5,7}}     => [[1,4],[2,6],[3,7],[5,8]]
{{1,3},{2,8},{4,6},{5,7}}     => [[1,3],[2,6],[4,7],[5,8]]
{{1,2},{3,8},{4,6},{5,7}}     => [[1,2],[3,6],[4,7],[5,8]]
{{1,2},{3,7},{4,6},{5,8}}     => [[1,2],[3,6],[4,7],[5,8]]
{{1,3},{2,7},{4,6},{5,8}}     => [[1,3],[2,6],[4,7],[5,8]]
{{1,4},{2,7},{3,6},{5,8}}     => [[1,4],[2,6],[3,7],[5,8]]

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Created: Jul 20, 2022 at 16:52 by Amritanshu Prasad

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Last Updated: Jul 20, 2022 at 16:52 by Amritanshu Prasad