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Identifier
Values
=>
Cc0025;cc-rep
[[1]]=>1 [[1],[1]]=>1 [[2]]=>1 [[1,1]]=>1 [[1],[1],[1]]=>1 [[2],[1]]=>2 [[1,1],[1]]=>2 [[3]]=>1 [[2,1]]=>2 [[1,1,1]]=>1 [[1],[1],[1],[1]]=>1 [[2],[1],[1]]=>2 [[2],[2]]=>1 [[1,1],[1],[1]]=>2 [[1,1],[1,1]]=>1 [[3],[1]]=>2 [[2,1],[1]]=>3 [[1,1,1],[1]]=>2 [[4]]=>1 [[3,1]]=>2 [[2,2]]=>1 [[2,1,1]]=>2 [[1,1,1,1]]=>1 [[1],[1],[1],[1],[1]]=>1 [[2],[1],[1],[1]]=>2 [[2],[2],[1]]=>2 [[1,1],[1],[1],[1]]=>2 [[1,1],[1,1],[1]]=>2 [[3],[1],[1]]=>2 [[3],[2]]=>2 [[2,1],[1],[1]]=>3 [[2,1],[2]]=>2 [[2,1],[1,1]]=>2 [[1,1,1],[1],[1]]=>2 [[1,1,1],[1,1]]=>2 [[4],[1]]=>2 [[3,1],[1]]=>3 [[2,2],[1]]=>2 [[2,1,1],[1]]=>3 [[1,1,1,1],[1]]=>2 [[5]]=>1 [[4,1]]=>2 [[3,2]]=>2 [[3,1,1]]=>2 [[2,2,1]]=>2 [[2,1,1,1]]=>2 [[1,1,1,1,1]]=>1 [[1],[1],[1],[1],[1],[1]]=>1 [[2],[1],[1],[1],[1]]=>2 [[2],[2],[1],[1]]=>2 [[2],[2],[2]]=>1 [[1,1],[1],[1],[1],[1]]=>2 [[1,1],[1,1],[1],[1]]=>2 [[1,1],[1,1],[1,1]]=>1 [[3],[1],[1],[1]]=>2 [[3],[2],[1]]=>3 [[3],[3]]=>1 [[2,1],[1],[1],[1]]=>3 [[2,1],[2],[1]]=>3 [[2,1],[1,1],[1]]=>3 [[2,1],[2,1]]=>2 [[1,1,1],[1],[1],[1]]=>2 [[1,1,1],[1,1],[1]]=>3 [[1,1,1],[1,1,1]]=>1 [[4],[1],[1]]=>2 [[4],[2]]=>2 [[3,1],[1],[1]]=>3 [[3,1],[2]]=>3 [[3,1],[1,1]]=>2 [[2,2],[1],[1]]=>2 [[2,2],[2]]=>2 [[2,2],[1,1]]=>2 [[2,1,1],[1],[1]]=>3 [[2,1,1],[2]]=>2 [[2,1,1],[1,1]]=>3 [[1,1,1,1],[1],[1]]=>2 [[1,1,1,1],[1,1]]=>2 [[5],[1]]=>2 [[4,1],[1]]=>3 [[3,2],[1]]=>3 [[3,1,1],[1]]=>3 [[2,2,1],[1]]=>3 [[2,1,1,1],[1]]=>3 [[1,1,1,1,1],[1]]=>2 [[6]]=>1 [[5,1]]=>2 [[4,2]]=>2 [[4,1,1]]=>2 [[3,3]]=>1 [[3,2,1]]=>3 [[3,1,1,1]]=>2 [[2,2,2]]=>1 [[2,2,1,1]]=>2 [[2,1,1,1,1]]=>2 [[1,1,1,1,1,1]]=>1 [[1],[1],[1],[1],[1],[1],[1]]=>1 [[2],[1],[1],[1],[1],[1]]=>2 [[2],[2],[1],[1],[1]]=>2 [[2],[2],[2],[1]]=>2 [[1,1],[1],[1],[1],[1],[1]]=>2 [[1,1],[1,1],[1],[1],[1]]=>2 [[1,1],[1,1],[1,1],[1]]=>2 [[3],[1],[1],[1],[1]]=>2 [[3],[2],[1],[1]]=>3 [[3],[2],[2]]=>2 [[3],[3],[1]]=>2 [[2,1],[1],[1],[1],[1]]=>3 [[2,1],[2],[1],[1]]=>3 [[2,1],[2],[2]]=>2 [[2,1],[1,1],[1],[1]]=>3 [[2,1],[1,1],[1,1]]=>2 [[2,1],[2,1],[1]]=>3 [[1,1,1],[1],[1],[1],[1]]=>2 [[1,1,1],[1,1],[1],[1]]=>3 [[1,1,1],[1,1],[1,1]]=>2 [[1,1,1],[1,1,1],[1]]=>2 [[4],[1],[1],[1]]=>2 [[4],[2],[1]]=>3 [[4],[3]]=>2 [[3,1],[1],[1],[1]]=>3 [[3,1],[2],[1]]=>4 [[3,1],[1,1],[1]]=>3 [[3,1],[3]]=>2 [[3,1],[2,1]]=>3 [[2,2],[1],[1],[1]]=>2 [[2,2],[2],[1]]=>3 [[2,2],[1,1],[1]]=>3 [[2,2],[2,1]]=>3 [[2,1,1],[1],[1],[1]]=>3 [[2,1,1],[2],[1]]=>3 [[2,1,1],[1,1],[1]]=>4 [[2,1,1],[2,1]]=>3 [[2,1,1],[1,1,1]]=>2 [[1,1,1,1],[1],[1],[1]]=>2 [[1,1,1,1],[1,1],[1]]=>3 [[1,1,1,1],[1,1,1]]=>2 [[5],[1],[1]]=>2 [[5],[2]]=>2 [[4,1],[1],[1]]=>3 [[4,1],[2]]=>3 [[4,1],[1,1]]=>2 [[3,2],[1],[1]]=>3 [[3,2],[2]]=>3 [[3,2],[1,1]]=>3 [[3,1,1],[1],[1]]=>3 [[3,1,1],[2]]=>3 [[3,1,1],[1,1]]=>3 [[2,2,1],[1],[1]]=>3 [[2,2,1],[2]]=>3 [[2,2,1],[1,1]]=>3 [[2,1,1,1],[1],[1]]=>3 [[2,1,1,1],[2]]=>2 [[2,1,1,1],[1,1]]=>3 [[1,1,1,1,1],[1],[1]]=>2 [[1,1,1,1,1],[1,1]]=>2 [[6],[1]]=>2 [[5,1],[1]]=>3 [[4,2],[1]]=>3 [[4,1,1],[1]]=>3 [[3,3],[1]]=>2 [[3,2,1],[1]]=>4 [[3,1,1,1],[1]]=>3 [[2,2,2],[1]]=>2 [[2,2,1,1],[1]]=>3 [[2,1,1,1,1],[1]]=>3 [[1,1,1,1,1,1],[1]]=>2 [[7]]=>1 [[6,1]]=>2 [[5,2]]=>2 [[5,1,1]]=>2 [[4,3]]=>2 [[4,2,1]]=>3 [[4,1,1,1]]=>2 [[3,3,1]]=>2 [[3,2,2]]=>2 [[3,2,1,1]]=>3 [[3,1,1,1,1]]=>2 [[2,2,2,1]]=>2 [[2,2,1,1,1]]=>2 [[2,1,1,1,1,1]]=>2 [[1,1,1,1,1,1,1]]=>1 [[1],[1],[1],[1],[1],[1],[1],[1]]=>1 [[2],[1],[1],[1],[1],[1],[1]]=>2 [[2],[2],[1],[1],[1],[1]]=>2 [[2],[2],[2],[1],[1]]=>2 [[2],[2],[2],[2]]=>1 [[1,1],[1],[1],[1],[1],[1],[1]]=>2 [[1,1],[1,1],[1],[1],[1],[1]]=>2 [[1,1],[1,1],[1,1],[1],[1]]=>2 [[1,1],[1,1],[1,1],[1,1]]=>1 [[3],[1],[1],[1],[1],[1]]=>2 [[3],[2],[1],[1],[1]]=>3 [[3],[2],[2],[1]]=>3 [[3],[3],[1],[1]]=>2 [[3],[3],[2]]=>2 [[2,1],[1],[1],[1],[1],[1]]=>3 [[2,1],[2],[1],[1],[1]]=>3 [[2,1],[2],[2],[1]]=>3 [[2,1],[1,1],[1],[1],[1]]=>3 [[2,1],[1,1],[1,1],[1]]=>3 [[2,1],[2,1],[1],[1]]=>3 [[2,1],[2,1],[2]]=>2 [[2,1],[2,1],[1,1]]=>2 [[1,1,1],[1],[1],[1],[1],[1]]=>2 [[1,1,1],[1,1],[1],[1],[1]]=>3 [[1,1,1],[1,1],[1,1],[1]]=>3 [[1,1,1],[1,1,1],[1],[1]]=>2 [[1,1,1],[1,1,1],[1,1]]=>2 [[4],[1],[1],[1],[1]]=>2 [[4],[2],[1],[1]]=>3 [[4],[2],[2]]=>2 [[4],[3],[1]]=>3 [[4],[4]]=>1 [[3,1],[1],[1],[1],[1]]=>3 [[3,1],[2],[1],[1]]=>4 [[3,1],[2],[2]]=>3 [[3,1],[1,1],[1],[1]]=>3 [[3,1],[1,1],[1,1]]=>2 [[3,1],[3],[1]]=>3 [[3,1],[2,1],[1]]=>4 [[3,1],[3,1]]=>2 [[2,2],[1],[1],[1],[1]]=>2 [[2,2],[2],[1],[1]]=>3 [[2,2],[2],[2]]=>2 [[2,2],[1,1],[1],[1]]=>3 [[2,2],[1,1],[1,1]]=>2 [[2,2],[2,1],[1]]=>4 [[2,2],[2,2]]=>1 [[2,1,1],[1],[1],[1],[1]]=>3 [[2,1,1],[2],[1],[1]]=>3 [[2,1,1],[2],[2]]=>2 [[2,1,1],[1,1],[1],[1]]=>4 [[2,1,1],[1,1],[1,1]]=>3 [[2,1,1],[2,1],[1]]=>4 [[2,1,1],[1,1,1],[1]]=>3 [[2,1,1],[2,1,1]]=>2 [[1,1,1,1],[1],[1],[1],[1]]=>2 [[1,1,1,1],[1,1],[1],[1]]=>3 [[1,1,1,1],[1,1],[1,1]]=>2 [[1,1,1,1],[1,1,1],[1]]=>3 [[1,1,1,1],[1,1,1,1]]=>1 [[5],[1],[1],[1]]=>2 [[5],[2],[1]]=>3 [[5],[3]]=>2 [[4,1],[1],[1],[1]]=>3 [[4,1],[2],[1]]=>4 [[4,1],[1,1],[1]]=>3 [[4,1],[3]]=>3 [[4,1],[2,1]]=>3 [[3,2],[1],[1],[1]]=>3 [[3,2],[2],[1]]=>4 [[3,2],[1,1],[1]]=>4 [[3,2],[3]]=>2 [[3,2],[2,1]]=>4 [[3,1,1],[1],[1],[1]]=>3 [[3,1,1],[2],[1]]=>4 [[3,1,1],[1,1],[1]]=>4 [[3,1,1],[3]]=>2 [[3,1,1],[2,1]]=>4 [[3,1,1],[1,1,1]]=>2 [[2,2,1],[1],[1],[1]]=>3 [[2,2,1],[2],[1]]=>4 [[2,2,1],[1,1],[1]]=>4 [[2,2,1],[2,1]]=>4 [[2,2,1],[1,1,1]]=>2 [[2,1,1,1],[1],[1],[1]]=>3 [[2,1,1,1],[2],[1]]=>3 [[2,1,1,1],[1,1],[1]]=>4 [[2,1,1,1],[2,1]]=>3 [[2,1,1,1],[1,1,1]]=>3 [[1,1,1,1,1],[1],[1],[1]]=>2 [[1,1,1,1,1],[1,1],[1]]=>3 [[1,1,1,1,1],[1,1,1]]=>2 [[6],[1],[1]]=>2 [[6],[2]]=>2 [[5,1],[1],[1]]=>3 [[5,1],[2]]=>3 [[5,1],[1,1]]=>2 [[4,2],[1],[1]]=>3 [[4,2],[2]]=>3 [[4,2],[1,1]]=>3 [[4,1,1],[1],[1]]=>3 [[4,1,1],[2]]=>3 [[4,1,1],[1,1]]=>3 [[3,3],[1],[1]]=>2 [[3,3],[2]]=>2 [[3,3],[1,1]]=>2 [[3,2,1],[1],[1]]=>4 [[3,2,1],[2]]=>4 [[3,2,1],[1,1]]=>4 [[3,1,1,1],[1],[1]]=>3 [[3,1,1,1],[2]]=>3 [[3,1,1,1],[1,1]]=>3 [[2,2,2],[1],[1]]=>2 [[2,2,2],[2]]=>2 [[2,2,2],[1,1]]=>2 [[2,2,1,1],[1],[1]]=>3 [[2,2,1,1],[2]]=>3 [[2,2,1,1],[1,1]]=>3 [[2,1,1,1,1],[1],[1]]=>3 [[2,1,1,1,1],[2]]=>2 [[2,1,1,1,1],[1,1]]=>3 [[1,1,1,1,1,1],[1],[1]]=>2 [[1,1,1,1,1,1],[1,1]]=>2 [[7],[1]]=>2 [[6,1],[1]]=>3 [[5,2],[1]]=>3 [[5,1,1],[1]]=>3 [[4,3],[1]]=>3 [[4,2,1],[1]]=>4 [[4,1,1,1],[1]]=>3 [[3,3,1],[1]]=>3 [[3,2,2],[1]]=>3 [[3,2,1,1],[1]]=>4 [[3,1,1,1,1],[1]]=>3 [[2,2,2,1],[1]]=>3 [[2,2,1,1,1],[1]]=>3 [[2,1,1,1,1,1],[1]]=>3 [[1,1,1,1,1,1,1],[1]]=>2 [[8]]=>1 [[7,1]]=>2 [[6,2]]=>2 [[6,1,1]]=>2 [[5,3]]=>2 [[5,2,1]]=>3 [[5,1,1,1]]=>2 [[4,4]]=>1 [[4,3,1]]=>3 [[4,2,2]]=>2 [[4,2,1,1]]=>3 [[4,1,1,1,1]]=>2 [[3,3,2]]=>2 [[3,3,1,1]]=>2 [[3,2,2,1]]=>3 [[3,2,1,1,1]]=>3 [[3,1,1,1,1,1]]=>2 [[2,2,2,2]]=>1 [[2,2,2,1,1]]=>2 [[2,2,1,1,1,1]]=>2 [[2,1,1,1,1,1,1]]=>2 [[1,1,1,1,1,1,1,1]]=>1 [[1],[1],[1],[1],[1],[1],[1],[1],[1]]=>1 [[2],[1],[1],[1],[1],[1],[1],[1]]=>2 [[2],[2],[1],[1],[1],[1],[1]]=>2 [[2],[2],[2],[1],[1],[1]]=>2 [[2],[2],[2],[2],[1]]=>2 [[1,1],[1],[1],[1],[1],[1],[1],[1]]=>2 [[1,1],[1,1],[1],[1],[1],[1],[1]]=>2 [[1,1],[1,1],[1,1],[1],[1],[1]]=>2 [[1,1],[1,1],[1,1],[1,1],[1]]=>2 [[3],[1],[1],[1],[1],[1],[1]]=>2 [[3],[2],[1],[1],[1],[1]]=>3 [[3],[2],[2],[1],[1]]=>3 [[3],[2],[2],[2]]=>2 [[3],[3],[1],[1],[1]]=>2 [[3],[3],[2],[1]]=>3 [[3],[3],[3]]=>1 [[2,1],[1],[1],[1],[1],[1],[1]]=>3 [[2,1],[2],[1],[1],[1],[1]]=>3 [[2,1],[2],[2],[1],[1]]=>3 [[2,1],[2],[2],[2]]=>2 [[2,1],[1,1],[1],[1],[1],[1]]=>3 [[2,1],[1,1],[1,1],[1],[1]]=>3 [[2,1],[1,1],[1,1],[1,1]]=>2 [[2,1],[2,1],[1],[1],[1]]=>3 [[2,1],[2,1],[2],[1]]=>3 [[2,1],[2,1],[1,1],[1]]=>3 [[2,1],[2,1],[2,1]]=>2 [[1,1,1],[1],[1],[1],[1],[1],[1]]=>2 [[1,1,1],[1,1],[1],[1],[1],[1]]=>3 [[1,1,1],[1,1],[1,1],[1],[1]]=>3 [[1,1,1],[1,1],[1,1],[1,1]]=>2 [[1,1,1],[1,1,1],[1],[1],[1]]=>2 [[1,1,1],[1,1,1],[1,1],[1]]=>3 [[1,1,1],[1,1,1],[1,1,1]]=>1 [[4],[1],[1],[1],[1],[1]]=>2 [[4],[2],[1],[1],[1]]=>3 [[4],[2],[2],[1]]=>3 [[4],[3],[1],[1]]=>3 [[4],[3],[2]]=>3 [[4],[4],[1]]=>2 [[3,1],[1],[1],[1],[1],[1]]=>3 [[3,1],[2],[1],[1],[1]]=>4 [[3,1],[2],[2],[1]]=>4 [[3,1],[1,1],[1],[1],[1]]=>3 [[3,1],[1,1],[1,1],[1]]=>3 [[3,1],[3],[1],[1]]=>3 [[3,1],[3],[2]]=>3 [[3,1],[2,1],[1],[1]]=>4 [[3,1],[2,1],[2]]=>3 [[3,1],[2,1],[1,1]]=>3 [[3,1],[3,1],[1]]=>3 [[2,2],[1],[1],[1],[1],[1]]=>2 [[2,2],[2],[1],[1],[1]]=>3 [[2,2],[2],[2],[1]]=>3 [[2,2],[1,1],[1],[1],[1]]=>3 [[2,2],[1,1],[1,1],[1]]=>3 [[2,2],[2,1],[1],[1]]=>4 [[2,2],[2,1],[2]]=>3 [[2,2],[2,1],[1,1]]=>3 [[2,2],[2,2],[1]]=>2 [[2,1,1],[1],[1],[1],[1],[1]]=>3 [[2,1,1],[2],[1],[1],[1]]=>3 [[2,1,1],[2],[2],[1]]=>3 [[2,1,1],[1,1],[1],[1],[1]]=>4 [[2,1,1],[1,1],[1,1],[1]]=>4 [[2,1,1],[2,1],[1],[1]]=>4 [[2,1,1],[2,1],[2]]=>3 [[2,1,1],[2,1],[1,1]]=>3 [[2,1,1],[1,1,1],[1],[1]]=>3 [[2,1,1],[1,1,1],[1,1]]=>3 [[2,1,1],[2,1,1],[1]]=>3 [[1,1,1,1],[1],[1],[1],[1],[1]]=>2 [[1,1,1,1],[1,1],[1],[1],[1]]=>3 [[1,1,1,1],[1,1],[1,1],[1]]=>3 [[1,1,1,1],[1,1,1],[1],[1]]=>3 [[1,1,1,1],[1,1,1],[1,1]]=>3 [[1,1,1,1],[1,1,1,1],[1]]=>2 [[5],[1],[1],[1],[1]]=>2 [[5],[2],[1],[1]]=>3 [[5],[2],[2]]=>2 [[5],[3],[1]]=>3 [[5],[4]]=>2 [[4,1],[1],[1],[1],[1]]=>3 [[4,1],[2],[1],[1]]=>4 [[4,1],[2],[2]]=>3 [[4,1],[1,1],[1],[1]]=>3 [[4,1],[1,1],[1,1]]=>2 [[4,1],[3],[1]]=>4 [[4,1],[2,1],[1]]=>4 [[4,1],[4]]=>2 [[4,1],[3,1]]=>3 [[3,2],[1],[1],[1],[1]]=>3 [[3,2],[2],[1],[1]]=>4 [[3,2],[2],[2]]=>3 [[3,2],[1,1],[1],[1]]=>4 [[3,2],[1,1],[1,1]]=>3 [[3,2],[3],[1]]=>3 [[3,2],[2,1],[1]]=>5 [[3,2],[3,1]]=>3 [[3,2],[2,2]]=>2 [[3,1,1],[1],[1],[1],[1]]=>3 [[3,1,1],[2],[1],[1]]=>4 [[3,1,1],[2],[2]]=>3 [[3,1,1],[1,1],[1],[1]]=>4 [[3,1,1],[1,1],[1,1]]=>3 [[3,1,1],[3],[1]]=>3 [[3,1,1],[2,1],[1]]=>5 [[3,1,1],[1,1,1],[1]]=>3 [[3,1,1],[3,1]]=>3 [[3,1,1],[2,1,1]]=>3 [[2,2,1],[1],[1],[1],[1]]=>3 [[2,2,1],[2],[1],[1]]=>4 [[2,2,1],[2],[2]]=>3 [[2,2,1],[1,1],[1],[1]]=>4 [[2,2,1],[1,1],[1,1]]=>3 [[2,2,1],[2,1],[1]]=>5 [[2,2,1],[1,1,1],[1]]=>3 [[2,2,1],[2,2]]=>2 [[2,2,1],[2,1,1]]=>3 [[2,1,1,1],[1],[1],[1],[1]]=>3 [[2,1,1,1],[2],[1],[1]]=>3 [[2,1,1,1],[2],[2]]=>2 [[2,1,1,1],[1,1],[1],[1]]=>4 [[2,1,1,1],[1,1],[1,1]]=>3 [[2,1,1,1],[2,1],[1]]=>4 [[2,1,1,1],[1,1,1],[1]]=>4 [[2,1,1,1],[2,1,1]]=>3 [[2,1,1,1],[1,1,1,1]]=>2 [[1,1,1,1,1],[1],[1],[1],[1]]=>2 [[1,1,1,1,1],[1,1],[1],[1]]=>3 [[1,1,1,1,1],[1,1],[1,1]]=>2 [[1,1,1,1,1],[1,1,1],[1]]=>3 [[1,1,1,1,1],[1,1,1,1]]=>2 [[6],[1],[1],[1]]=>2 [[6],[2],[1]]=>3 [[6],[3]]=>2 [[5,1],[1],[1],[1]]=>3 [[5,1],[2],[1]]=>4 [[5,1],[1,1],[1]]=>3 [[5,1],[3]]=>3 [[5,1],[2,1]]=>3 [[4,2],[1],[1],[1]]=>3 [[4,2],[2],[1]]=>4 [[4,2],[1,1],[1]]=>4 [[4,2],[3]]=>3 [[4,2],[2,1]]=>4 [[4,1,1],[1],[1],[1]]=>3 [[4,1,1],[2],[1]]=>4 [[4,1,1],[1,1],[1]]=>4 [[4,1,1],[3]]=>3 [[4,1,1],[2,1]]=>4 [[4,1,1],[1,1,1]]=>2 [[3,3],[1],[1],[1]]=>2 [[3,3],[2],[1]]=>3 [[3,3],[1,1],[1]]=>3 [[3,3],[3]]=>2 [[3,3],[2,1]]=>3 [[3,2,1],[1],[1],[1]]=>4 [[3,2,1],[2],[1]]=>5 [[3,2,1],[1,1],[1]]=>5 [[3,2,1],[3]]=>3 [[3,2,1],[2,1]]=>5 [[3,2,1],[1,1,1]]=>3 [[3,1,1,1],[1],[1],[1]]=>3 [[3,1,1,1],[2],[1]]=>4 [[3,1,1,1],[1,1],[1]]=>4 [[3,1,1,1],[3]]=>2 [[3,1,1,1],[2,1]]=>4 [[3,1,1,1],[1,1,1]]=>3 [[2,2,2],[1],[1],[1]]=>2 [[2,2,2],[2],[1]]=>3 [[2,2,2],[1,1],[1]]=>3 [[2,2,2],[2,1]]=>3 [[2,2,2],[1,1,1]]=>2 [[2,2,1,1],[1],[1],[1]]=>3 [[2,2,1,1],[2],[1]]=>4 [[2,2,1,1],[1,1],[1]]=>4 [[2,2,1,1],[2,1]]=>4 [[2,2,1,1],[1,1,1]]=>3 [[2,1,1,1,1],[1],[1],[1]]=>3 [[2,1,1,1,1],[2],[1]]=>3 [[2,1,1,1,1],[1,1],[1]]=>4 [[2,1,1,1,1],[2,1]]=>3 [[2,1,1,1,1],[1,1,1]]=>3 [[1,1,1,1,1,1],[1],[1],[1]]=>2 [[1,1,1,1,1,1],[1,1],[1]]=>3 [[1,1,1,1,1,1],[1,1,1]]=>2 [[7],[1],[1]]=>2 [[7],[2]]=>2 [[6,1],[1],[1]]=>3 [[6,1],[2]]=>3 [[6,1],[1,1]]=>2 [[5,2],[1],[1]]=>3 [[5,2],[2]]=>3 [[5,2],[1,1]]=>3 [[5,1,1],[1],[1]]=>3 [[5,1,1],[2]]=>3 [[5,1,1],[1,1]]=>3 [[4,3],[1],[1]]=>3 [[4,3],[2]]=>3 [[4,3],[1,1]]=>3 [[4,2,1],[1],[1]]=>4 [[4,2,1],[2]]=>4 [[4,2,1],[1,1]]=>4 [[4,1,1,1],[1],[1]]=>3 [[4,1,1,1],[2]]=>3 [[4,1,1,1],[1,1]]=>3 [[3,3,1],[1],[1]]=>3 [[3,3,1],[2]]=>3 [[3,3,1],[1,1]]=>3 [[3,2,2],[1],[1]]=>3 [[3,2,2],[2]]=>3 [[3,2,2],[1,1]]=>3 [[3,2,1,1],[1],[1]]=>4 [[3,2,1,1],[2]]=>4 [[3,2,1,1],[1,1]]=>4 [[3,1,1,1,1],[1],[1]]=>3 [[3,1,1,1,1],[2]]=>3 [[3,1,1,1,1],[1,1]]=>3 [[2,2,2,1],[1],[1]]=>3 [[2,2,2,1],[2]]=>3 [[2,2,2,1],[1,1]]=>3 [[2,2,1,1,1],[1],[1]]=>3 [[2,2,1,1,1],[2]]=>3 [[2,2,1,1,1],[1,1]]=>3 [[2,1,1,1,1,1],[1],[1]]=>3 [[2,1,1,1,1,1],[2]]=>2 [[2,1,1,1,1,1],[1,1]]=>3 [[1,1,1,1,1,1,1],[1],[1]]=>2 [[1,1,1,1,1,1,1],[1,1]]=>2 [[8],[1]]=>2 [[7,1],[1]]=>3 [[6,2],[1]]=>3 [[6,1,1],[1]]=>3 [[5,3],[1]]=>3 [[5,2,1],[1]]=>4 [[5,1,1,1],[1]]=>3 [[4,4],[1]]=>2 [[4,3,1],[1]]=>4 [[4,2,2],[1]]=>3 [[4,2,1,1],[1]]=>4 [[4,1,1,1,1],[1]]=>3 [[3,3,2],[1]]=>3 [[3,3,1,1],[1]]=>3 [[3,2,2,1],[1]]=>4 [[3,2,1,1,1],[1]]=>4 [[3,1,1,1,1,1],[1]]=>3 [[2,2,2,2],[1]]=>2 [[2,2,2,1,1],[1]]=>3 [[2,2,1,1,1,1],[1]]=>3 [[2,1,1,1,1,1,1],[1]]=>3 [[1,1,1,1,1,1,1,1],[1]]=>2 [[9]]=>1 [[8,1]]=>2 [[7,2]]=>2 [[7,1,1]]=>2 [[6,3]]=>2 [[6,2,1]]=>3 [[6,1,1,1]]=>2 [[5,4]]=>2 [[5,3,1]]=>3 [[5,2,2]]=>2 [[5,2,1,1]]=>3 [[5,1,1,1,1]]=>2 [[4,4,1]]=>2 [[4,3,2]]=>3 [[4,3,1,1]]=>3 [[4,2,2,1]]=>3 [[4,2,1,1,1]]=>3 [[4,1,1,1,1,1]]=>2 [[3,3,3]]=>1 [[3,3,2,1]]=>3 [[3,3,1,1,1]]=>2 [[3,2,2,2]]=>2 [[3,2,2,1,1]]=>3 [[3,2,1,1,1,1]]=>3 [[3,1,1,1,1,1,1]]=>2 [[2,2,2,2,1]]=>2 [[2,2,2,1,1,1]]=>2 [[2,2,1,1,1,1,1]]=>2 [[2,1,1,1,1,1,1,1]]=>2 [[1,1,1,1,1,1,1,1,1]]=>1 [[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]]=>1 [[2],[1],[1],[1],[1],[1],[1],[1],[1]]=>2 [[2],[2],[1],[1],[1],[1],[1],[1]]=>2 [[2],[2],[2],[1],[1],[1],[1]]=>2 [[2],[2],[2],[2],[1],[1]]=>2 [[2],[2],[2],[2],[2]]=>1 [[1,1],[1],[1],[1],[1],[1],[1],[1],[1]]=>2 [[1,1],[1,1],[1],[1],[1],[1],[1],[1]]=>2 [[1,1],[1,1],[1,1],[1],[1],[1],[1]]=>2 [[1,1],[1,1],[1,1],[1,1],[1],[1]]=>2 [[1,1],[1,1],[1,1],[1,1],[1,1]]=>1 [[3],[1],[1],[1],[1],[1],[1],[1]]=>2 [[3],[2],[1],[1],[1],[1],[1]]=>3 [[3],[2],[2],[1],[1],[1]]=>3 [[3],[2],[2],[2],[1]]=>3 [[3],[3],[1],[1],[1],[1]]=>2 [[3],[3],[2],[1],[1]]=>3 [[3],[3],[2],[2]]=>2 [[3],[3],[3],[1]]=>2 [[2,1],[1],[1],[1],[1],[1],[1],[1]]=>3 [[2,1],[2],[1],[1],[1],[1],[1]]=>3 [[2,1],[2],[2],[1],[1],[1]]=>3 [[2,1],[2],[2],[2],[1]]=>3 [[2,1],[1,1],[1],[1],[1],[1],[1]]=>3 [[2,1],[1,1],[1,1],[1],[1],[1]]=>3 [[2,1],[1,1],[1,1],[1,1],[1]]=>3 [[2,1],[2,1],[1],[1],[1],[1]]=>3 [[2,1],[2,1],[2],[1],[1]]=>3 [[2,1],[2,1],[2],[2]]=>2 [[2,1],[2,1],[1,1],[1],[1]]=>3 [[2,1],[2,1],[1,1],[1,1]]=>2 [[2,1],[2,1],[2,1],[1]]=>3 [[1,1,1],[1],[1],[1],[1],[1],[1],[1]]=>2 [[1,1,1],[1,1],[1],[1],[1],[1],[1]]=>3 [[1,1,1],[1,1],[1,1],[1],[1],[1]]=>3 [[1,1,1],[1,1],[1,1],[1,1],[1]]=>3 [[1,1,1],[1,1,1],[1],[1],[1],[1]]=>2 [[1,1,1],[1,1,1],[1,1],[1],[1]]=>3 [[1,1,1],[1,1,1],[1,1],[1,1]]=>2 [[1,1,1],[1,1,1],[1,1,1],[1]]=>2 [[4],[1],[1],[1],[1],[1],[1]]=>2 [[4],[2],[1],[1],[1],[1]]=>3 [[4],[2],[2],[1],[1]]=>3 [[4],[2],[2],[2]]=>2 [[4],[3],[1],[1],[1]]=>3 [[4],[3],[2],[1]]=>4 [[4],[3],[3]]=>2 [[4],[4],[1],[1]]=>2 [[4],[4],[2]]=>2 [[3,1],[1],[1],[1],[1],[1],[1]]=>3 [[3,1],[2],[1],[1],[1],[1]]=>4 [[3,1],[2],[2],[1],[1]]=>4 [[3,1],[2],[2],[2]]=>3 [[3,1],[1,1],[1],[1],[1],[1]]=>3 [[3,1],[1,1],[1,1],[1],[1]]=>3 [[3,1],[1,1],[1,1],[1,1]]=>2 [[3,1],[3],[1],[1],[1]]=>3 [[3,1],[3],[2],[1]]=>4 [[3,1],[3],[3]]=>2 [[3,1],[2,1],[1],[1],[1]]=>4 [[3,1],[2,1],[2],[1]]=>4 [[3,1],[2,1],[1,1],[1]]=>4 [[3,1],[2,1],[2,1]]=>3 [[3,1],[3,1],[1],[1]]=>3 [[3,1],[3,1],[2]]=>3 [[3,1],[3,1],[1,1]]=>2 [[2,2],[1],[1],[1],[1],[1],[1]]=>2 [[2,2],[2],[1],[1],[1],[1]]=>3 [[2,2],[2],[2],[1],[1]]=>3 [[2,2],[2],[2],[2]]=>2 [[2,2],[1,1],[1],[1],[1],[1]]=>3 [[2,2],[1,1],[1,1],[1],[1]]=>3 [[2,2],[1,1],[1,1],[1,1]]=>2 [[2,2],[2,1],[1],[1],[1]]=>4 [[2,2],[2,1],[2],[1]]=>4 [[2,2],[2,1],[1,1],[1]]=>4 [[2,2],[2,1],[2,1]]=>3 [[2,2],[2,2],[1],[1]]=>2 [[2,2],[2,2],[2]]=>2 [[2,2],[2,2],[1,1]]=>2 [[2,1,1],[1],[1],[1],[1],[1],[1]]=>3 [[2,1,1],[2],[1],[1],[1],[1]]=>3 [[2,1,1],[2],[2],[1],[1]]=>3 [[2,1,1],[2],[2],[2]]=>2 [[2,1,1],[1,1],[1],[1],[1],[1]]=>4 [[2,1,1],[1,1],[1,1],[1],[1]]=>4 [[2,1,1],[1,1],[1,1],[1,1]]=>3 [[2,1,1],[2,1],[1],[1],[1]]=>4 [[2,1,1],[2,1],[2],[1]]=>4 [[2,1,1],[2,1],[1,1],[1]]=>4 [[2,1,1],[2,1],[2,1]]=>3 [[2,1,1],[1,1,1],[1],[1],[1]]=>3 [[2,1,1],[1,1,1],[1,1],[1]]=>4 [[2,1,1],[1,1,1],[1,1,1]]=>2 [[2,1,1],[2,1,1],[1],[1]]=>3 [[2,1,1],[2,1,1],[2]]=>2 [[2,1,1],[2,1,1],[1,1]]=>3 [[1,1,1,1],[1],[1],[1],[1],[1],[1]]=>2 [[1,1,1,1],[1,1],[1],[1],[1],[1]]=>3 [[1,1,1,1],[1,1],[1,1],[1],[1]]=>3 [[1,1,1,1],[1,1],[1,1],[1,1]]=>2 [[1,1,1,1],[1,1,1],[1],[1],[1]]=>3 [[1,1,1,1],[1,1,1],[1,1],[1]]=>4 [[1,1,1,1],[1,1,1],[1,1,1]]=>2 [[1,1,1,1],[1,1,1,1],[1],[1]]=>2 [[1,1,1,1],[1,1,1,1],[1,1]]=>2 [[5],[1],[1],[1],[1],[1]]=>2 [[5],[2],[1],[1],[1]]=>3 [[5],[2],[2],[1]]=>3 [[5],[3],[1],[1]]=>3 [[5],[3],[2]]=>3 [[5],[4],[1]]=>3 [[5],[5]]=>1 [[4,1],[1],[1],[1],[1],[1]]=>3 [[4,1],[2],[1],[1],[1]]=>4 [[4,1],[2],[2],[1]]=>4 [[4,1],[1,1],[1],[1],[1]]=>3 [[4,1],[1,1],[1,1],[1]]=>3 [[4,1],[3],[1],[1]]=>4 [[4,1],[3],[2]]=>4 [[4,1],[2,1],[1],[1]]=>4 [[4,1],[2,1],[2]]=>3 [[4,1],[2,1],[1,1]]=>3 [[4,1],[4],[1]]=>3 [[4,1],[3,1],[1]]=>4 [[4,1],[4,1]]=>2 [[3,2],[1],[1],[1],[1],[1]]=>3 [[3,2],[2],[1],[1],[1]]=>4 [[3,2],[2],[2],[1]]=>4 [[3,2],[1,1],[1],[1],[1]]=>4 [[3,2],[1,1],[1,1],[1]]=>4 [[3,2],[3],[1],[1]]=>3 [[3,2],[3],[2]]=>3 [[3,2],[2,1],[1],[1]]=>5 [[3,2],[2,1],[2]]=>4 [[3,2],[2,1],[1,1]]=>4 [[3,2],[3,1],[1]]=>4 [[3,2],[2,2],[1]]=>3 [[3,2],[3,2]]=>2 [[3,1,1],[1],[1],[1],[1],[1]]=>3 [[3,1,1],[2],[1],[1],[1]]=>4 [[3,1,1],[2],[2],[1]]=>4 [[3,1,1],[1,1],[1],[1],[1]]=>4 [[3,1,1],[1,1],[1,1],[1]]=>4 [[3,1,1],[3],[1],[1]]=>3 [[3,1,1],[3],[2]]=>3 [[3,1,1],[2,1],[1],[1]]=>5 [[3,1,1],[2,1],[2]]=>4 [[3,1,1],[2,1],[1,1]]=>4 [[3,1,1],[1,1,1],[1],[1]]=>3 [[3,1,1],[1,1,1],[1,1]]=>3 [[3,1,1],[3,1],[1]]=>4 [[3,1,1],[2,1,1],[1]]=>4 [[3,1,1],[3,1,1]]=>2 [[2,2,1],[1],[1],[1],[1],[1]]=>3 [[2,2,1],[2],[1],[1],[1]]=>4 [[2,2,1],[2],[2],[1]]=>4 [[2,2,1],[1,1],[1],[1],[1]]=>4 [[2,2,1],[1,1],[1,1],[1]]=>4 [[2,2,1],[2,1],[1],[1]]=>5 [[2,2,1],[2,1],[2]]=>4 [[2,2,1],[2,1],[1,1]]=>4 [[2,2,1],[1,1,1],[1],[1]]=>3 [[2,2,1],[1,1,1],[1,1]]=>3 [[2,2,1],[2,2],[1]]=>3 [[2,2,1],[2,1,1],[1]]=>4 [[2,2,1],[2,2,1]]=>2 [[2,1,1,1],[1],[1],[1],[1],[1]]=>3 [[2,1,1,1],[2],[1],[1],[1]]=>3 [[2,1,1,1],[2],[2],[1]]=>3 [[2,1,1,1],[1,1],[1],[1],[1]]=>4 [[2,1,1,1],[1,1],[1,1],[1]]=>4 [[2,1,1,1],[2,1],[1],[1]]=>4 [[2,1,1,1],[2,1],[2]]=>3 [[2,1,1,1],[2,1],[1,1]]=>3 [[2,1,1,1],[1,1,1],[1],[1]]=>4 [[2,1,1,1],[1,1,1],[1,1]]=>4 [[2,1,1,1],[2,1,1],[1]]=>4 [[2,1,1,1],[1,1,1,1],[1]]=>3 [[2,1,1,1],[2,1,1,1]]=>2 [[1,1,1,1,1],[1],[1],[1],[1],[1]]=>2 [[1,1,1,1,1],[1,1],[1],[1],[1]]=>3 [[1,1,1,1,1],[1,1],[1,1],[1]]=>3 [[1,1,1,1,1],[1,1,1],[1],[1]]=>3 [[1,1,1,1,1],[1,1,1],[1,1]]=>3 [[1,1,1,1,1],[1,1,1,1],[1]]=>3 [[1,1,1,1,1],[1,1,1,1,1]]=>1 [[6],[1],[1],[1],[1]]=>2 [[6],[2],[1],[1]]=>3 [[6],[2],[2]]=>2 [[6],[3],[1]]=>3 [[6],[4]]=>2 [[5,1],[1],[1],[1],[1]]=>3 [[5,1],[2],[1],[1]]=>4 [[5,1],[2],[2]]=>3 [[5,1],[1,1],[1],[1]]=>3 [[5,1],[1,1],[1,1]]=>2 [[5,1],[3],[1]]=>4 [[5,1],[2,1],[1]]=>4 [[5,1],[4]]=>3 [[5,1],[3,1]]=>3 [[4,2],[1],[1],[1],[1]]=>3 [[4,2],[2],[1],[1]]=>4 [[4,2],[2],[2]]=>3 [[4,2],[1,1],[1],[1]]=>4 [[4,2],[1,1],[1,1]]=>3 [[4,2],[3],[1]]=>4 [[4,2],[2,1],[1]]=>5 [[4,2],[4]]=>2 [[4,2],[3,1]]=>4 [[4,2],[2,2]]=>2 [[4,1,1],[1],[1],[1],[1]]=>3 [[4,1,1],[2],[1],[1]]=>4 [[4,1,1],[2],[2]]=>3 [[4,1,1],[1,1],[1],[1]]=>4 [[4,1,1],[1,1],[1,1]]=>3 [[4,1,1],[3],[1]]=>4 [[4,1,1],[2,1],[1]]=>5 [[4,1,1],[1,1,1],[1]]=>3 [[4,1,1],[4]]=>2 [[4,1,1],[3,1]]=>4 [[4,1,1],[2,1,1]]=>3 [[3,3],[1],[1],[1],[1]]=>2 [[3,3],[2],[1],[1]]=>3 [[3,3],[2],[2]]=>2 [[3,3],[1,1],[1],[1]]=>3 [[3,3],[1,1],[1,1]]=>2 [[3,3],[3],[1]]=>3 [[3,3],[2,1],[1]]=>4 [[3,3],[3,1]]=>3 [[3,3],[2,2]]=>2 [[3,2,1],[1],[1],[1],[1]]=>4 [[3,2,1],[2],[1],[1]]=>5 [[3,2,1],[2],[2]]=>4 [[3,2,1],[1,1],[1],[1]]=>5 [[3,2,1],[1,1],[1,1]]=>4 [[3,2,1],[3],[1]]=>4 [[3,2,1],[2,1],[1]]=>6 [[3,2,1],[1,1,1],[1]]=>4 [[3,2,1],[3,1]]=>4 [[3,2,1],[2,2]]=>3 [[3,2,1],[2,1,1]]=>4 [[3,1,1,1],[1],[1],[1],[1]]=>3 [[3,1,1,1],[2],[1],[1]]=>4 [[3,1,1,1],[2],[2]]=>3 [[3,1,1,1],[1,1],[1],[1]]=>4 [[3,1,1,1],[1,1],[1,1]]=>3 [[3,1,1,1],[3],[1]]=>3 [[3,1,1,1],[2,1],[1]]=>5 [[3,1,1,1],[1,1,1],[1]]=>4 [[3,1,1,1],[3,1]]=>3 [[3,1,1,1],[2,1,1]]=>4 [[3,1,1,1],[1,1,1,1]]=>2 [[2,2,2],[1],[1],[1],[1]]=>2 [[2,2,2],[2],[1],[1]]=>3 [[2,2,2],[2],[2]]=>2 [[2,2,2],[1,1],[1],[1]]=>3 [[2,2,2],[1,1],[1,1]]=>2 [[2,2,2],[2,1],[1]]=>4 [[2,2,2],[1,1,1],[1]]=>3 [[2,2,2],[2,2]]=>2 [[2,2,2],[2,1,1]]=>3 [[2,2,1,1],[1],[1],[1],[1]]=>3 [[2,2,1,1],[2],[1],[1]]=>4 [[2,2,1,1],[2],[2]]=>3 [[2,2,1,1],[1,1],[1],[1]]=>4 [[2,2,1,1],[1,1],[1,1]]=>3 [[2,2,1,1],[2,1],[1]]=>5 [[2,2,1,1],[1,1,1],[1]]=>4 [[2,2,1,1],[2,2]]=>2 [[2,2,1,1],[2,1,1]]=>4 [[2,2,1,1],[1,1,1,1]]=>2 [[2,1,1,1,1],[1],[1],[1],[1]]=>3 [[2,1,1,1,1],[2],[1],[1]]=>3 [[2,1,1,1,1],[2],[2]]=>2 [[2,1,1,1,1],[1,1],[1],[1]]=>4 [[2,1,1,1,1],[1,1],[1,1]]=>3 [[2,1,1,1,1],[2,1],[1]]=>4 [[2,1,1,1,1],[1,1,1],[1]]=>4 [[2,1,1,1,1],[2,1,1]]=>3 [[2,1,1,1,1],[1,1,1,1]]=>3 [[1,1,1,1,1,1],[1],[1],[1],[1]]=>2 [[1,1,1,1,1,1],[1,1],[1],[1]]=>3 [[1,1,1,1,1,1],[1,1],[1,1]]=>2 [[1,1,1,1,1,1],[1,1,1],[1]]=>3 [[1,1,1,1,1,1],[1,1,1,1]]=>2 [[7],[1],[1],[1]]=>2 [[7],[2],[1]]=>3 [[7],[3]]=>2 [[6,1],[1],[1],[1]]=>3 [[6,1],[2],[1]]=>4 [[6,1],[1,1],[1]]=>3 [[6,1],[3]]=>3 [[6,1],[2,1]]=>3 [[5,2],[1],[1],[1]]=>3 [[5,2],[2],[1]]=>4 [[5,2],[1,1],[1]]=>4 [[5,2],[3]]=>3 [[5,2],[2,1]]=>4 [[5,1,1],[1],[1],[1]]=>3 [[5,1,1],[2],[1]]=>4 [[5,1,1],[1,1],[1]]=>4 [[5,1,1],[3]]=>3 [[5,1,1],[2,1]]=>4 [[5,1,1],[1,1,1]]=>2 [[4,3],[1],[1],[1]]=>3 [[4,3],[2],[1]]=>4 [[4,3],[1,1],[1]]=>4 [[4,3],[3]]=>3 [[4,3],[2,1]]=>4 [[4,2,1],[1],[1],[1]]=>4 [[4,2,1],[2],[1]]=>5 [[4,2,1],[1,1],[1]]=>5 [[4,2,1],[3]]=>4 [[4,2,1],[2,1]]=>5 [[4,2,1],[1,1,1]]=>3 [[4,1,1,1],[1],[1],[1]]=>3 [[4,1,1,1],[2],[1]]=>4 [[4,1,1,1],[1,1],[1]]=>4 [[4,1,1,1],[3]]=>3 [[4,1,1,1],[2,1]]=>4 [[4,1,1,1],[1,1,1]]=>3 [[3,3,1],[1],[1],[1]]=>3 [[3,3,1],[2],[1]]=>4 [[3,3,1],[1,1],[1]]=>4 [[3,3,1],[3]]=>3 [[3,3,1],[2,1]]=>4 [[3,3,1],[1,1,1]]=>2 [[3,2,2],[1],[1],[1]]=>3 [[3,2,2],[2],[1]]=>4 [[3,2,2],[1,1],[1]]=>4 [[3,2,2],[3]]=>2 [[3,2,2],[2,1]]=>4 [[3,2,2],[1,1,1]]=>3 [[3,2,1,1],[1],[1],[1]]=>4 [[3,2,1,1],[2],[1]]=>5 [[3,2,1,1],[1,1],[1]]=>5 [[3,2,1,1],[3]]=>3 [[3,2,1,1],[2,1]]=>5 [[3,2,1,1],[1,1,1]]=>4 [[3,1,1,1,1],[1],[1],[1]]=>3 [[3,1,1,1,1],[2],[1]]=>4 [[3,1,1,1,1],[1,1],[1]]=>4 [[3,1,1,1,1],[3]]=>2 [[3,1,1,1,1],[2,1]]=>4 [[3,1,1,1,1],[1,1,1]]=>3 [[2,2,2,1],[1],[1],[1]]=>3 [[2,2,2,1],[2],[1]]=>4 [[2,2,2,1],[1,1],[1]]=>4 [[2,2,2,1],[2,1]]=>4 [[2,2,2,1],[1,1,1]]=>3 [[2,2,1,1,1],[1],[1],[1]]=>3 [[2,2,1,1,1],[2],[1]]=>4 [[2,2,1,1,1],[1,1],[1]]=>4 [[2,2,1,1,1],[2,1]]=>4 [[2,2,1,1,1],[1,1,1]]=>3 [[2,1,1,1,1,1],[1],[1],[1]]=>3 [[2,1,1,1,1,1],[2],[1]]=>3 [[2,1,1,1,1,1],[1,1],[1]]=>4 [[2,1,1,1,1,1],[2,1]]=>3 [[2,1,1,1,1,1],[1,1,1]]=>3 [[1,1,1,1,1,1,1],[1],[1],[1]]=>2 [[1,1,1,1,1,1,1],[1,1],[1]]=>3 [[1,1,1,1,1,1,1],[1,1,1]]=>2 [[8],[1],[1]]=>2 [[8],[2]]=>2 [[7,1],[1],[1]]=>3 [[7,1],[2]]=>3 [[7,1],[1,1]]=>2 [[6,2],[1],[1]]=>3 [[6,2],[2]]=>3 [[6,2],[1,1]]=>3 [[6,1,1],[1],[1]]=>3 [[6,1,1],[2]]=>3 [[6,1,1],[1,1]]=>3 [[5,3],[1],[1]]=>3 [[5,3],[2]]=>3 [[5,3],[1,1]]=>3 [[5,2,1],[1],[1]]=>4 [[5,2,1],[2]]=>4 [[5,2,1],[1,1]]=>4 [[5,1,1,1],[1],[1]]=>3 [[5,1,1,1],[2]]=>3 [[5,1,1,1],[1,1]]=>3 [[4,4],[1],[1]]=>2 [[4,4],[2]]=>2 [[4,4],[1,1]]=>2 [[4,3,1],[1],[1]]=>4 [[4,3,1],[2]]=>4 [[4,3,1],[1,1]]=>4 [[4,2,2],[1],[1]]=>3 [[4,2,2],[2]]=>3 [[4,2,2],[1,1]]=>3 [[4,2,1,1],[1],[1]]=>4 [[4,2,1,1],[2]]=>4 [[4,2,1,1],[1,1]]=>4 [[4,1,1,1,1],[1],[1]]=>3 [[4,1,1,1,1],[2]]=>3 [[4,1,1,1,1],[1,1]]=>3 [[3,3,2],[1],[1]]=>3 [[3,3,2],[2]]=>3 [[3,3,2],[1,1]]=>3 [[3,3,1,1],[1],[1]]=>3 [[3,3,1,1],[2]]=>3 [[3,3,1,1],[1,1]]=>3 [[3,2,2,1],[1],[1]]=>4 [[3,2,2,1],[2]]=>4 [[3,2,2,1],[1,1]]=>4 [[3,2,1,1,1],[1],[1]]=>4 [[3,2,1,1,1],[2]]=>4 [[3,2,1,1,1],[1,1]]=>4 [[3,1,1,1,1,1],[1],[1]]=>3 [[3,1,1,1,1,1],[2]]=>3 [[3,1,1,1,1,1],[1,1]]=>3 [[2,2,2,2],[1],[1]]=>2 [[2,2,2,2],[2]]=>2 [[2,2,2,2],[1,1]]=>2 [[2,2,2,1,1],[1],[1]]=>3 [[2,2,2,1,1],[2]]=>3 [[2,2,2,1,1],[1,1]]=>3 [[2,2,1,1,1,1],[1],[1]]=>3 [[2,2,1,1,1,1],[2]]=>3 [[2,2,1,1,1,1],[1,1]]=>3 [[2,1,1,1,1,1,1],[1],[1]]=>3 [[2,1,1,1,1,1,1],[2]]=>2 [[2,1,1,1,1,1,1],[1,1]]=>3 [[1,1,1,1,1,1,1,1],[1],[1]]=>2 [[1,1,1,1,1,1,1,1],[1,1]]=>2 [[9],[1]]=>2 [[8,1],[1]]=>3 [[7,2],[1]]=>3 [[7,1,1],[1]]=>3 [[6,3],[1]]=>3 [[6,2,1],[1]]=>4 [[6,1,1,1],[1]]=>3 [[5,4],[1]]=>3 [[5,3,1],[1]]=>4 [[5,2,2],[1]]=>3 [[5,2,1,1],[1]]=>4 [[5,1,1,1,1],[1]]=>3 [[4,4,1],[1]]=>3 [[4,3,2],[1]]=>4 [[4,3,1,1],[1]]=>4 [[4,2,2,1],[1]]=>4 [[4,2,1,1,1],[1]]=>4 [[4,1,1,1,1,1],[1]]=>3 [[3,3,3],[1]]=>2 [[3,3,2,1],[1]]=>4 [[3,3,1,1,1],[1]]=>3 [[3,2,2,2],[1]]=>3 [[3,2,2,1,1],[1]]=>4 [[3,2,1,1,1,1],[1]]=>4 [[3,1,1,1,1,1,1],[1]]=>3 [[2,2,2,2,1],[1]]=>3 [[2,2,2,1,1,1],[1]]=>3 [[2,2,1,1,1,1,1],[1]]=>3 [[2,1,1,1,1,1,1,1],[1]]=>3 [[1,1,1,1,1,1,1,1,1],[1]]=>2 [[10]]=>1 [[9,1]]=>2 [[8,2]]=>2 [[8,1,1]]=>2 [[7,3]]=>2 [[7,2,1]]=>3 [[7,1,1,1]]=>2 [[6,4]]=>2 [[6,3,1]]=>3 [[6,2,2]]=>2 [[6,2,1,1]]=>3 [[6,1,1,1,1]]=>2 [[5,5]]=>1 [[5,4,1]]=>3 [[5,3,2]]=>3 [[5,3,1,1]]=>3 [[5,2,2,1]]=>3 [[5,2,1,1,1]]=>3 [[5,1,1,1,1,1]]=>2 [[4,4,2]]=>2 [[4,4,1,1]]=>2 [[4,3,3]]=>2 [[4,3,2,1]]=>4 [[4,3,1,1,1]]=>3 [[4,2,2,2]]=>2 [[4,2,2,1,1]]=>3 [[4,2,1,1,1,1]]=>3 [[4,1,1,1,1,1,1]]=>2 [[3,3,3,1]]=>2 [[3,3,2,2]]=>2 [[3,3,2,1,1]]=>3 [[3,3,1,1,1,1]]=>2 [[3,2,2,2,1]]=>3 [[3,2,2,1,1,1]]=>3 [[3,2,1,1,1,1,1]]=>3 [[3,1,1,1,1,1,1,1]]=>2 [[2,2,2,2,2]]=>1 [[2,2,2,2,1,1]]=>2 [[2,2,2,1,1,1,1]]=>2 [[2,2,1,1,1,1,1,1]]=>2 [[2,1,1,1,1,1,1,1,1]]=>2 [[1,1,1,1,1,1,1,1,1,1]]=>1
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Description
The number of maximal boxes of a plane partition.
This is the size of the antichain in the corresponding product of 3 chains poset. Equivalently, this is the number of boxes that can be removed from the plane partition, such that the result is a plane partition.
Code
def statistic(P):
    PP = PlanePartition(P)
    x = len(PP.z_tableau())
    y = len(PP.x_tableau())
    z = len(PP.y_tableau())
    C = Posets.ProductOfChains((x,y,z))
    oi_gens = []
    for i in range(x):
        for j in range(y):
            if PP.z_tableau()[i][j] != 0:
                oi_gens.append((i,j,PP.z_tableau()[i][j]-1))
    OI = C.order_ideal(oi_gens) #this is the ordeal ideal
    AC = C.order_ideal_generators(OI) #this is the antichain
    return len(AC)

def statistic_alternative(p):
    c = 0
    for i, row in enumerate(p):
        for j, entry in enumerate(row):
            h = None if len(row) == j+1 else row[j+1]
            v = None if len(p) == i+1 or len(p[i+1]) <= j else p[i+1][j]
            if (h is None or entry > h) and (v is None or entry > v):
                c += 1
    return c
Created
Jul 25, 2019 at 22:12 by Dylan Heuer
Updated
Aug 28, 2023 at 09:49 by Martin Rubey