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Identifier
Values
=>
Cc0019;cc-rep
[[1]]=>1 [[2]]=>2 [[3]]=>3 [[4]]=>4 [[5]]=>5 [[6]]=>6 [[1,1]]=>1 [[1,2]]=>1 [[2,2]]=>2 [[1],[2]]=>1 [[1,3]]=>1 [[2,3]]=>2 [[3,3]]=>3 [[1],[3]]=>1 [[2],[3]]=>2 [[1,4]]=>1 [[2,4]]=>2 [[3,4]]=>3 [[4,4]]=>4 [[1],[4]]=>1 [[2],[4]]=>2 [[3],[4]]=>3 [[1,5]]=>1 [[2,5]]=>2 [[3,5]]=>3 [[4,5]]=>4 [[5,5]]=>5 [[1],[5]]=>1 [[2],[5]]=>2 [[3],[5]]=>3 [[4],[5]]=>4 [[1,6]]=>1 [[2,6]]=>2 [[3,6]]=>3 [[4,6]]=>4 [[5,6]]=>5 [[6,6]]=>6 [[1],[6]]=>1 [[2],[6]]=>2 [[3],[6]]=>3 [[4],[6]]=>4 [[5],[6]]=>5 [[1,1,1]]=>1 [[1,1,2]]=>1 [[1,2,2]]=>1 [[2,2,2]]=>2 [[1,1],[2]]=>1 [[1,2],[2]]=>1 [[1,1,3]]=>1 [[1,2,3]]=>1 [[1,3,3]]=>1 [[2,2,3]]=>2 [[2,3,3]]=>2 [[3,3,3]]=>3 [[1,1],[3]]=>1 [[1,2],[3]]=>1 [[1,3],[2]]=>1 [[1,3],[3]]=>1 [[2,2],[3]]=>2 [[2,3],[3]]=>2 [[1],[2],[3]]=>1 [[1,1,4]]=>1 [[1,2,4]]=>1 [[1,3,4]]=>1 [[1,4,4]]=>1 [[2,2,4]]=>2 [[2,3,4]]=>2 [[2,4,4]]=>2 [[3,3,4]]=>3 [[3,4,4]]=>3 [[4,4,4]]=>4 [[1,1],[4]]=>1 [[1,2],[4]]=>1 [[1,4],[2]]=>1 [[1,3],[4]]=>1 [[1,4],[3]]=>1 [[1,4],[4]]=>1 [[2,2],[4]]=>2 [[2,3],[4]]=>2 [[2,4],[3]]=>2 [[2,4],[4]]=>2 [[3,3],[4]]=>3 [[3,4],[4]]=>3 [[1],[2],[4]]=>1 [[1],[3],[4]]=>1 [[2],[3],[4]]=>2 [[1,1,5]]=>1 [[1,2,5]]=>1 [[1,3,5]]=>1 [[1,4,5]]=>1 [[1,5,5]]=>1 [[2,2,5]]=>2 [[2,3,5]]=>2 [[2,4,5]]=>2 [[2,5,5]]=>2 [[3,3,5]]=>3 [[3,4,5]]=>3 [[3,5,5]]=>3 [[4,4,5]]=>4 [[4,5,5]]=>4 [[5,5,5]]=>5 [[1,1],[5]]=>1 [[1,2],[5]]=>1 [[1,5],[2]]=>1 [[1,3],[5]]=>1 [[1,5],[3]]=>1 [[1,4],[5]]=>1 [[1,5],[4]]=>1 [[1,5],[5]]=>1 [[2,2],[5]]=>2 [[2,3],[5]]=>2 [[2,5],[3]]=>2 [[2,4],[5]]=>2 [[2,5],[4]]=>2 [[2,5],[5]]=>2 [[3,3],[5]]=>3 [[3,4],[5]]=>3 [[3,5],[4]]=>3 [[3,5],[5]]=>3 [[4,4],[5]]=>4 [[4,5],[5]]=>4 [[1],[2],[5]]=>1 [[1],[3],[5]]=>1 [[1],[4],[5]]=>1 [[2],[3],[5]]=>2 [[2],[4],[5]]=>2 [[3],[4],[5]]=>3 [[1,1,1,1]]=>1 [[1,1,1,2]]=>1 [[1,1,2,2]]=>1 [[1,2,2,2]]=>1 [[2,2,2,2]]=>2 [[1,1,1],[2]]=>1 [[1,1,2],[2]]=>1 [[1,2,2],[2]]=>1 [[1,1],[2,2]]=>3 [[1,1,1,3]]=>1 [[1,1,2,3]]=>1 [[1,1,3,3]]=>1 [[1,2,2,3]]=>1 [[1,2,3,3]]=>1 [[1,3,3,3]]=>1 [[2,2,2,3]]=>2 [[2,2,3,3]]=>2 [[2,3,3,3]]=>2 [[3,3,3,3]]=>3 [[1,1,1],[3]]=>1 [[1,1,2],[3]]=>1 [[1,1,3],[2]]=>1 [[1,1,3],[3]]=>1 [[1,2,2],[3]]=>1 [[1,2,3],[2]]=>1 [[1,2,3],[3]]=>1 [[1,3,3],[2]]=>1 [[1,3,3],[3]]=>1 [[2,2,2],[3]]=>2 [[2,2,3],[3]]=>2 [[2,3,3],[3]]=>2 [[1,1],[2,3]]=>4 [[1,1],[3,3]]=>4 [[1,2],[2,3]]=>4 [[1,2],[3,3]]=>4 [[2,2],[3,3]]=>5 [[1,1],[2],[3]]=>1 [[1,2],[2],[3]]=>1 [[1,3],[2],[3]]=>1 [[1,1,1,4]]=>1 [[1,1,2,4]]=>1 [[1,1,3,4]]=>1 [[1,1,4,4]]=>1 [[1,2,2,4]]=>1 [[1,2,3,4]]=>1 [[1,2,4,4]]=>1 [[1,3,3,4]]=>1 [[1,3,4,4]]=>1 [[1,4,4,4]]=>1 [[2,2,2,4]]=>2 [[2,2,3,4]]=>2 [[2,2,4,4]]=>2 [[2,3,3,4]]=>2 [[2,3,4,4]]=>2 [[2,4,4,4]]=>2 [[3,3,3,4]]=>3 [[3,3,4,4]]=>3 [[3,4,4,4]]=>3 [[4,4,4,4]]=>4 [[1,1,1],[4]]=>1 [[1,1,2],[4]]=>1 [[1,1,4],[2]]=>1 [[1,1,3],[4]]=>1 [[1,1,4],[3]]=>1 [[1,1,4],[4]]=>1 [[1,2,2],[4]]=>1 [[1,2,4],[2]]=>1 [[1,2,3],[4]]=>1 [[1,2,4],[3]]=>1 [[1,3,4],[2]]=>1 [[1,2,4],[4]]=>1 [[1,4,4],[2]]=>1 [[1,3,3],[4]]=>1 [[1,3,4],[3]]=>1 [[1,3,4],[4]]=>1 [[1,4,4],[3]]=>1 [[1,4,4],[4]]=>1 [[2,2,2],[4]]=>2 [[2,2,3],[4]]=>2 [[2,2,4],[3]]=>2 [[2,2,4],[4]]=>2 [[2,3,3],[4]]=>2 [[2,3,4],[3]]=>2 [[2,3,4],[4]]=>2 [[2,4,4],[3]]=>2 [[2,4,4],[4]]=>2 [[3,3,3],[4]]=>3 [[3,3,4],[4]]=>3 [[3,4,4],[4]]=>3 [[1,1],[2,4]]=>5 [[1,1],[3,4]]=>5 [[1,1],[4,4]]=>5 [[1,2],[2,4]]=>5 [[1,2],[3,4]]=>5 [[1,3],[2,4]]=>5 [[1,2],[4,4]]=>5 [[1,3],[3,4]]=>5 [[1,3],[4,4]]=>5 [[2,2],[3,4]]=>6 [[2,2],[4,4]]=>6 [[2,3],[3,4]]=>6 [[2,3],[4,4]]=>6 [[3,3],[4,4]]=>7 [[1,1],[2],[4]]=>1 [[1,1],[3],[4]]=>1 [[1,2],[2],[4]]=>1 [[1,2],[3],[4]]=>1 [[1,3],[2],[4]]=>1 [[1,4],[2],[3]]=>1 [[1,4],[2],[4]]=>1 [[1,3],[3],[4]]=>1 [[1,4],[3],[4]]=>1 [[2,2],[3],[4]]=>2 [[2,3],[3],[4]]=>2 [[2,4],[3],[4]]=>2 [[1],[2],[3],[4]]=>1 [[1,1,1,1,1]]=>1 [[1,1,1,1,2]]=>1 [[1,1,1,2,2]]=>1 [[1,1,2,2,2]]=>1 [[1,2,2,2,2]]=>1 [[2,2,2,2,2]]=>2 [[1,1,1,1],[2]]=>1 [[1,1,1,2],[2]]=>1 [[1,1,2,2],[2]]=>1 [[1,2,2,2],[2]]=>1 [[1,1,1],[2,2]]=>3 [[1,1,2],[2,2]]=>3 [[1,1,1,1,3]]=>1 [[1,1,1,2,3]]=>1 [[1,1,1,3,3]]=>1 [[1,1,2,2,3]]=>1 [[1,1,2,3,3]]=>1 [[1,1,3,3,3]]=>1 [[1,2,2,2,3]]=>1 [[1,2,2,3,3]]=>1 [[1,2,3,3,3]]=>1 [[1,3,3,3,3]]=>1 [[2,2,2,2,3]]=>2 [[2,2,2,3,3]]=>2 [[2,2,3,3,3]]=>2 [[2,3,3,3,3]]=>2 [[3,3,3,3,3]]=>3 [[1,1,1,1],[3]]=>1 [[1,1,1,2],[3]]=>1 [[1,1,1,3],[2]]=>1 [[1,1,1,3],[3]]=>1 [[1,1,2,2],[3]]=>1 [[1,1,2,3],[2]]=>1 [[1,1,2,3],[3]]=>1 [[1,1,3,3],[2]]=>1 [[1,1,3,3],[3]]=>1 [[1,2,2,2],[3]]=>1 [[1,2,2,3],[2]]=>1 [[1,2,2,3],[3]]=>1 [[1,2,3,3],[2]]=>1 [[1,2,3,3],[3]]=>1 [[1,3,3,3],[2]]=>1 [[1,3,3,3],[3]]=>1 [[2,2,2,2],[3]]=>2 [[2,2,2,3],[3]]=>2 [[2,2,3,3],[3]]=>2 [[2,3,3,3],[3]]=>2 [[1,1,1],[2,3]]=>4 [[1,1,1],[3,3]]=>4 [[1,1,2],[2,3]]=>4 [[1,1,3],[2,2]]=>3 [[1,1,2],[3,3]]=>4 [[1,1,3],[2,3]]=>4 [[1,1,3],[3,3]]=>4 [[1,2,2],[2,3]]=>4 [[1,2,2],[3,3]]=>4 [[1,2,3],[2,3]]=>4 [[1,2,3],[3,3]]=>4 [[2,2,2],[3,3]]=>5 [[2,2,3],[3,3]]=>5 [[1,1,1],[2],[3]]=>1 [[1,1,2],[2],[3]]=>1 [[1,1,3],[2],[3]]=>1 [[1,2,2],[2],[3]]=>1 [[1,2,3],[2],[3]]=>1 [[1,3,3],[2],[3]]=>1 [[1,1],[2,2],[3]]=>3 [[1,1],[2,3],[3]]=>4 [[1,2],[2,3],[3]]=>4 [[1,2,3,4,5]]=>1 [[1,2,3,4],[5]]=>1 [[1,2,3,5],[4]]=>1 [[1,2,4,5],[3]]=>1 [[1,3,4,5],[2]]=>1 [[1,2,3],[4,5]]=>6 [[1,2,4],[3,5]]=>6 [[1,2,5],[3,4]]=>5 [[1,3,4],[2,5]]=>6 [[1,3,5],[2,4]]=>5 [[1,2,3],[4],[5]]=>1 [[1,2,4],[3],[5]]=>1 [[1,2,5],[3],[4]]=>1 [[1,3,4],[2],[5]]=>1 [[1,3,5],[2],[4]]=>1 [[1,4,5],[2],[3]]=>1 [[1,2],[3,4],[5]]=>5 [[1,2],[3,5],[4]]=>6 [[1,3],[2,4],[5]]=>5 [[1,3],[2,5],[4]]=>6 [[1,4],[2,5],[3]]=>6 [[1,2],[3],[4],[5]]=>1 [[1,3],[2],[4],[5]]=>1 [[1,4],[2],[3],[5]]=>1 [[1,5],[2],[3],[4]]=>1 [[1],[2],[3],[4],[5]]=>1 [[1,1,1,1,1,2]]=>1 [[1,1,1,1,2,2]]=>1 [[1,1,1,2,2,2]]=>1 [[1,1,2,2,2,2]]=>1 [[1,2,2,2,2,2]]=>1 [[2,2,2,2,2,2]]=>2 [[1,1,1,1,1],[2]]=>1 [[1,1,1,1,2],[2]]=>1 [[1,1,1,2,2],[2]]=>1 [[1,1,2,2,2],[2]]=>1 [[1,2,2,2,2],[2]]=>1 [[1,1,1,1],[2,2]]=>3 [[1,1,1,2],[2,2]]=>3 [[1,1,2,2],[2,2]]=>3 [[1,1,1],[2,2,2]]=>3 [[1,1,1,2,2],[3]]=>1 [[1,1,1,2,3],[3]]=>1 [[1,1,2,2,2],[3]]=>1 [[1,1,2,2,3],[3]]=>1 [[1,1,2,3,3],[3]]=>1 [[1,2,2,2,3],[3]]=>1 [[1,2,2,3,3],[3]]=>1 [[1,1,1],[2,2],[3]]=>3 [[1,1,1],[2,3],[3]]=>4 [[1,1,2],[2,2],[3]]=>3 [[1,1,2],[2,3],[3]]=>4 [[1,1,3],[2,3],[3]]=>4 [[1,2,2],[2,3],[3]]=>4 [[1,2,3],[2,3],[3]]=>4 [[1,2,3,4,5,6]]=>1 [[1,2,3,4,5],[6]]=>1 [[1,2,3,4,6],[5]]=>1 [[1,2,3,4],[5],[6]]=>1 [[1,2,3,5,6],[4]]=>1 [[1,2,3,5],[4,6]]=>7 [[1,2,3,5],[4],[6]]=>1 [[1,2,3,4],[5,6]]=>7 [[1,2,3,6],[4],[5]]=>1 [[1,2,3],[4],[5],[6]]=>1 [[1,2,4,5,6],[3]]=>1 [[1,2,4,5],[3,6]]=>7 [[1,2,4,6],[3,5]]=>6 [[1,2,4],[3,5],[6]]=>6 [[1,2,4,5],[3],[6]]=>1 [[1,2,4,6],[3],[5]]=>1 [[1,2,4],[3],[5],[6]]=>1 [[1,2,3,6],[4,5]]=>6 [[1,2,3],[4,5],[6]]=>6 [[1,2,5,6],[3],[4]]=>1 [[1,2,5],[3,6],[4]]=>7 [[1,2,5],[3],[4],[6]]=>1 [[1,2,3],[4,6],[5]]=>7 [[1,2,4],[3,6],[5]]=>7 [[1,2,6],[3],[4],[5]]=>1 [[1,2],[3],[4],[5],[6]]=>1 [[1,3,4,5,6],[2]]=>1 [[1,3,4,5],[2,6]]=>7 [[1,3,4,6],[2,5]]=>6 [[1,3,4],[2,5],[6]]=>6 [[1,3,5,6],[2,4]]=>5 [[1,3,5],[2,4,6]]=>5 [[1,3,5],[2,4],[6]]=>5 [[1,3,4],[2,5,6]]=>6 [[1,3,6],[2,4],[5]]=>5 [[1,3],[2,4],[5],[6]]=>5 [[1,3,4,5],[2],[6]]=>1 [[1,3,4,6],[2],[5]]=>1 [[1,3,4],[2],[5],[6]]=>1 [[1,3,5,6],[2],[4]]=>1 [[1,3,5],[2,6],[4]]=>7 [[1,3,5],[2],[4],[6]]=>1 [[1,3,4],[2,6],[5]]=>7 [[1,3,6],[2],[4],[5]]=>1 [[1,3],[2],[4],[5],[6]]=>1 [[1,2,5,6],[3,4]]=>5 [[1,2,5],[3,4,6]]=>5 [[1,2,5],[3,4],[6]]=>5 [[1,2,4],[3,5,6]]=>6 [[1,2,6],[3,4],[5]]=>5 [[1,2],[3,4],[5],[6]]=>5 [[1,4,5,6],[2],[3]]=>1 [[1,4,5],[2,6],[3]]=>7 [[1,4,6],[2,5],[3]]=>6 [[1,4],[2,5],[3,6]]=>6 [[1,4],[2,5],[3],[6]]=>6 [[1,4,5],[2],[3],[6]]=>1 [[1,4,6],[2],[3],[5]]=>1 [[1,4],[2],[3],[5],[6]]=>1 [[1,2,3],[4,5,6]]=>6 [[1,2,6],[3,5],[4]]=>6 [[1,2],[3,5],[4],[6]]=>6 [[1,3,6],[2,5],[4]]=>6 [[1,3],[2,5],[4,6]]=>6 [[1,3],[2,5],[4],[6]]=>6 [[1,2],[3,5],[4,6]]=>6 [[1,5,6],[2],[3],[4]]=>1 [[1,5],[2,6],[3],[4]]=>7 [[1,5],[2],[3],[4],[6]]=>1 [[1,2],[3,6],[4],[5]]=>7 [[1,3],[2,4],[5,6]]=>5 [[1,3],[2,6],[4],[5]]=>7 [[1,2],[3,4],[5,6]]=>5 [[1,4],[2,6],[3],[5]]=>7 [[1,6],[2],[3],[4],[5]]=>1 [[1],[2],[3],[4],[5],[6]]=>1 [[1,1,1,1],[2,2,2],[3,3],[4]]=>3 [[1,1,1,2],[2,2,2],[3,3],[4]]=>3 [[1,1,1,1],[2,2,3],[3,3],[4]]=>3 [[1,1,1,2],[2,2,3],[3,3],[4]]=>3 [[1,1,1,3],[2,2,3],[3,3],[4]]=>3 [[1,1,2,2],[2,2,3],[3,3],[4]]=>3 [[1,1,2,3],[2,2,3],[3,3],[4]]=>3 [[1,1,1,1],[2,2,2],[3,4],[4]]=>3 [[1,1,1,2],[2,2,2],[3,4],[4]]=>3 [[1,1,1,1],[2,2,3],[3,4],[4]]=>3 [[1,1,1,2],[2,2,3],[3,4],[4]]=>3 [[1,1,1,3],[2,2,3],[3,4],[4]]=>3 [[1,1,2,2],[2,2,3],[3,4],[4]]=>3 [[1,1,2,3],[2,2,3],[3,4],[4]]=>3 [[1,1,1,1],[2,2,4],[3,4],[4]]=>3 [[1,1,1,2],[2,2,4],[3,4],[4]]=>3 [[1,1,1,3],[2,2,4],[3,4],[4]]=>3 [[1,1,1,4],[2,2,4],[3,4],[4]]=>3 [[1,1,2,2],[2,2,4],[3,4],[4]]=>3 [[1,1,2,3],[2,2,4],[3,4],[4]]=>3 [[1,1,2,4],[2,2,4],[3,4],[4]]=>3 [[1,1,1,1],[2,3,3],[3,4],[4]]=>4 [[1,1,1,2],[2,3,3],[3,4],[4]]=>4 [[1,1,1,3],[2,3,3],[3,4],[4]]=>4 [[1,1,2,2],[2,3,3],[3,4],[4]]=>4 [[1,1,2,3],[2,3,3],[3,4],[4]]=>4 [[1,1,1,1],[2,3,4],[3,4],[4]]=>4 [[1,1,1,2],[2,3,4],[3,4],[4]]=>4 [[1,1,1,3],[2,3,4],[3,4],[4]]=>4 [[1,1,1,4],[2,3,4],[3,4],[4]]=>4 [[1,1,2,2],[2,3,4],[3,4],[4]]=>4 [[1,1,2,3],[2,3,4],[3,4],[4]]=>4 [[1,1,2,4],[2,3,4],[3,4],[4]]=>4 [[1,1,3,3],[2,3,4],[3,4],[4]]=>4 [[1,1,3,4],[2,3,4],[3,4],[4]]=>4 [[1,2,2,2],[2,3,3],[3,4],[4]]=>4 [[1,2,2,3],[2,3,3],[3,4],[4]]=>4 [[1,2,2,2],[2,3,4],[3,4],[4]]=>4 [[1,2,2,3],[2,3,4],[3,4],[4]]=>4 [[1,2,2,4],[2,3,4],[3,4],[4]]=>4 [[1,2,3,3],[2,3,4],[3,4],[4]]=>4 [[1,2,3,4],[2,3,4],[3,4],[4]]=>4 [[1,1,1,1,2,2,2],[3,3],[4]]=>4 [[1,1,1,2,2,2,2],[3,3],[4]]=>4 [[1,1,1,1,2,2,3],[3,3],[4]]=>4 [[1,1,1,2,2,2,3],[3,3],[4]]=>4 [[1,1,1,2,2,3,3],[3,3],[4]]=>4 [[1,1,2,2,2,2,3],[3,3],[4]]=>4 [[1,1,2,2,2,3,3],[3,3],[4]]=>4 [[1,1,1,1,2,2,2],[3,4],[4]]=>5 [[1,1,1,2,2,2,2],[3,4],[4]]=>5 [[1,1,1,1,2,2,3],[3,4],[4]]=>5 [[1,1,1,2,2,2,3],[3,4],[4]]=>5 [[1,1,1,2,2,3],[3,3,4],[4]]=>4 [[1,1,2,2,2,2,3],[3,4],[4]]=>5 [[1,1,2,2,2,3],[3,3,4],[4]]=>4 [[1,1,1,1,2,2,4],[3,4],[4]]=>5 [[1,1,1,2,2,2,4],[3,4],[4]]=>5 [[1,1,1,2,2,4,4],[3,3],[4]]=>4 [[1,1,1,2,2,4,4],[3,4],[4]]=>5 [[1,1,2,2,2,2,4],[3,4],[4]]=>5 [[1,1,2,2,2,4,4],[3,3],[4]]=>4 [[1,1,2,2,2,4,4],[3,4],[4]]=>5 [[1,1,1,1,2,3,3],[3,4],[4]]=>5 [[1,1,1,2,2,3,3],[3,4],[4]]=>5 [[1,1,1,2,3,3,3],[3,4],[4]]=>5 [[1,1,2,2,2,3,3],[3,4],[4]]=>5 [[1,1,2,2,3,3,3],[3,4],[4]]=>5 [[1,1,1,1,2,3,4],[3,4],[4]]=>5 [[1,1,1,2,2,3,4],[3,4],[4]]=>5 [[1,1,1,2,3,3,4],[3,4],[4]]=>5 [[1,1,1,2,3,4,4],[3,4],[4]]=>5 [[1,1,2,2,2,3,4],[3,4],[4]]=>5 [[1,1,2,2,3,3,4],[3,4],[4]]=>5 [[1,1,2,2,3,4,4],[3,4],[4]]=>5 [[1,1,2,3,3,3,4],[3,4],[4]]=>5 [[1,1,2,3,3,4,4],[3,4],[4]]=>5 [[1,2,2,2,2,3,3],[3,4],[4]]=>5 [[1,2,2,2,3,3,3],[3,4],[4]]=>5 [[1,2,2,2,2,3,4],[3,4],[4]]=>5 [[1,2,2,2,3,3,4],[3,4],[4]]=>5 [[1,2,2,2,3,4,4],[3,4],[4]]=>5 [[1,2,2,3,3,3,4],[3,4],[4]]=>5 [[1,2,2,3,3,4,4],[3,4],[4]]=>5 [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,4],[5]]=>6 [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,4],[5]]=>6 [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,4],[5]]=>6 [[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,4],[5]]=>6 [[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,4],[5]]=>6 [[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,4],[5]]=>6 [[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,4],[5]]=>6 [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,4],[5]]=>7 [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,4],[5]]=>7 [[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,4],[5]]=>7 [[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,4],[5]]=>7 [[1,1,1,1,3],[2,2,2,3],[3,3,4],[4,4],[5]]=>7 [[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,4],[5]]=>7 [[1,1,1,1,1],[2,2,2,4],[3,3,4],[4,4],[5]]=>7 [[1,1,1,1,2],[2,2,2,4],[3,3,4],[4,4],[5]]=>7 [[1,1,1,1,3],[2,2,2,4],[3,3,4],[4,4],[5]]=>7 [[1,1,1,1,4],[2,2,2,4],[3,3,4],[4,4],[5]]=>7 [[1,1,1,2,2],[2,2,2,4],[3,3,4],[4,4],[5]]=>7 [[1,1,1,2,4],[2,2,2,4],[3,3,4],[4,4],[5]]=>7 [[1,1,1,1,1],[2,2,3,3],[3,3,4],[4,4],[5]]=>7 [[1,1,1,1,3],[2,2,3,3],[3,3,4],[4,4],[5]]=>7 [[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,4],[5]]=>7 [[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,4],[5]]=>7 [[1,1,1,1,4],[2,2,3,4],[3,3,4],[4,4],[5]]=>7 [[1,1,1,2,3],[2,2,3,4],[3,3,4],[4,4],[5]]=>7 [[1,1,1,3,3],[2,2,3,4],[3,3,4],[4,4],[5]]=>7 [[1,1,1,3,4],[2,2,3,4],[3,3,4],[4,4],[5]]=>7 [[1,1,2,2,2],[2,2,3,3],[3,3,4],[4,4],[5]]=>7 [[1,1,2,2,3],[2,2,3,3],[3,3,4],[4,4],[5]]=>7 [[1,1,2,2,2],[2,2,3,4],[3,3,4],[4,4],[5]]=>7 [[1,1,2,2,4],[2,2,3,4],[3,3,4],[4,4],[5]]=>7 [[1,1,2,3,3],[2,2,3,4],[3,3,4],[4,4],[5]]=>7 [[1,1,2,3,4],[2,2,3,4],[3,3,4],[4,4],[5]]=>7 [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,5],[5]]=>6 [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,5],[5]]=>6 [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,5],[5]]=>6 [[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,5],[5]]=>6 [[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,5],[5]]=>6 [[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,5],[5]]=>6 [[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,5],[5]]=>6 [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,5],[5]]=>7 [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,5],[5]]=>7 [[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,5],[5]]=>7 [[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,5],[5]]=>7 [[1,1,1,1,3],[2,2,2,3],[3,3,4],[4,5],[5]]=>7 [[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,5],[5]]=>7 [[1,1,1,1,1],[2,2,2,4],[3,3,4],[4,5],[5]]=>7 [[1,1,1,1,2],[2,2,2,4],[3,3,4],[4,5],[5]]=>7 [[1,1,1,1,3],[2,2,2,4],[3,3,4],[4,5],[5]]=>7 [[1,1,1,1,4],[2,2,2,4],[3,3,4],[4,5],[5]]=>7 [[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,5],[5]]=>7 [[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,5],[5]]=>7 [[1,1,1,2,3],[2,2,3,4],[3,3,4],[4,5],[5]]=>7 [[1,1,2,3,4],[2,2,3,4],[3,3,4],[4,5],[5]]=>7 [[1,1,1,1,1],[2,2,2,2],[3,3,5],[4,5],[5]]=>8 [[1,1,1,1,2],[2,2,2,2],[3,3,5],[4,5],[5]]=>8 [[1,1,1,1,1],[2,2,2,3],[3,3,5],[4,5],[5]]=>8 [[1,1,1,1,2],[2,2,2,3],[3,3,5],[4,5],[5]]=>8 [[1,1,1,1,3],[2,2,2,3],[3,3,5],[4,5],[5]]=>8 [[1,1,1,1,1],[2,2,2,4],[3,3,5],[4,5],[5]]=>8 [[1,1,1,1,2],[2,2,2,4],[3,3,5],[4,5],[5]]=>8 [[1,1,1,1,3],[2,2,2,4],[3,3,5],[4,5],[5]]=>8 [[1,1,1,1,4],[2,2,2,4],[3,3,5],[4,5],[5]]=>8 [[1,1,1,1,1],[2,2,2,5],[3,3,5],[4,5],[5]]=>8 [[1,1,1,1,2],[2,2,2,5],[3,3,5],[4,5],[5]]=>8 [[1,1,1,1,3],[2,2,2,5],[3,3,5],[4,5],[5]]=>8 [[1,1,1,1,4],[2,2,2,5],[3,3,5],[4,5],[5]]=>8 [[1,1,1,1,5],[2,2,2,5],[3,3,5],[4,5],[5]]=>8 [[1,1,1,2,2],[2,2,2,5],[3,3,5],[4,5],[5]]=>8 [[1,1,1,2,5],[2,2,2,5],[3,3,5],[4,5],[5]]=>8 [[1,1,1,1,1],[2,2,3,3],[3,3,5],[4,5],[5]]=>8 [[1,1,1,1,3],[2,2,3,3],[3,3,5],[4,5],[5]]=>8 [[1,1,1,1,1],[2,2,3,5],[3,3,5],[4,5],[5]]=>8 [[1,1,1,1,5],[2,2,3,5],[3,3,5],[4,5],[5]]=>8 [[1,1,1,3,3],[2,2,3,5],[3,3,5],[4,5],[5]]=>8 [[1,1,1,3,5],[2,2,3,5],[3,3,5],[4,5],[5]]=>8 [[1,1,2,2,2],[2,2,3,3],[3,3,5],[4,5],[5]]=>8 [[1,1,2,2,3],[2,2,3,3],[3,3,5],[4,5],[5]]=>8 [[1,1,2,2,2],[2,2,3,5],[3,3,5],[4,5],[5]]=>8 [[1,1,2,2,5],[2,2,3,5],[3,3,5],[4,5],[5]]=>8 [[1,1,2,3,3],[2,2,3,5],[3,3,5],[4,5],[5]]=>8 [[1,1,2,3,5],[2,2,3,5],[3,3,5],[4,5],[5]]=>8 [[1,1,1,1,1],[2,2,2,2],[3,4,4],[4,5],[5]]=>7 [[1,1,1,1,2],[2,2,2,2],[3,4,4],[4,5],[5]]=>7 [[1,1,1,1,1],[2,2,2,4],[3,4,4],[4,5],[5]]=>7 [[1,1,1,1,4],[2,2,2,4],[3,4,4],[4,5],[5]]=>7 [[1,1,1,2,2],[2,2,2,4],[3,4,4],[4,5],[5]]=>7 [[1,1,1,2,4],[2,2,2,4],[3,4,4],[4,5],[5]]=>7 [[1,1,1,1,1],[2,2,2,2],[3,4,5],[4,5],[5]]=>8 [[1,1,1,1,2],[2,2,2,2],[3,4,5],[4,5],[5]]=>8 [[1,1,1,1,1],[2,2,2,3],[3,4,5],[4,5],[5]]=>8 [[1,1,1,1,2],[2,2,2,3],[3,4,5],[4,5],[5]]=>8 [[1,1,1,2,3],[2,2,2,3],[3,4,5],[4,5],[5]]=>8 [[1,1,1,1,1],[2,2,2,5],[3,4,5],[4,5],[5]]=>8 [[1,1,1,1,5],[2,2,2,5],[3,4,5],[4,5],[5]]=>8 [[1,1,1,2,2],[2,2,2,5],[3,4,5],[4,5],[5]]=>8 [[1,1,1,2,5],[2,2,2,5],[3,4,5],[4,5],[5]]=>8 [[1,1,1,1,1],[2,2,3,4],[3,4,5],[4,5],[5]]=>8 [[1,1,1,1,2],[2,2,3,4],[3,4,5],[4,5],[5]]=>8 [[1,1,1,2,3],[2,2,3,4],[3,4,5],[4,5],[5]]=>8 [[1,1,2,3,4],[2,2,3,4],[3,4,5],[4,5],[5]]=>8 [[1,1,1,1,1],[2,2,4,4],[3,4,5],[4,5],[5]]=>8 [[1,1,1,1,4],[2,2,4,4],[3,4,5],[4,5],[5]]=>8 [[1,1,1,1,1],[2,2,4,5],[3,4,5],[4,5],[5]]=>8 [[1,1,1,1,5],[2,2,4,5],[3,4,5],[4,5],[5]]=>8 [[1,1,1,4,4],[2,2,4,5],[3,4,5],[4,5],[5]]=>8 [[1,1,1,4,5],[2,2,4,5],[3,4,5],[4,5],[5]]=>8 [[1,1,2,2,2],[2,2,4,4],[3,4,5],[4,5],[5]]=>8 [[1,1,2,2,4],[2,2,4,4],[3,4,5],[4,5],[5]]=>8 [[1,1,2,2,2],[2,2,4,5],[3,4,5],[4,5],[5]]=>8 [[1,1,2,2,5],[2,2,4,5],[3,4,5],[4,5],[5]]=>8 [[1,1,2,4,4],[2,2,4,5],[3,4,5],[4,5],[5]]=>8 [[1,1,2,4,5],[2,2,4,5],[3,4,5],[4,5],[5]]=>8 [[1,1,1,1,1],[2,3,3,3],[3,4,4],[4,5],[5]]=>8 [[1,1,1,1,3],[2,3,3,3],[3,4,4],[4,5],[5]]=>8 [[1,1,1,1,1],[2,3,3,4],[3,4,4],[4,5],[5]]=>8 [[1,1,1,1,4],[2,3,3,4],[3,4,4],[4,5],[5]]=>8 [[1,1,1,3,3],[2,3,3,4],[3,4,4],[4,5],[5]]=>8 [[1,1,1,3,4],[2,3,3,4],[3,4,4],[4,5],[5]]=>8 [[1,1,1,1,1],[2,3,3,3],[3,4,5],[4,5],[5]]=>9 [[1,1,1,1,3],[2,3,3,3],[3,4,5],[4,5],[5]]=>9 [[1,1,1,1,1],[2,3,3,5],[3,4,5],[4,5],[5]]=>9 [[1,1,1,1,5],[2,3,3,5],[3,4,5],[4,5],[5]]=>9 [[1,1,1,3,3],[2,3,3,5],[3,4,5],[4,5],[5]]=>9 [[1,1,1,3,5],[2,3,3,5],[3,4,5],[4,5],[5]]=>9 [[1,1,1,1,1],[2,3,4,4],[3,4,5],[4,5],[5]]=>9 [[1,1,1,1,4],[2,3,4,4],[3,4,5],[4,5],[5]]=>9 [[1,1,1,1,1],[2,3,4,5],[3,4,5],[4,5],[5]]=>9 [[1,1,1,1,2],[2,3,4,5],[3,4,5],[4,5],[5]]=>9 [[1,1,1,1,5],[2,3,4,5],[3,4,5],[4,5],[5]]=>9 [[1,1,1,2,3],[2,3,4,5],[3,4,5],[4,5],[5]]=>9 [[1,1,1,4,4],[2,3,4,5],[3,4,5],[4,5],[5]]=>9 [[1,1,1,4,5],[2,3,4,5],[3,4,5],[4,5],[5]]=>9 [[1,1,2,3,4],[2,3,4,5],[3,4,5],[4,5],[5]]=>9 [[1,1,3,3,3],[2,3,4,4],[3,4,5],[4,5],[5]]=>9 [[1,1,3,3,4],[2,3,4,4],[3,4,5],[4,5],[5]]=>9 [[1,1,3,3,3],[2,3,4,5],[3,4,5],[4,5],[5]]=>9 [[1,1,3,3,5],[2,3,4,5],[3,4,5],[4,5],[5]]=>9 [[1,1,3,4,4],[2,3,4,5],[3,4,5],[4,5],[5]]=>9 [[1,1,3,4,5],[2,3,4,5],[3,4,5],[4,5],[5]]=>9 [[1,2,2,2,2],[2,3,3,3],[3,4,4],[4,5],[5]]=>8 [[1,2,2,2,3],[2,3,3,3],[3,4,4],[4,5],[5]]=>8 [[1,2,2,2,2],[2,3,3,4],[3,4,4],[4,5],[5]]=>8 [[1,2,2,2,4],[2,3,3,4],[3,4,4],[4,5],[5]]=>8 [[1,2,2,3,3],[2,3,3,4],[3,4,4],[4,5],[5]]=>8 [[1,2,2,3,4],[2,3,3,4],[3,4,4],[4,5],[5]]=>8 [[1,2,2,2,2],[2,3,3,3],[3,4,5],[4,5],[5]]=>9 [[1,2,2,2,3],[2,3,3,3],[3,4,5],[4,5],[5]]=>9 [[1,2,2,2,2],[2,3,3,5],[3,4,5],[4,5],[5]]=>9 [[1,2,2,2,5],[2,3,3,5],[3,4,5],[4,5],[5]]=>9 [[1,2,2,3,3],[2,3,3,5],[3,4,5],[4,5],[5]]=>9 [[1,2,2,3,5],[2,3,3,5],[3,4,5],[4,5],[5]]=>9 [[1,2,2,2,2],[2,3,4,4],[3,4,5],[4,5],[5]]=>9 [[1,2,2,2,4],[2,3,4,4],[3,4,5],[4,5],[5]]=>9 [[1,2,2,2,2],[2,3,4,5],[3,4,5],[4,5],[5]]=>9 [[1,2,2,2,5],[2,3,4,5],[3,4,5],[4,5],[5]]=>9 [[1,2,2,4,4],[2,3,4,5],[3,4,5],[4,5],[5]]=>9 [[1,2,2,4,5],[2,3,4,5],[3,4,5],[4,5],[5]]=>9 [[1,2,3,3,3],[2,3,4,4],[3,4,5],[4,5],[5]]=>9 [[1,2,3,3,4],[2,3,4,4],[3,4,5],[4,5],[5]]=>9 [[1,2,3,3,3],[2,3,4,5],[3,4,5],[4,5],[5]]=>9 [[1,2,3,3,5],[2,3,4,5],[3,4,5],[4,5],[5]]=>9 [[1,2,3,4,4],[2,3,4,5],[3,4,5],[4,5],[5]]=>9 [[1,2,3,4,5],[2,3,4,5],[3,4,5],[4,5],[5]]=>9 [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]]=>6 [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]]=>6 [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]]=>6 [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]]=>6 [[1,1,1,1,2,3],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]]=>6 [[1,1,1,2,3,4],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,2,3],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]]=>6 [[1,1,1,2,3,4],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,5],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,5],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,4],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,5],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,5],[6]]=>7 [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,5],[6]]=>7 [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,5],[6]]=>7 [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,5],[6]]=>7 [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,5],[6]]=>7 [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]=>7 [[1,1,1,1,1,2],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]=>7 [[1,1,1,1,2,3],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]=>7 [[1,1,1,2,3,4],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]]=>7 [[1,1,1,1,1,1],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]=>7 [[1,1,1,1,1,2],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]=>7 [[1,1,1,1,2,3],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]=>7 [[1,1,1,2,3,4],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]=>7 [[1,1,2,3,4,5],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]]=>7 [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]]=>6 [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]]=>6 [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,6],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,6],[6]]=>6 [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]]=>6 [[1,1,1,1,2,3],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]]=>6 [[1,1,1,2,3,4],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,2,3],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]]=>6 [[1,1,1,2,3,4],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,5],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,5],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,4],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,5],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,6],[6]]=>7 [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,6],[6]]=>7 [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,6],[6]]=>7 [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,6],[6]]=>7 [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,6],[6]]=>7 [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]]=>7 [[1,1,1,1,1,2],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]]=>7 [[1,1,1,1,2,3],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]]=>7 [[1,1,1,2,3,4],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]]=>7 [[1,1,1,1,1,1],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]=>7 [[1,1,1,1,1,2],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]=>7 [[1,1,1,1,2,3],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]=>7 [[1,1,1,2,3,4],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]=>7 [[1,1,2,3,4,5],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,6],[6]]=>7 [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,4],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,4],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,4],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,4],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,5],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,5],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,5],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,5],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,5],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,5],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,5],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,5],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,5],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,5],[3,3,3,5],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,5],[3,3,3,5],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,5],[3,3,3,5],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,4],[2,2,2,2,5],[3,3,3,5],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,5],[2,2,2,2,5],[3,3,3,5],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,6],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,6],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,6],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,6],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,6],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,6],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,6],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,6],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,6],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,5],[3,3,3,6],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,5],[3,3,3,6],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,5],[3,3,3,6],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,4],[2,2,2,2,5],[3,3,3,6],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,5],[2,2,2,2,5],[3,3,3,6],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,6],[3,3,3,6],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,6],[3,3,3,6],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,3],[2,2,2,2,6],[3,3,3,6],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,4],[2,2,2,2,6],[3,3,3,6],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,5],[2,2,2,2,6],[3,3,3,6],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,6],[2,2,2,2,6],[3,3,3,6],[4,4,6],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,5,6],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,5,6],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,5,6],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,5,6],[5,6],[6]]=>6 [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,3],[4,5,6],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,5,6],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,5,6],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,5,6],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,5,6],[5,6],[6]]=>6 [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,4],[4,5,6],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,5,6],[5,6],[6]]=>6 [[1,1,1,1,1,2],[2,2,2,3,4],[3,3,3,4],[4,5,6],[5,6],[6]]=>6 [[1,1,1,1,2,3],[2,2,2,3,4],[3,3,3,4],[4,5,6],[5,6],[6]]=>6 [[1,1,1,2,3,4],[2,2,2,3,4],[3,3,3,4],[4,5,6],[5,6],[6]]=>6 [[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,5,6],[5,6],[6]]=>7 [[1,1,1,1,1,2],[2,2,2,2,2],[3,3,4,5],[4,5,6],[5,6],[6]]=>7 [[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,5,6],[5,6],[6]]=>7 [[1,1,1,1,1,2],[2,2,2,2,3],[3,3,4,5],[4,5,6],[5,6],[6]]=>7 [[1,1,1,1,2,3],[2,2,2,2,3],[3,3,4,5],[4,5,6],[5,6],[6]]=>7 [[1,1,1,1,1,1],[2,2,2,3,4],[3,3,4,5],[4,5,6],[5,6],[6]]=>7 [[1,1,1,1,1,2],[2,2,2,3,4],[3,3,4,5],[4,5,6],[5,6],[6]]=>7 [[1,1,1,1,2,3],[2,2,2,3,4],[3,3,4,5],[4,5,6],[5,6],[6]]=>7 [[1,1,1,2,3,4],[2,2,2,3,4],[3,3,4,5],[4,5,6],[5,6],[6]]=>7 [[1,1,1,1,1,1],[2,2,3,4,5],[3,3,4,5],[4,5,6],[5,6],[6]]=>7 [[1,1,1,1,1,2],[2,2,3,4,5],[3,3,4,5],[4,5,6],[5,6],[6]]=>7 [[1,1,1,1,2,3],[2,2,3,4,5],[3,3,4,5],[4,5,6],[5,6],[6]]=>7 [[1,1,1,2,3,4],[2,2,3,4,5],[3,3,4,5],[4,5,6],[5,6],[6]]=>7 [[1,1,2,3,4,5],[2,2,3,4,5],[3,3,4,5],[4,5,6],[5,6],[6]]=>7 [[1,1,1,1,1,1],[2,2,2,2,2],[3,4,5,6],[4,5,6],[5,6],[6]]=>8 [[1,1,1,1,1,2],[2,2,2,2,2],[3,4,5,6],[4,5,6],[5,6],[6]]=>8 [[1,1,1,1,1,1],[2,2,2,2,3],[3,4,5,6],[4,5,6],[5,6],[6]]=>8 [[1,1,1,1,1,2],[2,2,2,2,3],[3,4,5,6],[4,5,6],[5,6],[6]]=>8 [[1,1,1,1,2,3],[2,2,2,2,3],[3,4,5,6],[4,5,6],[5,6],[6]]=>8 [[1,1,1,1,1,1],[2,2,2,3,4],[3,4,5,6],[4,5,6],[5,6],[6]]=>8 [[1,1,1,1,1,2],[2,2,2,3,4],[3,4,5,6],[4,5,6],[5,6],[6]]=>8 [[1,1,1,1,2,3],[2,2,2,3,4],[3,4,5,6],[4,5,6],[5,6],[6]]=>8 [[1,1,1,2,3,4],[2,2,2,3,4],[3,4,5,6],[4,5,6],[5,6],[6]]=>8 [[1,1,1,1,1,1],[2,2,3,4,5],[3,4,5,6],[4,5,6],[5,6],[6]]=>8 [[1,1,1,1,1,2],[2,2,3,4,5],[3,4,5,6],[4,5,6],[5,6],[6]]=>8 [[1,1,1,1,2,3],[2,2,3,4,5],[3,4,5,6],[4,5,6],[5,6],[6]]=>8 [[1,1,1,2,3,4],[2,2,3,4,5],[3,4,5,6],[4,5,6],[5,6],[6]]=>8 [[1,1,2,3,4,5],[2,2,3,4,5],[3,4,5,6],[4,5,6],[5,6],[6]]=>8 [[1,1,1,1,1,1],[2,3,4,5,6],[3,4,5,6],[4,5,6],[5,6],[6]]=>9 [[1,1,1,1,1,2],[2,3,4,5,6],[3,4,5,6],[4,5,6],[5,6],[6]]=>9 [[1,1,1,1,2,3],[2,3,4,5,6],[3,4,5,6],[4,5,6],[5,6],[6]]=>9 [[1,1,1,2,3,4],[2,3,4,5,6],[3,4,5,6],[4,5,6],[5,6],[6]]=>9 [[1,1,2,3,4,5],[2,3,4,5,6],[3,4,5,6],[4,5,6],[5,6],[6]]=>9 [[1,2,3,4,5,6],[2,3,4,5,6],[3,4,5,6],[4,5,6],[5,6],[6]]=>9
search for individual values
searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
Description
The trace of a semistandard tableau.
This is the sum of the entries on the diagonal.
References
[1] Stanley, R. P. The conjugate trace and trace of a plane partition MathSciNet:0309748
[2] Gansner, E. R. The Hillman-Grassl correspondence and the enumeration of reverse plane partitions MathSciNet:0607040
[3] Gansner, E. R. The enumeration of plane partitions via the Burge correspondence MathSciNet:0630832
[4] Krattenthaler, C. Generating functions for plane partitions of a given shape MathSciNet:1072987
Code
def statistic(T):
    m = 0
    for i, row in enumerate(T):
        try:
            m += row[i]
        except IndexError:
            break
    return m
Created
Nov 29, 2013 at 23:28 by Christian Krattenthaler
Updated
Aug 09, 2019 at 12:47 by Martin Rubey