Identifier
Values
=>
Cc0025;cc-rep-0 Cc0002;cc-rep
[[1]]=>[1]=>1 [[1],[1]]=>[1,1]=>0 [[2]]=>[2]=>2 [[1,1]]=>[2]=>2 [[1],[1],[1]]=>[1,1,1]=>1 [[2],[1]]=>[2,1]=>1 [[1,1],[1]]=>[2,1]=>1 [[3]]=>[3]=>3 [[2,1]]=>[3]=>3 [[1,1,1]]=>[3]=>3 [[1],[1],[1],[1]]=>[1,1,1,1]=>0 [[2],[1],[1]]=>[2,1,1]=>2 [[2],[2]]=>[2,2]=>0 [[1,1],[1],[1]]=>[2,1,1]=>2 [[1,1],[1,1]]=>[2,2]=>0 [[3],[1]]=>[3,1]=>2 [[2,1],[1]]=>[3,1]=>2 [[1,1,1],[1]]=>[3,1]=>2 [[4]]=>[4]=>4 [[3,1]]=>[4]=>4 [[2,2]]=>[4]=>4 [[2,1,1]]=>[4]=>4 [[1,1,1,1]]=>[4]=>4 [[1],[1],[1],[1],[1]]=>[1,1,1,1,1]=>1 [[2],[1],[1],[1]]=>[2,1,1,1]=>1 [[2],[2],[1]]=>[2,2,1]=>1 [[1,1],[1],[1],[1]]=>[2,1,1,1]=>1 [[1,1],[1,1],[1]]=>[2,2,1]=>1 [[3],[1],[1]]=>[3,1,1]=>3 [[3],[2]]=>[3,2]=>1 [[2,1],[1],[1]]=>[3,1,1]=>3 [[2,1],[2]]=>[3,2]=>1 [[2,1],[1,1]]=>[3,2]=>1 [[1,1,1],[1],[1]]=>[3,1,1]=>3 [[1,1,1],[1,1]]=>[3,2]=>1 [[4],[1]]=>[4,1]=>3 [[3,1],[1]]=>[4,1]=>3 [[2,2],[1]]=>[4,1]=>3 [[2,1,1],[1]]=>[4,1]=>3 [[1,1,1,1],[1]]=>[4,1]=>3 [[5]]=>[5]=>5 [[4,1]]=>[5]=>5 [[3,2]]=>[5]=>5 [[3,1,1]]=>[5]=>5 [[2,2,1]]=>[5]=>5 [[2,1,1,1]]=>[5]=>5 [[1,1,1,1,1]]=>[5]=>5 [[1],[1],[1],[1],[1],[1]]=>[1,1,1,1,1,1]=>0 [[2],[1],[1],[1],[1]]=>[2,1,1,1,1]=>2 [[2],[2],[1],[1]]=>[2,2,1,1]=>0 [[2],[2],[2]]=>[2,2,2]=>2 [[1,1],[1],[1],[1],[1]]=>[2,1,1,1,1]=>2 [[1,1],[1,1],[1],[1]]=>[2,2,1,1]=>0 [[1,1],[1,1],[1,1]]=>[2,2,2]=>2 [[3],[1],[1],[1]]=>[3,1,1,1]=>2 [[3],[2],[1]]=>[3,2,1]=>2 [[3],[3]]=>[3,3]=>0 [[2,1],[1],[1],[1]]=>[3,1,1,1]=>2 [[2,1],[2],[1]]=>[3,2,1]=>2 [[2,1],[1,1],[1]]=>[3,2,1]=>2 [[2,1],[2,1]]=>[3,3]=>0 [[1,1,1],[1],[1],[1]]=>[3,1,1,1]=>2 [[1,1,1],[1,1],[1]]=>[3,2,1]=>2 [[1,1,1],[1,1,1]]=>[3,3]=>0 [[4],[1],[1]]=>[4,1,1]=>4 [[4],[2]]=>[4,2]=>2 [[3,1],[1],[1]]=>[4,1,1]=>4 [[3,1],[2]]=>[4,2]=>2 [[3,1],[1,1]]=>[4,2]=>2 [[2,2],[1],[1]]=>[4,1,1]=>4 [[2,2],[2]]=>[4,2]=>2 [[2,2],[1,1]]=>[4,2]=>2 [[2,1,1],[1],[1]]=>[4,1,1]=>4 [[2,1,1],[2]]=>[4,2]=>2 [[2,1,1],[1,1]]=>[4,2]=>2 [[1,1,1,1],[1],[1]]=>[4,1,1]=>4 [[1,1,1,1],[1,1]]=>[4,2]=>2 [[5],[1]]=>[5,1]=>4 [[4,1],[1]]=>[5,1]=>4 [[3,2],[1]]=>[5,1]=>4 [[3,1,1],[1]]=>[5,1]=>4 [[2,2,1],[1]]=>[5,1]=>4 [[2,1,1,1],[1]]=>[5,1]=>4 [[1,1,1,1,1],[1]]=>[5,1]=>4 [[6]]=>[6]=>6 [[5,1]]=>[6]=>6 [[4,2]]=>[6]=>6 [[4,1,1]]=>[6]=>6 [[3,3]]=>[6]=>6 [[3,2,1]]=>[6]=>6 [[3,1,1,1]]=>[6]=>6 [[2,2,2]]=>[6]=>6 [[2,2,1,1]]=>[6]=>6 [[2,1,1,1,1]]=>[6]=>6 [[1,1,1,1,1,1]]=>[6]=>6 [[1],[1],[1],[1],[1],[1],[1]]=>[1,1,1,1,1,1,1]=>1 [[2],[1],[1],[1],[1],[1]]=>[2,1,1,1,1,1]=>1 [[2],[2],[1],[1],[1]]=>[2,2,1,1,1]=>1 [[2],[2],[2],[1]]=>[2,2,2,1]=>1 [[1,1],[1],[1],[1],[1],[1]]=>[2,1,1,1,1,1]=>1 [[1,1],[1,1],[1],[1],[1]]=>[2,2,1,1,1]=>1 [[1,1],[1,1],[1,1],[1]]=>[2,2,2,1]=>1 [[3],[1],[1],[1],[1]]=>[3,1,1,1,1]=>3 [[3],[2],[1],[1]]=>[3,2,1,1]=>1 [[3],[2],[2]]=>[3,2,2]=>3 [[3],[3],[1]]=>[3,3,1]=>1 [[2,1],[1],[1],[1],[1]]=>[3,1,1,1,1]=>3 [[2,1],[2],[1],[1]]=>[3,2,1,1]=>1 [[2,1],[2],[2]]=>[3,2,2]=>3 [[2,1],[1,1],[1],[1]]=>[3,2,1,1]=>1 [[2,1],[1,1],[1,1]]=>[3,2,2]=>3 [[2,1],[2,1],[1]]=>[3,3,1]=>1 [[1,1,1],[1],[1],[1],[1]]=>[3,1,1,1,1]=>3 [[1,1,1],[1,1],[1],[1]]=>[3,2,1,1]=>1 [[1,1,1],[1,1],[1,1]]=>[3,2,2]=>3 [[1,1,1],[1,1,1],[1]]=>[3,3,1]=>1 [[4],[1],[1],[1]]=>[4,1,1,1]=>3 [[4],[2],[1]]=>[4,2,1]=>3 [[4],[3]]=>[4,3]=>1 [[3,1],[1],[1],[1]]=>[4,1,1,1]=>3 [[3,1],[2],[1]]=>[4,2,1]=>3 [[3,1],[1,1],[1]]=>[4,2,1]=>3 [[3,1],[3]]=>[4,3]=>1 [[3,1],[2,1]]=>[4,3]=>1 [[2,2],[1],[1],[1]]=>[4,1,1,1]=>3 [[2,2],[2],[1]]=>[4,2,1]=>3 [[2,2],[1,1],[1]]=>[4,2,1]=>3 [[2,2],[2,1]]=>[4,3]=>1 [[2,1,1],[1],[1],[1]]=>[4,1,1,1]=>3 [[2,1,1],[2],[1]]=>[4,2,1]=>3 [[2,1,1],[1,1],[1]]=>[4,2,1]=>3 [[2,1,1],[2,1]]=>[4,3]=>1 [[2,1,1],[1,1,1]]=>[4,3]=>1 [[1,1,1,1],[1],[1],[1]]=>[4,1,1,1]=>3 [[1,1,1,1],[1,1],[1]]=>[4,2,1]=>3 [[1,1,1,1],[1,1,1]]=>[4,3]=>1 [[5],[1],[1]]=>[5,1,1]=>5 [[5],[2]]=>[5,2]=>3 [[4,1],[1],[1]]=>[5,1,1]=>5 [[4,1],[2]]=>[5,2]=>3 [[4,1],[1,1]]=>[5,2]=>3 [[3,2],[1],[1]]=>[5,1,1]=>5 [[3,2],[2]]=>[5,2]=>3 [[3,2],[1,1]]=>[5,2]=>3 [[3,1,1],[1],[1]]=>[5,1,1]=>5 [[3,1,1],[2]]=>[5,2]=>3 [[3,1,1],[1,1]]=>[5,2]=>3 [[2,2,1],[1],[1]]=>[5,1,1]=>5 [[2,2,1],[2]]=>[5,2]=>3 [[2,2,1],[1,1]]=>[5,2]=>3 [[2,1,1,1],[1],[1]]=>[5,1,1]=>5 [[2,1,1,1],[2]]=>[5,2]=>3 [[2,1,1,1],[1,1]]=>[5,2]=>3 [[1,1,1,1,1],[1],[1]]=>[5,1,1]=>5 [[1,1,1,1,1],[1,1]]=>[5,2]=>3 [[6],[1]]=>[6,1]=>5 [[5,1],[1]]=>[6,1]=>5 [[4,2],[1]]=>[6,1]=>5 [[4,1,1],[1]]=>[6,1]=>5 [[3,3],[1]]=>[6,1]=>5 [[3,2,1],[1]]=>[6,1]=>5 [[3,1,1,1],[1]]=>[6,1]=>5 [[2,2,2],[1]]=>[6,1]=>5 [[2,2,1,1],[1]]=>[6,1]=>5 [[2,1,1,1,1],[1]]=>[6,1]=>5 [[1,1,1,1,1,1],[1]]=>[6,1]=>5 [[7]]=>[7]=>7 [[6,1]]=>[7]=>7 [[5,2]]=>[7]=>7 [[5,1,1]]=>[7]=>7 [[4,3]]=>[7]=>7 [[4,2,1]]=>[7]=>7 [[4,1,1,1]]=>[7]=>7 [[3,3,1]]=>[7]=>7 [[3,2,2]]=>[7]=>7 [[3,2,1,1]]=>[7]=>7 [[3,1,1,1,1]]=>[7]=>7 [[2,2,2,1]]=>[7]=>7 [[2,2,1,1,1]]=>[7]=>7 [[2,1,1,1,1,1]]=>[7]=>7 [[1,1,1,1,1,1,1]]=>[7]=>7 [[1],[1],[1],[1],[1],[1],[1],[1]]=>[1,1,1,1,1,1,1,1]=>0 [[2],[1],[1],[1],[1],[1],[1]]=>[2,1,1,1,1,1,1]=>2 [[2],[2],[1],[1],[1],[1]]=>[2,2,1,1,1,1]=>0 [[2],[2],[2],[1],[1]]=>[2,2,2,1,1]=>2 [[2],[2],[2],[2]]=>[2,2,2,2]=>0 [[1,1],[1],[1],[1],[1],[1],[1]]=>[2,1,1,1,1,1,1]=>2 [[1,1],[1,1],[1],[1],[1],[1]]=>[2,2,1,1,1,1]=>0 [[1,1],[1,1],[1,1],[1],[1]]=>[2,2,2,1,1]=>2 [[1,1],[1,1],[1,1],[1,1]]=>[2,2,2,2]=>0 [[3],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1]=>2 [[3],[2],[1],[1],[1]]=>[3,2,1,1,1]=>2 [[3],[2],[2],[1]]=>[3,2,2,1]=>2 [[3],[3],[1],[1]]=>[3,3,1,1]=>0 [[3],[3],[2]]=>[3,3,2]=>2 [[2,1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1]=>2 [[2,1],[2],[1],[1],[1]]=>[3,2,1,1,1]=>2 [[2,1],[2],[2],[1]]=>[3,2,2,1]=>2 [[2,1],[1,1],[1],[1],[1]]=>[3,2,1,1,1]=>2 [[2,1],[1,1],[1,1],[1]]=>[3,2,2,1]=>2 [[2,1],[2,1],[1],[1]]=>[3,3,1,1]=>0 [[2,1],[2,1],[2]]=>[3,3,2]=>2 [[2,1],[2,1],[1,1]]=>[3,3,2]=>2 [[1,1,1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1]=>2 [[1,1,1],[1,1],[1],[1],[1]]=>[3,2,1,1,1]=>2 [[1,1,1],[1,1],[1,1],[1]]=>[3,2,2,1]=>2 [[1,1,1],[1,1,1],[1],[1]]=>[3,3,1,1]=>0 [[1,1,1],[1,1,1],[1,1]]=>[3,3,2]=>2 [[4],[1],[1],[1],[1]]=>[4,1,1,1,1]=>4 [[4],[2],[1],[1]]=>[4,2,1,1]=>2 [[4],[2],[2]]=>[4,2,2]=>4 [[4],[3],[1]]=>[4,3,1]=>2 [[4],[4]]=>[4,4]=>0 [[3,1],[1],[1],[1],[1]]=>[4,1,1,1,1]=>4 [[3,1],[2],[1],[1]]=>[4,2,1,1]=>2 [[3,1],[2],[2]]=>[4,2,2]=>4 [[3,1],[1,1],[1],[1]]=>[4,2,1,1]=>2 [[3,1],[1,1],[1,1]]=>[4,2,2]=>4 [[3,1],[3],[1]]=>[4,3,1]=>2 [[3,1],[2,1],[1]]=>[4,3,1]=>2 [[3,1],[3,1]]=>[4,4]=>0 [[2,2],[1],[1],[1],[1]]=>[4,1,1,1,1]=>4 [[2,2],[2],[1],[1]]=>[4,2,1,1]=>2 [[2,2],[2],[2]]=>[4,2,2]=>4 [[2,2],[1,1],[1],[1]]=>[4,2,1,1]=>2 [[2,2],[1,1],[1,1]]=>[4,2,2]=>4 [[2,2],[2,1],[1]]=>[4,3,1]=>2 [[2,2],[2,2]]=>[4,4]=>0 [[2,1,1],[1],[1],[1],[1]]=>[4,1,1,1,1]=>4 [[2,1,1],[2],[1],[1]]=>[4,2,1,1]=>2 [[2,1,1],[2],[2]]=>[4,2,2]=>4 [[2,1,1],[1,1],[1],[1]]=>[4,2,1,1]=>2 [[2,1,1],[1,1],[1,1]]=>[4,2,2]=>4 [[2,1,1],[2,1],[1]]=>[4,3,1]=>2 [[2,1,1],[1,1,1],[1]]=>[4,3,1]=>2 [[2,1,1],[2,1,1]]=>[4,4]=>0 [[1,1,1,1],[1],[1],[1],[1]]=>[4,1,1,1,1]=>4 [[1,1,1,1],[1,1],[1],[1]]=>[4,2,1,1]=>2 [[1,1,1,1],[1,1],[1,1]]=>[4,2,2]=>4 [[1,1,1,1],[1,1,1],[1]]=>[4,3,1]=>2 [[1,1,1,1],[1,1,1,1]]=>[4,4]=>0 [[5],[1],[1],[1]]=>[5,1,1,1]=>4 [[5],[2],[1]]=>[5,2,1]=>4 [[5],[3]]=>[5,3]=>2 [[4,1],[1],[1],[1]]=>[5,1,1,1]=>4 [[4,1],[2],[1]]=>[5,2,1]=>4 [[4,1],[1,1],[1]]=>[5,2,1]=>4 [[4,1],[3]]=>[5,3]=>2 [[4,1],[2,1]]=>[5,3]=>2 [[3,2],[1],[1],[1]]=>[5,1,1,1]=>4 [[3,2],[2],[1]]=>[5,2,1]=>4 [[3,2],[1,1],[1]]=>[5,2,1]=>4 [[3,2],[3]]=>[5,3]=>2 [[3,2],[2,1]]=>[5,3]=>2 [[3,1,1],[1],[1],[1]]=>[5,1,1,1]=>4 [[3,1,1],[2],[1]]=>[5,2,1]=>4 [[3,1,1],[1,1],[1]]=>[5,2,1]=>4 [[3,1,1],[3]]=>[5,3]=>2 [[3,1,1],[2,1]]=>[5,3]=>2 [[3,1,1],[1,1,1]]=>[5,3]=>2 [[2,2,1],[1],[1],[1]]=>[5,1,1,1]=>4 [[2,2,1],[2],[1]]=>[5,2,1]=>4 [[2,2,1],[1,1],[1]]=>[5,2,1]=>4 [[2,2,1],[2,1]]=>[5,3]=>2 [[2,2,1],[1,1,1]]=>[5,3]=>2 [[2,1,1,1],[1],[1],[1]]=>[5,1,1,1]=>4 [[2,1,1,1],[2],[1]]=>[5,2,1]=>4 [[2,1,1,1],[1,1],[1]]=>[5,2,1]=>4 [[2,1,1,1],[2,1]]=>[5,3]=>2 [[2,1,1,1],[1,1,1]]=>[5,3]=>2 [[1,1,1,1,1],[1],[1],[1]]=>[5,1,1,1]=>4 [[1,1,1,1,1],[1,1],[1]]=>[5,2,1]=>4 [[1,1,1,1,1],[1,1,1]]=>[5,3]=>2 [[6],[1],[1]]=>[6,1,1]=>6 [[6],[2]]=>[6,2]=>4 [[5,1],[1],[1]]=>[6,1,1]=>6 [[5,1],[2]]=>[6,2]=>4 [[5,1],[1,1]]=>[6,2]=>4 [[4,2],[1],[1]]=>[6,1,1]=>6 [[4,2],[2]]=>[6,2]=>4 [[4,2],[1,1]]=>[6,2]=>4 [[4,1,1],[1],[1]]=>[6,1,1]=>6 [[4,1,1],[2]]=>[6,2]=>4 [[4,1,1],[1,1]]=>[6,2]=>4 [[3,3],[1],[1]]=>[6,1,1]=>6 [[3,3],[2]]=>[6,2]=>4 [[3,3],[1,1]]=>[6,2]=>4 [[3,2,1],[1],[1]]=>[6,1,1]=>6 [[3,2,1],[2]]=>[6,2]=>4 [[3,2,1],[1,1]]=>[6,2]=>4 [[3,1,1,1],[1],[1]]=>[6,1,1]=>6 [[3,1,1,1],[2]]=>[6,2]=>4 [[3,1,1,1],[1,1]]=>[6,2]=>4 [[2,2,2],[1],[1]]=>[6,1,1]=>6 [[2,2,2],[2]]=>[6,2]=>4 [[2,2,2],[1,1]]=>[6,2]=>4 [[2,2,1,1],[1],[1]]=>[6,1,1]=>6 [[2,2,1,1],[2]]=>[6,2]=>4 [[2,2,1,1],[1,1]]=>[6,2]=>4 [[2,1,1,1,1],[1],[1]]=>[6,1,1]=>6 [[2,1,1,1,1],[2]]=>[6,2]=>4 [[2,1,1,1,1],[1,1]]=>[6,2]=>4 [[1,1,1,1,1,1],[1],[1]]=>[6,1,1]=>6 [[1,1,1,1,1,1],[1,1]]=>[6,2]=>4 [[7],[1]]=>[7,1]=>6 [[6,1],[1]]=>[7,1]=>6 [[5,2],[1]]=>[7,1]=>6 [[5,1,1],[1]]=>[7,1]=>6 [[4,3],[1]]=>[7,1]=>6 [[4,2,1],[1]]=>[7,1]=>6 [[4,1,1,1],[1]]=>[7,1]=>6 [[3,3,1],[1]]=>[7,1]=>6 [[3,2,2],[1]]=>[7,1]=>6 [[3,2,1,1],[1]]=>[7,1]=>6 [[3,1,1,1,1],[1]]=>[7,1]=>6 [[2,2,2,1],[1]]=>[7,1]=>6 [[2,2,1,1,1],[1]]=>[7,1]=>6 [[2,1,1,1,1,1],[1]]=>[7,1]=>6 [[1,1,1,1,1,1,1],[1]]=>[7,1]=>6 [[8]]=>[8]=>8 [[7,1]]=>[8]=>8 [[6,2]]=>[8]=>8 [[6,1,1]]=>[8]=>8 [[5,3]]=>[8]=>8 [[5,2,1]]=>[8]=>8 [[5,1,1,1]]=>[8]=>8 [[4,4]]=>[8]=>8 [[4,3,1]]=>[8]=>8 [[4,2,2]]=>[8]=>8 [[4,2,1,1]]=>[8]=>8 [[4,1,1,1,1]]=>[8]=>8 [[3,3,2]]=>[8]=>8 [[3,3,1,1]]=>[8]=>8 [[3,2,2,1]]=>[8]=>8 [[3,2,1,1,1]]=>[8]=>8 [[3,1,1,1,1,1]]=>[8]=>8 [[2,2,2,2]]=>[8]=>8 [[2,2,2,1,1]]=>[8]=>8 [[2,2,1,1,1,1]]=>[8]=>8 [[2,1,1,1,1,1,1]]=>[8]=>8 [[1,1,1,1,1,1,1,1]]=>[8]=>8 [[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]]=>[2,1,1,1,1,1,1,1]=>1 [[2],[2],[1],[1],[1],[1],[1]]=>[2,2,1,1,1,1,1]=>1 [[2],[2],[2],[1],[1],[1]]=>[2,2,2,1,1,1]=>1 [[2],[2],[2],[2],[1]]=>[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],[1,1],[1],[1],[1],[1],[1]]=>[2,2,1,1,1,1,1]=>1 [[1,1],[1,1],[1,1],[1],[1],[1]]=>[2,2,2,1,1,1]=>1 [[1,1],[1,1],[1,1],[1,1],[1]]=>[2,2,2,2,1]=>1 [[3],[1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1,1]=>3 [[3],[2],[1],[1],[1],[1]]=>[3,2,1,1,1,1]=>1 [[3],[2],[2],[1],[1]]=>[3,2,2,1,1]=>3 [[3],[2],[2],[2]]=>[3,2,2,2]=>1 [[3],[3],[1],[1],[1]]=>[3,3,1,1,1]=>1 [[3],[3],[2],[1]]=>[3,3,2,1]=>1 [[3],[3],[3]]=>[3,3,3]=>3 [[2,1],[1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1,1]=>3 [[2,1],[2],[1],[1],[1],[1]]=>[3,2,1,1,1,1]=>1 [[2,1],[2],[2],[1],[1]]=>[3,2,2,1,1]=>3 [[2,1],[2],[2],[2]]=>[3,2,2,2]=>1 [[2,1],[1,1],[1],[1],[1],[1]]=>[3,2,1,1,1,1]=>1 [[2,1],[1,1],[1,1],[1],[1]]=>[3,2,2,1,1]=>3 [[2,1],[1,1],[1,1],[1,1]]=>[3,2,2,2]=>1 [[2,1],[2,1],[1],[1],[1]]=>[3,3,1,1,1]=>1 [[2,1],[2,1],[2],[1]]=>[3,3,2,1]=>1 [[2,1],[2,1],[1,1],[1]]=>[3,3,2,1]=>1 [[2,1],[2,1],[2,1]]=>[3,3,3]=>3 [[1,1,1],[1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1,1]=>3 [[1,1,1],[1,1],[1],[1],[1],[1]]=>[3,2,1,1,1,1]=>1 [[1,1,1],[1,1],[1,1],[1],[1]]=>[3,2,2,1,1]=>3 [[1,1,1],[1,1],[1,1],[1,1]]=>[3,2,2,2]=>1 [[1,1,1],[1,1,1],[1],[1],[1]]=>[3,3,1,1,1]=>1 [[1,1,1],[1,1,1],[1,1],[1]]=>[3,3,2,1]=>1 [[1,1,1],[1,1,1],[1,1,1]]=>[3,3,3]=>3 [[4],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1]=>3 [[4],[2],[1],[1],[1]]=>[4,2,1,1,1]=>3 [[4],[2],[2],[1]]=>[4,2,2,1]=>3 [[4],[3],[1],[1]]=>[4,3,1,1]=>1 [[4],[3],[2]]=>[4,3,2]=>3 [[4],[4],[1]]=>[4,4,1]=>1 [[3,1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1]=>3 [[3,1],[2],[1],[1],[1]]=>[4,2,1,1,1]=>3 [[3,1],[2],[2],[1]]=>[4,2,2,1]=>3 [[3,1],[1,1],[1],[1],[1]]=>[4,2,1,1,1]=>3 [[3,1],[1,1],[1,1],[1]]=>[4,2,2,1]=>3 [[3,1],[3],[1],[1]]=>[4,3,1,1]=>1 [[3,1],[3],[2]]=>[4,3,2]=>3 [[3,1],[2,1],[1],[1]]=>[4,3,1,1]=>1 [[3,1],[2,1],[2]]=>[4,3,2]=>3 [[3,1],[2,1],[1,1]]=>[4,3,2]=>3 [[3,1],[3,1],[1]]=>[4,4,1]=>1 [[2,2],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1]=>3 [[2,2],[2],[1],[1],[1]]=>[4,2,1,1,1]=>3 [[2,2],[2],[2],[1]]=>[4,2,2,1]=>3 [[2,2],[1,1],[1],[1],[1]]=>[4,2,1,1,1]=>3 [[2,2],[1,1],[1,1],[1]]=>[4,2,2,1]=>3 [[2,2],[2,1],[1],[1]]=>[4,3,1,1]=>1 [[2,2],[2,1],[2]]=>[4,3,2]=>3 [[2,2],[2,1],[1,1]]=>[4,3,2]=>3 [[2,2],[2,2],[1]]=>[4,4,1]=>1 [[2,1,1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1]=>3 [[2,1,1],[2],[1],[1],[1]]=>[4,2,1,1,1]=>3 [[2,1,1],[2],[2],[1]]=>[4,2,2,1]=>3 [[2,1,1],[1,1],[1],[1],[1]]=>[4,2,1,1,1]=>3 [[2,1,1],[1,1],[1,1],[1]]=>[4,2,2,1]=>3 [[2,1,1],[2,1],[1],[1]]=>[4,3,1,1]=>1 [[2,1,1],[2,1],[2]]=>[4,3,2]=>3 [[2,1,1],[2,1],[1,1]]=>[4,3,2]=>3 [[2,1,1],[1,1,1],[1],[1]]=>[4,3,1,1]=>1 [[2,1,1],[1,1,1],[1,1]]=>[4,3,2]=>3 [[2,1,1],[2,1,1],[1]]=>[4,4,1]=>1 [[1,1,1,1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1]=>3 [[1,1,1,1],[1,1],[1],[1],[1]]=>[4,2,1,1,1]=>3 [[1,1,1,1],[1,1],[1,1],[1]]=>[4,2,2,1]=>3 [[1,1,1,1],[1,1,1],[1],[1]]=>[4,3,1,1]=>1 [[1,1,1,1],[1,1,1],[1,1]]=>[4,3,2]=>3 [[1,1,1,1],[1,1,1,1],[1]]=>[4,4,1]=>1 [[5],[1],[1],[1],[1]]=>[5,1,1,1,1]=>5 [[5],[2],[1],[1]]=>[5,2,1,1]=>3 [[5],[2],[2]]=>[5,2,2]=>5 [[5],[3],[1]]=>[5,3,1]=>3 [[5],[4]]=>[5,4]=>1 [[4,1],[1],[1],[1],[1]]=>[5,1,1,1,1]=>5 [[4,1],[2],[1],[1]]=>[5,2,1,1]=>3 [[4,1],[2],[2]]=>[5,2,2]=>5 [[4,1],[1,1],[1],[1]]=>[5,2,1,1]=>3 [[4,1],[1,1],[1,1]]=>[5,2,2]=>5 [[4,1],[3],[1]]=>[5,3,1]=>3 [[4,1],[2,1],[1]]=>[5,3,1]=>3 [[4,1],[4]]=>[5,4]=>1 [[4,1],[3,1]]=>[5,4]=>1 [[3,2],[1],[1],[1],[1]]=>[5,1,1,1,1]=>5 [[3,2],[2],[1],[1]]=>[5,2,1,1]=>3 [[3,2],[2],[2]]=>[5,2,2]=>5 [[3,2],[1,1],[1],[1]]=>[5,2,1,1]=>3 [[3,2],[1,1],[1,1]]=>[5,2,2]=>5 [[3,2],[3],[1]]=>[5,3,1]=>3 [[3,2],[2,1],[1]]=>[5,3,1]=>3 [[3,2],[3,1]]=>[5,4]=>1 [[3,2],[2,2]]=>[5,4]=>1 [[3,1,1],[1],[1],[1],[1]]=>[5,1,1,1,1]=>5 [[3,1,1],[2],[1],[1]]=>[5,2,1,1]=>3 [[3,1,1],[2],[2]]=>[5,2,2]=>5 [[3,1,1],[1,1],[1],[1]]=>[5,2,1,1]=>3 [[3,1,1],[1,1],[1,1]]=>[5,2,2]=>5 [[3,1,1],[3],[1]]=>[5,3,1]=>3 [[3,1,1],[2,1],[1]]=>[5,3,1]=>3 [[3,1,1],[1,1,1],[1]]=>[5,3,1]=>3 [[3,1,1],[3,1]]=>[5,4]=>1 [[3,1,1],[2,1,1]]=>[5,4]=>1 [[2,2,1],[1],[1],[1],[1]]=>[5,1,1,1,1]=>5 [[2,2,1],[2],[1],[1]]=>[5,2,1,1]=>3 [[2,2,1],[2],[2]]=>[5,2,2]=>5 [[2,2,1],[1,1],[1],[1]]=>[5,2,1,1]=>3 [[2,2,1],[1,1],[1,1]]=>[5,2,2]=>5 [[2,2,1],[2,1],[1]]=>[5,3,1]=>3 [[2,2,1],[1,1,1],[1]]=>[5,3,1]=>3 [[2,2,1],[2,2]]=>[5,4]=>1 [[2,2,1],[2,1,1]]=>[5,4]=>1 [[2,1,1,1],[1],[1],[1],[1]]=>[5,1,1,1,1]=>5 [[2,1,1,1],[2],[1],[1]]=>[5,2,1,1]=>3 [[2,1,1,1],[2],[2]]=>[5,2,2]=>5 [[2,1,1,1],[1,1],[1],[1]]=>[5,2,1,1]=>3 [[2,1,1,1],[1,1],[1,1]]=>[5,2,2]=>5 [[2,1,1,1],[2,1],[1]]=>[5,3,1]=>3 [[2,1,1,1],[1,1,1],[1]]=>[5,3,1]=>3 [[2,1,1,1],[2,1,1]]=>[5,4]=>1 [[2,1,1,1],[1,1,1,1]]=>[5,4]=>1 [[1,1,1,1,1],[1],[1],[1],[1]]=>[5,1,1,1,1]=>5 [[1,1,1,1,1],[1,1],[1],[1]]=>[5,2,1,1]=>3 [[1,1,1,1,1],[1,1],[1,1]]=>[5,2,2]=>5 [[1,1,1,1,1],[1,1,1],[1]]=>[5,3,1]=>3 [[1,1,1,1,1],[1,1,1,1]]=>[5,4]=>1 [[6],[1],[1],[1]]=>[6,1,1,1]=>5 [[6],[2],[1]]=>[6,2,1]=>5 [[6],[3]]=>[6,3]=>3 [[5,1],[1],[1],[1]]=>[6,1,1,1]=>5 [[5,1],[2],[1]]=>[6,2,1]=>5 [[5,1],[1,1],[1]]=>[6,2,1]=>5 [[5,1],[3]]=>[6,3]=>3 [[5,1],[2,1]]=>[6,3]=>3 [[4,2],[1],[1],[1]]=>[6,1,1,1]=>5 [[4,2],[2],[1]]=>[6,2,1]=>5 [[4,2],[1,1],[1]]=>[6,2,1]=>5 [[4,2],[3]]=>[6,3]=>3 [[4,2],[2,1]]=>[6,3]=>3 [[4,1,1],[1],[1],[1]]=>[6,1,1,1]=>5 [[4,1,1],[2],[1]]=>[6,2,1]=>5 [[4,1,1],[1,1],[1]]=>[6,2,1]=>5 [[4,1,1],[3]]=>[6,3]=>3 [[4,1,1],[2,1]]=>[6,3]=>3 [[4,1,1],[1,1,1]]=>[6,3]=>3 [[3,3],[1],[1],[1]]=>[6,1,1,1]=>5 [[3,3],[2],[1]]=>[6,2,1]=>5 [[3,3],[1,1],[1]]=>[6,2,1]=>5 [[3,3],[3]]=>[6,3]=>3 [[3,3],[2,1]]=>[6,3]=>3 [[3,2,1],[1],[1],[1]]=>[6,1,1,1]=>5 [[3,2,1],[2],[1]]=>[6,2,1]=>5 [[3,2,1],[1,1],[1]]=>[6,2,1]=>5 [[3,2,1],[3]]=>[6,3]=>3 [[3,2,1],[2,1]]=>[6,3]=>3 [[3,2,1],[1,1,1]]=>[6,3]=>3 [[3,1,1,1],[1],[1],[1]]=>[6,1,1,1]=>5 [[3,1,1,1],[2],[1]]=>[6,2,1]=>5 [[3,1,1,1],[1,1],[1]]=>[6,2,1]=>5 [[3,1,1,1],[3]]=>[6,3]=>3 [[3,1,1,1],[2,1]]=>[6,3]=>3 [[3,1,1,1],[1,1,1]]=>[6,3]=>3 [[2,2,2],[1],[1],[1]]=>[6,1,1,1]=>5 [[2,2,2],[2],[1]]=>[6,2,1]=>5 [[2,2,2],[1,1],[1]]=>[6,2,1]=>5 [[2,2,2],[2,1]]=>[6,3]=>3 [[2,2,2],[1,1,1]]=>[6,3]=>3 [[2,2,1,1],[1],[1],[1]]=>[6,1,1,1]=>5 [[2,2,1,1],[2],[1]]=>[6,2,1]=>5 [[2,2,1,1],[1,1],[1]]=>[6,2,1]=>5 [[2,2,1,1],[2,1]]=>[6,3]=>3 [[2,2,1,1],[1,1,1]]=>[6,3]=>3 [[2,1,1,1,1],[1],[1],[1]]=>[6,1,1,1]=>5 [[2,1,1,1,1],[2],[1]]=>[6,2,1]=>5 [[2,1,1,1,1],[1,1],[1]]=>[6,2,1]=>5 [[2,1,1,1,1],[2,1]]=>[6,3]=>3 [[2,1,1,1,1],[1,1,1]]=>[6,3]=>3 [[1,1,1,1,1,1],[1],[1],[1]]=>[6,1,1,1]=>5 [[1,1,1,1,1,1],[1,1],[1]]=>[6,2,1]=>5 [[1,1,1,1,1,1],[1,1,1]]=>[6,3]=>3 [[7],[1],[1]]=>[7,1,1]=>7 [[7],[2]]=>[7,2]=>5 [[6,1],[1],[1]]=>[7,1,1]=>7 [[6,1],[2]]=>[7,2]=>5 [[6,1],[1,1]]=>[7,2]=>5 [[5,2],[1],[1]]=>[7,1,1]=>7 [[5,2],[2]]=>[7,2]=>5 [[5,2],[1,1]]=>[7,2]=>5 [[5,1,1],[1],[1]]=>[7,1,1]=>7 [[5,1,1],[2]]=>[7,2]=>5 [[5,1,1],[1,1]]=>[7,2]=>5 [[4,3],[1],[1]]=>[7,1,1]=>7 [[4,3],[2]]=>[7,2]=>5 [[4,3],[1,1]]=>[7,2]=>5 [[4,2,1],[1],[1]]=>[7,1,1]=>7 [[4,2,1],[2]]=>[7,2]=>5 [[4,2,1],[1,1]]=>[7,2]=>5 [[4,1,1,1],[1],[1]]=>[7,1,1]=>7 [[4,1,1,1],[2]]=>[7,2]=>5 [[4,1,1,1],[1,1]]=>[7,2]=>5 [[3,3,1],[1],[1]]=>[7,1,1]=>7 [[3,3,1],[2]]=>[7,2]=>5 [[3,3,1],[1,1]]=>[7,2]=>5 [[3,2,2],[1],[1]]=>[7,1,1]=>7 [[3,2,2],[2]]=>[7,2]=>5 [[3,2,2],[1,1]]=>[7,2]=>5 [[3,2,1,1],[1],[1]]=>[7,1,1]=>7 [[3,2,1,1],[2]]=>[7,2]=>5 [[3,2,1,1],[1,1]]=>[7,2]=>5 [[3,1,1,1,1],[1],[1]]=>[7,1,1]=>7 [[3,1,1,1,1],[2]]=>[7,2]=>5 [[3,1,1,1,1],[1,1]]=>[7,2]=>5 [[2,2,2,1],[1],[1]]=>[7,1,1]=>7 [[2,2,2,1],[2]]=>[7,2]=>5 [[2,2,2,1],[1,1]]=>[7,2]=>5 [[2,2,1,1,1],[1],[1]]=>[7,1,1]=>7 [[2,2,1,1,1],[2]]=>[7,2]=>5 [[2,2,1,1,1],[1,1]]=>[7,2]=>5 [[2,1,1,1,1,1],[1],[1]]=>[7,1,1]=>7 [[2,1,1,1,1,1],[2]]=>[7,2]=>5 [[2,1,1,1,1,1],[1,1]]=>[7,2]=>5 [[1,1,1,1,1,1,1],[1],[1]]=>[7,1,1]=>7 [[1,1,1,1,1,1,1],[1,1]]=>[7,2]=>5 [[8],[1]]=>[8,1]=>7 [[7,1],[1]]=>[8,1]=>7 [[6,2],[1]]=>[8,1]=>7 [[6,1,1],[1]]=>[8,1]=>7 [[5,3],[1]]=>[8,1]=>7 [[5,2,1],[1]]=>[8,1]=>7 [[5,1,1,1],[1]]=>[8,1]=>7 [[4,4],[1]]=>[8,1]=>7 [[4,3,1],[1]]=>[8,1]=>7 [[4,2,2],[1]]=>[8,1]=>7 [[4,2,1,1],[1]]=>[8,1]=>7 [[4,1,1,1,1],[1]]=>[8,1]=>7 [[3,3,2],[1]]=>[8,1]=>7 [[3,3,1,1],[1]]=>[8,1]=>7 [[3,2,2,1],[1]]=>[8,1]=>7 [[3,2,1,1,1],[1]]=>[8,1]=>7 [[3,1,1,1,1,1],[1]]=>[8,1]=>7 [[2,2,2,2],[1]]=>[8,1]=>7 [[2,2,2,1,1],[1]]=>[8,1]=>7 [[2,2,1,1,1,1],[1]]=>[8,1]=>7 [[2,1,1,1,1,1,1],[1]]=>[8,1]=>7 [[1,1,1,1,1,1,1,1],[1]]=>[8,1]=>7 [[9]]=>[9]=>9 [[8,1]]=>[9]=>9 [[7,2]]=>[9]=>9 [[7,1,1]]=>[9]=>9 [[6,3]]=>[9]=>9 [[6,2,1]]=>[9]=>9 [[6,1,1,1]]=>[9]=>9 [[5,4]]=>[9]=>9 [[5,3,1]]=>[9]=>9 [[5,2,2]]=>[9]=>9 [[5,2,1,1]]=>[9]=>9 [[5,1,1,1,1]]=>[9]=>9 [[4,4,1]]=>[9]=>9 [[4,3,2]]=>[9]=>9 [[4,3,1,1]]=>[9]=>9 [[4,2,2,1]]=>[9]=>9 [[4,2,1,1,1]]=>[9]=>9 [[4,1,1,1,1,1]]=>[9]=>9 [[3,3,3]]=>[9]=>9 [[3,3,2,1]]=>[9]=>9 [[3,3,1,1,1]]=>[9]=>9 [[3,2,2,2]]=>[9]=>9 [[3,2,2,1,1]]=>[9]=>9 [[3,2,1,1,1,1]]=>[9]=>9 [[3,1,1,1,1,1,1]]=>[9]=>9 [[2,2,2,2,1]]=>[9]=>9 [[2,2,2,1,1,1]]=>[9]=>9 [[2,2,1,1,1,1,1]]=>[9]=>9 [[2,1,1,1,1,1,1,1]]=>[9]=>9 [[1,1,1,1,1,1,1,1,1]]=>[9]=>9 [[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]]=>[1,1,1,1,1,1,1,1,1,1]=>0 [[2],[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]]=>[2,2,1,1,1,1,1,1]=>0 [[2],[2],[2],[1],[1],[1],[1]]=>[2,2,2,1,1,1,1]=>2 [[2],[2],[2],[2],[1],[1]]=>[2,2,2,2,1,1]=>0 [[2],[2],[2],[2],[2]]=>[2,2,2,2,2]=>2 [[1,1],[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],[1],[1]]=>[2,2,1,1,1,1,1,1]=>0 [[1,1],[1,1],[1,1],[1],[1],[1],[1]]=>[2,2,2,1,1,1,1]=>2 [[1,1],[1,1],[1,1],[1,1],[1],[1]]=>[2,2,2,2,1,1]=>0 [[1,1],[1,1],[1,1],[1,1],[1,1]]=>[2,2,2,2,2]=>2 [[3],[1],[1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1,1,1]=>2 [[3],[2],[1],[1],[1],[1],[1]]=>[3,2,1,1,1,1,1]=>2 [[3],[2],[2],[1],[1],[1]]=>[3,2,2,1,1,1]=>2 [[3],[2],[2],[2],[1]]=>[3,2,2,2,1]=>2 [[3],[3],[1],[1],[1],[1]]=>[3,3,1,1,1,1]=>0 [[3],[3],[2],[1],[1]]=>[3,3,2,1,1]=>2 [[3],[3],[2],[2]]=>[3,3,2,2]=>0 [[3],[3],[3],[1]]=>[3,3,3,1]=>2 [[2,1],[1],[1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1,1,1]=>2 [[2,1],[2],[1],[1],[1],[1],[1]]=>[3,2,1,1,1,1,1]=>2 [[2,1],[2],[2],[1],[1],[1]]=>[3,2,2,1,1,1]=>2 [[2,1],[2],[2],[2],[1]]=>[3,2,2,2,1]=>2 [[2,1],[1,1],[1],[1],[1],[1],[1]]=>[3,2,1,1,1,1,1]=>2 [[2,1],[1,1],[1,1],[1],[1],[1]]=>[3,2,2,1,1,1]=>2 [[2,1],[1,1],[1,1],[1,1],[1]]=>[3,2,2,2,1]=>2 [[2,1],[2,1],[1],[1],[1],[1]]=>[3,3,1,1,1,1]=>0 [[2,1],[2,1],[2],[1],[1]]=>[3,3,2,1,1]=>2 [[2,1],[2,1],[2],[2]]=>[3,3,2,2]=>0 [[2,1],[2,1],[1,1],[1],[1]]=>[3,3,2,1,1]=>2 [[2,1],[2,1],[1,1],[1,1]]=>[3,3,2,2]=>0 [[2,1],[2,1],[2,1],[1]]=>[3,3,3,1]=>2 [[1,1,1],[1],[1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1,1,1]=>2 [[1,1,1],[1,1],[1],[1],[1],[1],[1]]=>[3,2,1,1,1,1,1]=>2 [[1,1,1],[1,1],[1,1],[1],[1],[1]]=>[3,2,2,1,1,1]=>2 [[1,1,1],[1,1],[1,1],[1,1],[1]]=>[3,2,2,2,1]=>2 [[1,1,1],[1,1,1],[1],[1],[1],[1]]=>[3,3,1,1,1,1]=>0 [[1,1,1],[1,1,1],[1,1],[1],[1]]=>[3,3,2,1,1]=>2 [[1,1,1],[1,1,1],[1,1],[1,1]]=>[3,3,2,2]=>0 [[1,1,1],[1,1,1],[1,1,1],[1]]=>[3,3,3,1]=>2 [[4],[1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1,1]=>4 [[4],[2],[1],[1],[1],[1]]=>[4,2,1,1,1,1]=>2 [[4],[2],[2],[1],[1]]=>[4,2,2,1,1]=>4 [[4],[2],[2],[2]]=>[4,2,2,2]=>2 [[4],[3],[1],[1],[1]]=>[4,3,1,1,1]=>2 [[4],[3],[2],[1]]=>[4,3,2,1]=>2 [[4],[3],[3]]=>[4,3,3]=>4 [[4],[4],[1],[1]]=>[4,4,1,1]=>0 [[4],[4],[2]]=>[4,4,2]=>2 [[3,1],[1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1,1]=>4 [[3,1],[2],[1],[1],[1],[1]]=>[4,2,1,1,1,1]=>2 [[3,1],[2],[2],[1],[1]]=>[4,2,2,1,1]=>4 [[3,1],[2],[2],[2]]=>[4,2,2,2]=>2 [[3,1],[1,1],[1],[1],[1],[1]]=>[4,2,1,1,1,1]=>2 [[3,1],[1,1],[1,1],[1],[1]]=>[4,2,2,1,1]=>4 [[3,1],[1,1],[1,1],[1,1]]=>[4,2,2,2]=>2 [[3,1],[3],[1],[1],[1]]=>[4,3,1,1,1]=>2 [[3,1],[3],[2],[1]]=>[4,3,2,1]=>2 [[3,1],[3],[3]]=>[4,3,3]=>4 [[3,1],[2,1],[1],[1],[1]]=>[4,3,1,1,1]=>2 [[3,1],[2,1],[2],[1]]=>[4,3,2,1]=>2 [[3,1],[2,1],[1,1],[1]]=>[4,3,2,1]=>2 [[3,1],[2,1],[2,1]]=>[4,3,3]=>4 [[3,1],[3,1],[1],[1]]=>[4,4,1,1]=>0 [[3,1],[3,1],[2]]=>[4,4,2]=>2 [[3,1],[3,1],[1,1]]=>[4,4,2]=>2 [[2,2],[1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1,1]=>4 [[2,2],[2],[1],[1],[1],[1]]=>[4,2,1,1,1,1]=>2 [[2,2],[2],[2],[1],[1]]=>[4,2,2,1,1]=>4 [[2,2],[2],[2],[2]]=>[4,2,2,2]=>2 [[2,2],[1,1],[1],[1],[1],[1]]=>[4,2,1,1,1,1]=>2 [[2,2],[1,1],[1,1],[1],[1]]=>[4,2,2,1,1]=>4 [[2,2],[1,1],[1,1],[1,1]]=>[4,2,2,2]=>2 [[2,2],[2,1],[1],[1],[1]]=>[4,3,1,1,1]=>2 [[2,2],[2,1],[2],[1]]=>[4,3,2,1]=>2 [[2,2],[2,1],[1,1],[1]]=>[4,3,2,1]=>2 [[2,2],[2,1],[2,1]]=>[4,3,3]=>4 [[2,2],[2,2],[1],[1]]=>[4,4,1,1]=>0 [[2,2],[2,2],[2]]=>[4,4,2]=>2 [[2,2],[2,2],[1,1]]=>[4,4,2]=>2 [[2,1,1],[1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1,1]=>4 [[2,1,1],[2],[1],[1],[1],[1]]=>[4,2,1,1,1,1]=>2 [[2,1,1],[2],[2],[1],[1]]=>[4,2,2,1,1]=>4 [[2,1,1],[2],[2],[2]]=>[4,2,2,2]=>2 [[2,1,1],[1,1],[1],[1],[1],[1]]=>[4,2,1,1,1,1]=>2 [[2,1,1],[1,1],[1,1],[1],[1]]=>[4,2,2,1,1]=>4 [[2,1,1],[1,1],[1,1],[1,1]]=>[4,2,2,2]=>2 [[2,1,1],[2,1],[1],[1],[1]]=>[4,3,1,1,1]=>2 [[2,1,1],[2,1],[2],[1]]=>[4,3,2,1]=>2 [[2,1,1],[2,1],[1,1],[1]]=>[4,3,2,1]=>2 [[2,1,1],[2,1],[2,1]]=>[4,3,3]=>4 [[2,1,1],[1,1,1],[1],[1],[1]]=>[4,3,1,1,1]=>2 [[2,1,1],[1,1,1],[1,1],[1]]=>[4,3,2,1]=>2 [[2,1,1],[1,1,1],[1,1,1]]=>[4,3,3]=>4 [[2,1,1],[2,1,1],[1],[1]]=>[4,4,1,1]=>0 [[2,1,1],[2,1,1],[2]]=>[4,4,2]=>2 [[2,1,1],[2,1,1],[1,1]]=>[4,4,2]=>2 [[1,1,1,1],[1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1,1]=>4 [[1,1,1,1],[1,1],[1],[1],[1],[1]]=>[4,2,1,1,1,1]=>2 [[1,1,1,1],[1,1],[1,1],[1],[1]]=>[4,2,2,1,1]=>4 [[1,1,1,1],[1,1],[1,1],[1,1]]=>[4,2,2,2]=>2 [[1,1,1,1],[1,1,1],[1],[1],[1]]=>[4,3,1,1,1]=>2 [[1,1,1,1],[1,1,1],[1,1],[1]]=>[4,3,2,1]=>2 [[1,1,1,1],[1,1,1],[1,1,1]]=>[4,3,3]=>4 [[1,1,1,1],[1,1,1,1],[1],[1]]=>[4,4,1,1]=>0 [[1,1,1,1],[1,1,1,1],[1,1]]=>[4,4,2]=>2 [[5],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1]=>4 [[5],[2],[1],[1],[1]]=>[5,2,1,1,1]=>4 [[5],[2],[2],[1]]=>[5,2,2,1]=>4 [[5],[3],[1],[1]]=>[5,3,1,1]=>2 [[5],[3],[2]]=>[5,3,2]=>4 [[5],[4],[1]]=>[5,4,1]=>2 [[5],[5]]=>[5,5]=>0 [[4,1],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1]=>4 [[4,1],[2],[1],[1],[1]]=>[5,2,1,1,1]=>4 [[4,1],[2],[2],[1]]=>[5,2,2,1]=>4 [[4,1],[1,1],[1],[1],[1]]=>[5,2,1,1,1]=>4 [[4,1],[1,1],[1,1],[1]]=>[5,2,2,1]=>4 [[4,1],[3],[1],[1]]=>[5,3,1,1]=>2 [[4,1],[3],[2]]=>[5,3,2]=>4 [[4,1],[2,1],[1],[1]]=>[5,3,1,1]=>2 [[4,1],[2,1],[2]]=>[5,3,2]=>4 [[4,1],[2,1],[1,1]]=>[5,3,2]=>4 [[4,1],[4],[1]]=>[5,4,1]=>2 [[4,1],[3,1],[1]]=>[5,4,1]=>2 [[4,1],[4,1]]=>[5,5]=>0 [[3,2],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1]=>4 [[3,2],[2],[1],[1],[1]]=>[5,2,1,1,1]=>4 [[3,2],[2],[2],[1]]=>[5,2,2,1]=>4 [[3,2],[1,1],[1],[1],[1]]=>[5,2,1,1,1]=>4 [[3,2],[1,1],[1,1],[1]]=>[5,2,2,1]=>4 [[3,2],[3],[1],[1]]=>[5,3,1,1]=>2 [[3,2],[3],[2]]=>[5,3,2]=>4 [[3,2],[2,1],[1],[1]]=>[5,3,1,1]=>2 [[3,2],[2,1],[2]]=>[5,3,2]=>4 [[3,2],[2,1],[1,1]]=>[5,3,2]=>4 [[3,2],[3,1],[1]]=>[5,4,1]=>2 [[3,2],[2,2],[1]]=>[5,4,1]=>2 [[3,2],[3,2]]=>[5,5]=>0 [[3,1,1],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1]=>4 [[3,1,1],[2],[1],[1],[1]]=>[5,2,1,1,1]=>4 [[3,1,1],[2],[2],[1]]=>[5,2,2,1]=>4 [[3,1,1],[1,1],[1],[1],[1]]=>[5,2,1,1,1]=>4 [[3,1,1],[1,1],[1,1],[1]]=>[5,2,2,1]=>4 [[3,1,1],[3],[1],[1]]=>[5,3,1,1]=>2 [[3,1,1],[3],[2]]=>[5,3,2]=>4 [[3,1,1],[2,1],[1],[1]]=>[5,3,1,1]=>2 [[3,1,1],[2,1],[2]]=>[5,3,2]=>4 [[3,1,1],[2,1],[1,1]]=>[5,3,2]=>4 [[3,1,1],[1,1,1],[1],[1]]=>[5,3,1,1]=>2 [[3,1,1],[1,1,1],[1,1]]=>[5,3,2]=>4 [[3,1,1],[3,1],[1]]=>[5,4,1]=>2 [[3,1,1],[2,1,1],[1]]=>[5,4,1]=>2 [[3,1,1],[3,1,1]]=>[5,5]=>0 [[2,2,1],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1]=>4 [[2,2,1],[2],[1],[1],[1]]=>[5,2,1,1,1]=>4 [[2,2,1],[2],[2],[1]]=>[5,2,2,1]=>4 [[2,2,1],[1,1],[1],[1],[1]]=>[5,2,1,1,1]=>4 [[2,2,1],[1,1],[1,1],[1]]=>[5,2,2,1]=>4 [[2,2,1],[2,1],[1],[1]]=>[5,3,1,1]=>2 [[2,2,1],[2,1],[2]]=>[5,3,2]=>4 [[2,2,1],[2,1],[1,1]]=>[5,3,2]=>4 [[2,2,1],[1,1,1],[1],[1]]=>[5,3,1,1]=>2 [[2,2,1],[1,1,1],[1,1]]=>[5,3,2]=>4 [[2,2,1],[2,2],[1]]=>[5,4,1]=>2 [[2,2,1],[2,1,1],[1]]=>[5,4,1]=>2 [[2,2,1],[2,2,1]]=>[5,5]=>0 [[2,1,1,1],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1]=>4 [[2,1,1,1],[2],[1],[1],[1]]=>[5,2,1,1,1]=>4 [[2,1,1,1],[2],[2],[1]]=>[5,2,2,1]=>4 [[2,1,1,1],[1,1],[1],[1],[1]]=>[5,2,1,1,1]=>4 [[2,1,1,1],[1,1],[1,1],[1]]=>[5,2,2,1]=>4 [[2,1,1,1],[2,1],[1],[1]]=>[5,3,1,1]=>2 [[2,1,1,1],[2,1],[2]]=>[5,3,2]=>4 [[2,1,1,1],[2,1],[1,1]]=>[5,3,2]=>4 [[2,1,1,1],[1,1,1],[1],[1]]=>[5,3,1,1]=>2 [[2,1,1,1],[1,1,1],[1,1]]=>[5,3,2]=>4 [[2,1,1,1],[2,1,1],[1]]=>[5,4,1]=>2 [[2,1,1,1],[1,1,1,1],[1]]=>[5,4,1]=>2 [[2,1,1,1],[2,1,1,1]]=>[5,5]=>0 [[1,1,1,1,1],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1]=>4 [[1,1,1,1,1],[1,1],[1],[1],[1]]=>[5,2,1,1,1]=>4 [[1,1,1,1,1],[1,1],[1,1],[1]]=>[5,2,2,1]=>4 [[1,1,1,1,1],[1,1,1],[1],[1]]=>[5,3,1,1]=>2 [[1,1,1,1,1],[1,1,1],[1,1]]=>[5,3,2]=>4 [[1,1,1,1,1],[1,1,1,1],[1]]=>[5,4,1]=>2 [[1,1,1,1,1],[1,1,1,1,1]]=>[5,5]=>0 [[6],[1],[1],[1],[1]]=>[6,1,1,1,1]=>6 [[6],[2],[1],[1]]=>[6,2,1,1]=>4 [[6],[2],[2]]=>[6,2,2]=>6 [[6],[3],[1]]=>[6,3,1]=>4 [[6],[4]]=>[6,4]=>2 [[5,1],[1],[1],[1],[1]]=>[6,1,1,1,1]=>6 [[5,1],[2],[1],[1]]=>[6,2,1,1]=>4 [[5,1],[2],[2]]=>[6,2,2]=>6 [[5,1],[1,1],[1],[1]]=>[6,2,1,1]=>4 [[5,1],[1,1],[1,1]]=>[6,2,2]=>6 [[5,1],[3],[1]]=>[6,3,1]=>4 [[5,1],[2,1],[1]]=>[6,3,1]=>4 [[5,1],[4]]=>[6,4]=>2 [[5,1],[3,1]]=>[6,4]=>2 [[4,2],[1],[1],[1],[1]]=>[6,1,1,1,1]=>6 [[4,2],[2],[1],[1]]=>[6,2,1,1]=>4 [[4,2],[2],[2]]=>[6,2,2]=>6 [[4,2],[1,1],[1],[1]]=>[6,2,1,1]=>4 [[4,2],[1,1],[1,1]]=>[6,2,2]=>6 [[4,2],[3],[1]]=>[6,3,1]=>4 [[4,2],[2,1],[1]]=>[6,3,1]=>4 [[4,2],[4]]=>[6,4]=>2 [[4,2],[3,1]]=>[6,4]=>2 [[4,2],[2,2]]=>[6,4]=>2 [[4,1,1],[1],[1],[1],[1]]=>[6,1,1,1,1]=>6 [[4,1,1],[2],[1],[1]]=>[6,2,1,1]=>4 [[4,1,1],[2],[2]]=>[6,2,2]=>6 [[4,1,1],[1,1],[1],[1]]=>[6,2,1,1]=>4 [[4,1,1],[1,1],[1,1]]=>[6,2,2]=>6 [[4,1,1],[3],[1]]=>[6,3,1]=>4 [[4,1,1],[2,1],[1]]=>[6,3,1]=>4 [[4,1,1],[1,1,1],[1]]=>[6,3,1]=>4 [[4,1,1],[4]]=>[6,4]=>2 [[4,1,1],[3,1]]=>[6,4]=>2 [[4,1,1],[2,1,1]]=>[6,4]=>2 [[3,3],[1],[1],[1],[1]]=>[6,1,1,1,1]=>6 [[3,3],[2],[1],[1]]=>[6,2,1,1]=>4 [[3,3],[2],[2]]=>[6,2,2]=>6 [[3,3],[1,1],[1],[1]]=>[6,2,1,1]=>4 [[3,3],[1,1],[1,1]]=>[6,2,2]=>6 [[3,3],[3],[1]]=>[6,3,1]=>4 [[3,3],[2,1],[1]]=>[6,3,1]=>4 [[3,3],[3,1]]=>[6,4]=>2 [[3,3],[2,2]]=>[6,4]=>2 [[3,2,1],[1],[1],[1],[1]]=>[6,1,1,1,1]=>6 [[3,2,1],[2],[1],[1]]=>[6,2,1,1]=>4 [[3,2,1],[2],[2]]=>[6,2,2]=>6 [[3,2,1],[1,1],[1],[1]]=>[6,2,1,1]=>4 [[3,2,1],[1,1],[1,1]]=>[6,2,2]=>6 [[3,2,1],[3],[1]]=>[6,3,1]=>4 [[3,2,1],[2,1],[1]]=>[6,3,1]=>4 [[3,2,1],[1,1,1],[1]]=>[6,3,1]=>4 [[3,2,1],[3,1]]=>[6,4]=>2 [[3,2,1],[2,2]]=>[6,4]=>2 [[3,2,1],[2,1,1]]=>[6,4]=>2 [[3,1,1,1],[1],[1],[1],[1]]=>[6,1,1,1,1]=>6 [[3,1,1,1],[2],[1],[1]]=>[6,2,1,1]=>4 [[3,1,1,1],[2],[2]]=>[6,2,2]=>6 [[3,1,1,1],[1,1],[1],[1]]=>[6,2,1,1]=>4 [[3,1,1,1],[1,1],[1,1]]=>[6,2,2]=>6 [[3,1,1,1],[3],[1]]=>[6,3,1]=>4 [[3,1,1,1],[2,1],[1]]=>[6,3,1]=>4 [[3,1,1,1],[1,1,1],[1]]=>[6,3,1]=>4 [[3,1,1,1],[3,1]]=>[6,4]=>2 [[3,1,1,1],[2,1,1]]=>[6,4]=>2 [[3,1,1,1],[1,1,1,1]]=>[6,4]=>2 [[2,2,2],[1],[1],[1],[1]]=>[6,1,1,1,1]=>6 [[2,2,2],[2],[1],[1]]=>[6,2,1,1]=>4 [[2,2,2],[2],[2]]=>[6,2,2]=>6 [[2,2,2],[1,1],[1],[1]]=>[6,2,1,1]=>4 [[2,2,2],[1,1],[1,1]]=>[6,2,2]=>6 [[2,2,2],[2,1],[1]]=>[6,3,1]=>4 [[2,2,2],[1,1,1],[1]]=>[6,3,1]=>4 [[2,2,2],[2,2]]=>[6,4]=>2 [[2,2,2],[2,1,1]]=>[6,4]=>2 [[2,2,1,1],[1],[1],[1],[1]]=>[6,1,1,1,1]=>6 [[2,2,1,1],[2],[1],[1]]=>[6,2,1,1]=>4 [[2,2,1,1],[2],[2]]=>[6,2,2]=>6 [[2,2,1,1],[1,1],[1],[1]]=>[6,2,1,1]=>4 [[2,2,1,1],[1,1],[1,1]]=>[6,2,2]=>6 [[2,2,1,1],[2,1],[1]]=>[6,3,1]=>4 [[2,2,1,1],[1,1,1],[1]]=>[6,3,1]=>4 [[2,2,1,1],[2,2]]=>[6,4]=>2 [[2,2,1,1],[2,1,1]]=>[6,4]=>2 [[2,2,1,1],[1,1,1,1]]=>[6,4]=>2 [[2,1,1,1,1],[1],[1],[1],[1]]=>[6,1,1,1,1]=>6 [[2,1,1,1,1],[2],[1],[1]]=>[6,2,1,1]=>4 [[2,1,1,1,1],[2],[2]]=>[6,2,2]=>6 [[2,1,1,1,1],[1,1],[1],[1]]=>[6,2,1,1]=>4 [[2,1,1,1,1],[1,1],[1,1]]=>[6,2,2]=>6 [[2,1,1,1,1],[2,1],[1]]=>[6,3,1]=>4 [[2,1,1,1,1],[1,1,1],[1]]=>[6,3,1]=>4 [[2,1,1,1,1],[2,1,1]]=>[6,4]=>2 [[2,1,1,1,1],[1,1,1,1]]=>[6,4]=>2 [[1,1,1,1,1,1],[1],[1],[1],[1]]=>[6,1,1,1,1]=>6 [[1,1,1,1,1,1],[1,1],[1],[1]]=>[6,2,1,1]=>4 [[1,1,1,1,1,1],[1,1],[1,1]]=>[6,2,2]=>6 [[1,1,1,1,1,1],[1,1,1],[1]]=>[6,3,1]=>4 [[1,1,1,1,1,1],[1,1,1,1]]=>[6,4]=>2 [[7],[1],[1],[1]]=>[7,1,1,1]=>6 [[7],[2],[1]]=>[7,2,1]=>6 [[7],[3]]=>[7,3]=>4 [[6,1],[1],[1],[1]]=>[7,1,1,1]=>6 [[6,1],[2],[1]]=>[7,2,1]=>6 [[6,1],[1,1],[1]]=>[7,2,1]=>6 [[6,1],[3]]=>[7,3]=>4 [[6,1],[2,1]]=>[7,3]=>4 [[5,2],[1],[1],[1]]=>[7,1,1,1]=>6 [[5,2],[2],[1]]=>[7,2,1]=>6 [[5,2],[1,1],[1]]=>[7,2,1]=>6 [[5,2],[3]]=>[7,3]=>4 [[5,2],[2,1]]=>[7,3]=>4 [[5,1,1],[1],[1],[1]]=>[7,1,1,1]=>6 [[5,1,1],[2],[1]]=>[7,2,1]=>6 [[5,1,1],[1,1],[1]]=>[7,2,1]=>6 [[5,1,1],[3]]=>[7,3]=>4 [[5,1,1],[2,1]]=>[7,3]=>4 [[5,1,1],[1,1,1]]=>[7,3]=>4 [[4,3],[1],[1],[1]]=>[7,1,1,1]=>6 [[4,3],[2],[1]]=>[7,2,1]=>6 [[4,3],[1,1],[1]]=>[7,2,1]=>6 [[4,3],[3]]=>[7,3]=>4 [[4,3],[2,1]]=>[7,3]=>4 [[4,2,1],[1],[1],[1]]=>[7,1,1,1]=>6 [[4,2,1],[2],[1]]=>[7,2,1]=>6 [[4,2,1],[1,1],[1]]=>[7,2,1]=>6 [[4,2,1],[3]]=>[7,3]=>4 [[4,2,1],[2,1]]=>[7,3]=>4 [[4,2,1],[1,1,1]]=>[7,3]=>4 [[4,1,1,1],[1],[1],[1]]=>[7,1,1,1]=>6 [[4,1,1,1],[2],[1]]=>[7,2,1]=>6 [[4,1,1,1],[1,1],[1]]=>[7,2,1]=>6 [[4,1,1,1],[3]]=>[7,3]=>4 [[4,1,1,1],[2,1]]=>[7,3]=>4 [[4,1,1,1],[1,1,1]]=>[7,3]=>4 [[3,3,1],[1],[1],[1]]=>[7,1,1,1]=>6 [[3,3,1],[2],[1]]=>[7,2,1]=>6 [[3,3,1],[1,1],[1]]=>[7,2,1]=>6 [[3,3,1],[3]]=>[7,3]=>4 [[3,3,1],[2,1]]=>[7,3]=>4 [[3,3,1],[1,1,1]]=>[7,3]=>4 [[3,2,2],[1],[1],[1]]=>[7,1,1,1]=>6 [[3,2,2],[2],[1]]=>[7,2,1]=>6 [[3,2,2],[1,1],[1]]=>[7,2,1]=>6 [[3,2,2],[3]]=>[7,3]=>4 [[3,2,2],[2,1]]=>[7,3]=>4 [[3,2,2],[1,1,1]]=>[7,3]=>4 [[3,2,1,1],[1],[1],[1]]=>[7,1,1,1]=>6 [[3,2,1,1],[2],[1]]=>[7,2,1]=>6 [[3,2,1,1],[1,1],[1]]=>[7,2,1]=>6 [[3,2,1,1],[3]]=>[7,3]=>4 [[3,2,1,1],[2,1]]=>[7,3]=>4 [[3,2,1,1],[1,1,1]]=>[7,3]=>4 [[3,1,1,1,1],[1],[1],[1]]=>[7,1,1,1]=>6 [[3,1,1,1,1],[2],[1]]=>[7,2,1]=>6 [[3,1,1,1,1],[1,1],[1]]=>[7,2,1]=>6 [[3,1,1,1,1],[3]]=>[7,3]=>4 [[3,1,1,1,1],[2,1]]=>[7,3]=>4 [[3,1,1,1,1],[1,1,1]]=>[7,3]=>4 [[2,2,2,1],[1],[1],[1]]=>[7,1,1,1]=>6 [[2,2,2,1],[2],[1]]=>[7,2,1]=>6 [[2,2,2,1],[1,1],[1]]=>[7,2,1]=>6 [[2,2,2,1],[2,1]]=>[7,3]=>4 [[2,2,2,1],[1,1,1]]=>[7,3]=>4 [[2,2,1,1,1],[1],[1],[1]]=>[7,1,1,1]=>6 [[2,2,1,1,1],[2],[1]]=>[7,2,1]=>6 [[2,2,1,1,1],[1,1],[1]]=>[7,2,1]=>6 [[2,2,1,1,1],[2,1]]=>[7,3]=>4 [[2,2,1,1,1],[1,1,1]]=>[7,3]=>4 [[2,1,1,1,1,1],[1],[1],[1]]=>[7,1,1,1]=>6 [[2,1,1,1,1,1],[2],[1]]=>[7,2,1]=>6 [[2,1,1,1,1,1],[1,1],[1]]=>[7,2,1]=>6 [[2,1,1,1,1,1],[2,1]]=>[7,3]=>4 [[2,1,1,1,1,1],[1,1,1]]=>[7,3]=>4 [[1,1,1,1,1,1,1],[1],[1],[1]]=>[7,1,1,1]=>6 [[1,1,1,1,1,1,1],[1,1],[1]]=>[7,2,1]=>6 [[1,1,1,1,1,1,1],[1,1,1]]=>[7,3]=>4 [[8],[1],[1]]=>[8,1,1]=>8 [[8],[2]]=>[8,2]=>6 [[7,1],[1],[1]]=>[8,1,1]=>8 [[7,1],[2]]=>[8,2]=>6 [[7,1],[1,1]]=>[8,2]=>6 [[6,2],[1],[1]]=>[8,1,1]=>8 [[6,2],[2]]=>[8,2]=>6 [[6,2],[1,1]]=>[8,2]=>6 [[6,1,1],[1],[1]]=>[8,1,1]=>8 [[6,1,1],[2]]=>[8,2]=>6 [[6,1,1],[1,1]]=>[8,2]=>6 [[5,3],[1],[1]]=>[8,1,1]=>8 [[5,3],[2]]=>[8,2]=>6 [[5,3],[1,1]]=>[8,2]=>6 [[5,2,1],[1],[1]]=>[8,1,1]=>8 [[5,2,1],[2]]=>[8,2]=>6 [[5,2,1],[1,1]]=>[8,2]=>6 [[5,1,1,1],[1],[1]]=>[8,1,1]=>8 [[5,1,1,1],[2]]=>[8,2]=>6 [[5,1,1,1],[1,1]]=>[8,2]=>6 [[4,4],[1],[1]]=>[8,1,1]=>8 [[4,4],[2]]=>[8,2]=>6 [[4,4],[1,1]]=>[8,2]=>6 [[4,3,1],[1],[1]]=>[8,1,1]=>8 [[4,3,1],[2]]=>[8,2]=>6 [[4,3,1],[1,1]]=>[8,2]=>6 [[4,2,2],[1],[1]]=>[8,1,1]=>8 [[4,2,2],[2]]=>[8,2]=>6 [[4,2,2],[1,1]]=>[8,2]=>6 [[4,2,1,1],[1],[1]]=>[8,1,1]=>8 [[4,2,1,1],[2]]=>[8,2]=>6 [[4,2,1,1],[1,1]]=>[8,2]=>6 [[4,1,1,1,1],[1],[1]]=>[8,1,1]=>8 [[4,1,1,1,1],[2]]=>[8,2]=>6 [[4,1,1,1,1],[1,1]]=>[8,2]=>6 [[3,3,2],[1],[1]]=>[8,1,1]=>8 [[3,3,2],[2]]=>[8,2]=>6 [[3,3,2],[1,1]]=>[8,2]=>6 [[3,3,1,1],[1],[1]]=>[8,1,1]=>8 [[3,3,1,1],[2]]=>[8,2]=>6 [[3,3,1,1],[1,1]]=>[8,2]=>6 [[3,2,2,1],[1],[1]]=>[8,1,1]=>8 [[3,2,2,1],[2]]=>[8,2]=>6 [[3,2,2,1],[1,1]]=>[8,2]=>6 [[3,2,1,1,1],[1],[1]]=>[8,1,1]=>8 [[3,2,1,1,1],[2]]=>[8,2]=>6 [[3,2,1,1,1],[1,1]]=>[8,2]=>6 [[3,1,1,1,1,1],[1],[1]]=>[8,1,1]=>8 [[3,1,1,1,1,1],[2]]=>[8,2]=>6 [[3,1,1,1,1,1],[1,1]]=>[8,2]=>6 [[2,2,2,2],[1],[1]]=>[8,1,1]=>8 [[2,2,2,2],[2]]=>[8,2]=>6 [[2,2,2,2],[1,1]]=>[8,2]=>6 [[2,2,2,1,1],[1],[1]]=>[8,1,1]=>8 [[2,2,2,1,1],[2]]=>[8,2]=>6 [[2,2,2,1,1],[1,1]]=>[8,2]=>6 [[2,2,1,1,1,1],[1],[1]]=>[8,1,1]=>8 [[2,2,1,1,1,1],[2]]=>[8,2]=>6 [[2,2,1,1,1,1],[1,1]]=>[8,2]=>6 [[2,1,1,1,1,1,1],[1],[1]]=>[8,1,1]=>8 [[2,1,1,1,1,1,1],[2]]=>[8,2]=>6 [[2,1,1,1,1,1,1],[1,1]]=>[8,2]=>6 [[1,1,1,1,1,1,1,1],[1],[1]]=>[8,1,1]=>8 [[1,1,1,1,1,1,1,1],[1,1]]=>[8,2]=>6 [[9],[1]]=>[9,1]=>8 [[8,1],[1]]=>[9,1]=>8 [[7,2],[1]]=>[9,1]=>8 [[7,1,1],[1]]=>[9,1]=>8 [[6,3],[1]]=>[9,1]=>8 [[6,2,1],[1]]=>[9,1]=>8 [[6,1,1,1],[1]]=>[9,1]=>8 [[5,4],[1]]=>[9,1]=>8 [[5,3,1],[1]]=>[9,1]=>8 [[5,2,2],[1]]=>[9,1]=>8 [[5,2,1,1],[1]]=>[9,1]=>8 [[5,1,1,1,1],[1]]=>[9,1]=>8 [[4,4,1],[1]]=>[9,1]=>8 [[4,3,2],[1]]=>[9,1]=>8 [[4,3,1,1],[1]]=>[9,1]=>8 [[4,2,2,1],[1]]=>[9,1]=>8 [[4,2,1,1,1],[1]]=>[9,1]=>8 [[4,1,1,1,1,1],[1]]=>[9,1]=>8 [[3,3,3],[1]]=>[9,1]=>8 [[3,3,2,1],[1]]=>[9,1]=>8 [[3,3,1,1,1],[1]]=>[9,1]=>8 [[3,2,2,2],[1]]=>[9,1]=>8 [[3,2,2,1,1],[1]]=>[9,1]=>8 [[3,2,1,1,1,1],[1]]=>[9,1]=>8 [[3,1,1,1,1,1,1],[1]]=>[9,1]=>8 [[2,2,2,2,1],[1]]=>[9,1]=>8 [[2,2,2,1,1,1],[1]]=>[9,1]=>8 [[2,2,1,1,1,1,1],[1]]=>[9,1]=>8 [[2,1,1,1,1,1,1,1],[1]]=>[9,1]=>8 [[1,1,1,1,1,1,1,1,1],[1]]=>[9,1]=>8 [[10]]=>[10]=>10 [[9,1]]=>[10]=>10 [[8,2]]=>[10]=>10 [[8,1,1]]=>[10]=>10 [[7,3]]=>[10]=>10 [[7,2,1]]=>[10]=>10 [[7,1,1,1]]=>[10]=>10 [[6,4]]=>[10]=>10 [[6,3,1]]=>[10]=>10 [[6,2,2]]=>[10]=>10 [[6,2,1,1]]=>[10]=>10 [[6,1,1,1,1]]=>[10]=>10 [[5,5]]=>[10]=>10 [[5,4,1]]=>[10]=>10 [[5,3,2]]=>[10]=>10 [[5,3,1,1]]=>[10]=>10 [[5,2,2,1]]=>[10]=>10 [[5,2,1,1,1]]=>[10]=>10 [[5,1,1,1,1,1]]=>[10]=>10 [[4,4,2]]=>[10]=>10 [[4,4,1,1]]=>[10]=>10 [[4,3,3]]=>[10]=>10 [[4,3,2,1]]=>[10]=>10 [[4,3,1,1,1]]=>[10]=>10 [[4,2,2,2]]=>[10]=>10 [[4,2,2,1,1]]=>[10]=>10 [[4,2,1,1,1,1]]=>[10]=>10 [[4,1,1,1,1,1,1]]=>[10]=>10 [[3,3,3,1]]=>[10]=>10 [[3,3,2,2]]=>[10]=>10 [[3,3,2,1,1]]=>[10]=>10 [[3,3,1,1,1,1]]=>[10]=>10 [[3,2,2,2,1]]=>[10]=>10 [[3,2,2,1,1,1]]=>[10]=>10 [[3,2,1,1,1,1,1]]=>[10]=>10 [[3,1,1,1,1,1,1,1]]=>[10]=>10 [[2,2,2,2,2]]=>[10]=>10 [[2,2,2,2,1,1]]=>[10]=>10 [[2,2,2,1,1,1,1]]=>[10]=>10 [[2,2,1,1,1,1,1,1]]=>[10]=>10 [[2,1,1,1,1,1,1,1,1]]=>[10]=>10 [[1,1,1,1,1,1,1,1,1,1]]=>[10]=>10
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The alternating sum of the parts of an integer partition.
For a partition $\lambda = (\lambda_1,\ldots,\lambda_k)$, this is $\lambda_1 - \lambda_2 + \cdots \pm \lambda_k$.
Map
to partition
Description
The underlying integer partition of a plane partition.
This is the partition whose parts are the sums of the individual rows of the plane partition.