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Identifier
Mp00181: Skew partitions —row lengths⟶ Integer compositions
Images
=>
Cc0028;cc-rep-0
[[1],[]]=>[1] [[2],[]]=>[2] [[1,1],[]]=>[1,1] [[2,1],[1]]=>[1,1] [[3],[]]=>[3] [[2,1],[]]=>[2,1] [[3,1],[1]]=>[2,1] [[2,2],[1]]=>[1,2] [[3,2],[2]]=>[1,2] [[1,1,1],[]]=>[1,1,1] [[2,2,1],[1,1]]=>[1,1,1] [[2,1,1],[1]]=>[1,1,1] [[3,2,1],[2,1]]=>[1,1,1] [[4],[]]=>[4] [[3,1],[]]=>[3,1] [[4,1],[1]]=>[3,1] [[2,2],[]]=>[2,2] [[3,2],[1]]=>[2,2] [[4,2],[2]]=>[2,2] [[2,1,1],[]]=>[2,1,1] [[3,2,1],[1,1]]=>[2,1,1] [[3,1,1],[1]]=>[2,1,1] [[4,2,1],[2,1]]=>[2,1,1] [[3,3],[2]]=>[1,3] [[4,3],[3]]=>[1,3] [[2,2,1],[1]]=>[1,2,1] [[3,3,1],[2,1]]=>[1,2,1] [[3,2,1],[2]]=>[1,2,1] [[4,3,1],[3,1]]=>[1,2,1] [[2,2,2],[1,1]]=>[1,1,2] [[3,3,2],[2,2]]=>[1,1,2] [[3,2,2],[2,1]]=>[1,1,2] [[4,3,2],[3,2]]=>[1,1,2] [[1,1,1,1],[]]=>[1,1,1,1] [[2,2,2,1],[1,1,1]]=>[1,1,1,1] [[2,2,1,1],[1,1]]=>[1,1,1,1] [[3,3,2,1],[2,2,1]]=>[1,1,1,1] [[2,1,1,1],[1]]=>[1,1,1,1] [[3,2,2,1],[2,1,1]]=>[1,1,1,1] [[3,2,1,1],[2,1]]=>[1,1,1,1] [[4,3,2,1],[3,2,1]]=>[1,1,1,1] [[5],[]]=>[5] [[4,1],[]]=>[4,1] [[5,1],[1]]=>[4,1] [[3,2],[]]=>[3,2] [[4,2],[1]]=>[3,2] [[5,2],[2]]=>[3,2] [[3,1,1],[]]=>[3,1,1] [[4,2,1],[1,1]]=>[3,1,1] [[4,1,1],[1]]=>[3,1,1] [[5,2,1],[2,1]]=>[3,1,1] [[3,3],[1]]=>[2,3] [[4,3],[2]]=>[2,3] [[5,3],[3]]=>[2,3] [[2,2,1],[]]=>[2,2,1] [[3,3,1],[1,1]]=>[2,2,1] [[3,2,1],[1]]=>[2,2,1] [[4,3,1],[2,1]]=>[2,2,1] [[4,2,1],[2]]=>[2,2,1] [[5,3,1],[3,1]]=>[2,2,1] [[3,2,2],[1,1]]=>[2,1,2] [[4,3,2],[2,2]]=>[2,1,2] [[4,2,2],[2,1]]=>[2,1,2] [[5,3,2],[3,2]]=>[2,1,2] [[2,1,1,1],[]]=>[2,1,1,1] [[3,2,2,1],[1,1,1]]=>[2,1,1,1] [[3,2,1,1],[1,1]]=>[2,1,1,1] [[4,3,2,1],[2,2,1]]=>[2,1,1,1] [[3,1,1,1],[1]]=>[2,1,1,1] [[4,2,2,1],[2,1,1]]=>[2,1,1,1] [[4,2,1,1],[2,1]]=>[2,1,1,1] [[5,3,2,1],[3,2,1]]=>[2,1,1,1] [[4,4],[3]]=>[1,4] [[5,4],[4]]=>[1,4] [[3,3,1],[2]]=>[1,3,1] [[4,4,1],[3,1]]=>[1,3,1] [[4,3,1],[3]]=>[1,3,1] [[5,4,1],[4,1]]=>[1,3,1] [[2,2,2],[1]]=>[1,2,2] [[3,3,2],[2,1]]=>[1,2,2] [[4,4,2],[3,2]]=>[1,2,2] [[3,2,2],[2]]=>[1,2,2] [[4,3,2],[3,1]]=>[1,2,2] [[5,4,2],[4,2]]=>[1,2,2] [[2,2,1,1],[1]]=>[1,2,1,1] [[3,3,2,1],[2,1,1]]=>[1,2,1,1] [[3,3,1,1],[2,1]]=>[1,2,1,1] [[4,4,2,1],[3,2,1]]=>[1,2,1,1] [[3,2,1,1],[2]]=>[1,2,1,1] [[4,3,2,1],[3,1,1]]=>[1,2,1,1] [[4,3,1,1],[3,1]]=>[1,2,1,1] [[5,4,2,1],[4,2,1]]=>[1,2,1,1] [[3,3,3],[2,2]]=>[1,1,3] [[4,4,3],[3,3]]=>[1,1,3] [[4,3,3],[3,2]]=>[1,1,3] [[5,4,3],[4,3]]=>[1,1,3] [[2,2,2,1],[1,1]]=>[1,1,2,1] [[3,3,3,1],[2,2,1]]=>[1,1,2,1] [[3,3,2,1],[2,2]]=>[1,1,2,1] [[4,4,3,1],[3,3,1]]=>[1,1,2,1] [[3,2,2,1],[2,1]]=>[1,1,2,1] [[4,3,3,1],[3,2,1]]=>[1,1,2,1] [[4,3,2,1],[3,2]]=>[1,1,2,1] [[5,4,3,1],[4,3,1]]=>[1,1,2,1] [[2,2,2,2],[1,1,1]]=>[1,1,1,2] [[3,3,3,2],[2,2,2]]=>[1,1,1,2] [[3,3,2,2],[2,2,1]]=>[1,1,1,2] [[4,4,3,2],[3,3,2]]=>[1,1,1,2] [[3,2,2,2],[2,1,1]]=>[1,1,1,2] [[4,3,3,2],[3,2,2]]=>[1,1,1,2] [[4,3,2,2],[3,2,1]]=>[1,1,1,2] [[5,4,3,2],[4,3,2]]=>[1,1,1,2] [[1,1,1,1,1],[]]=>[1,1,1,1,1] [[2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1,1] [[2,2,2,1,1],[1,1,1]]=>[1,1,1,1,1] [[3,3,3,2,1],[2,2,2,1]]=>[1,1,1,1,1] [[2,2,1,1,1],[1,1]]=>[1,1,1,1,1] [[3,3,2,2,1],[2,2,1,1]]=>[1,1,1,1,1] [[3,3,2,1,1],[2,2,1]]=>[1,1,1,1,1] [[4,4,3,2,1],[3,3,2,1]]=>[1,1,1,1,1] [[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] [[3,2,2,1,1],[2,1,1]]=>[1,1,1,1,1] [[4,3,3,2,1],[3,2,2,1]]=>[1,1,1,1,1] [[3,2,1,1,1],[2,1]]=>[1,1,1,1,1] [[4,3,2,2,1],[3,2,1,1]]=>[1,1,1,1,1] [[4,3,2,1,1],[3,2,1]]=>[1,1,1,1,1] [[5,4,3,2,1],[4,3,2,1]]=>[1,1,1,1,1] [[6],[]]=>[6] [[5,1],[]]=>[5,1] [[6,1],[1]]=>[5,1] [[4,2],[]]=>[4,2] [[5,2],[1]]=>[4,2] [[6,2],[2]]=>[4,2] [[4,1,1],[]]=>[4,1,1] [[5,2,1],[1,1]]=>[4,1,1] [[5,1,1],[1]]=>[4,1,1] [[6,2,1],[2,1]]=>[4,1,1] [[3,3],[]]=>[3,3] [[4,3],[1]]=>[3,3] [[5,3],[2]]=>[3,3] [[6,3],[3]]=>[3,3] [[3,2,1],[]]=>[3,2,1] [[4,3,1],[1,1]]=>[3,2,1] [[4,2,1],[1]]=>[3,2,1] [[5,3,1],[2,1]]=>[3,2,1] [[5,2,1],[2]]=>[3,2,1] [[6,3,1],[3,1]]=>[3,2,1] [[4,2,2],[1,1]]=>[3,1,2] [[5,3,2],[2,2]]=>[3,1,2] [[5,2,2],[2,1]]=>[3,1,2] [[6,3,2],[3,2]]=>[3,1,2] [[3,1,1,1],[]]=>[3,1,1,1] [[4,2,2,1],[1,1,1]]=>[3,1,1,1] [[4,2,1,1],[1,1]]=>[3,1,1,1] [[5,3,2,1],[2,2,1]]=>[3,1,1,1] [[4,1,1,1],[1]]=>[3,1,1,1] [[5,2,2,1],[2,1,1]]=>[3,1,1,1] [[5,2,1,1],[2,1]]=>[3,1,1,1] [[6,3,2,1],[3,2,1]]=>[3,1,1,1] [[4,4],[2]]=>[2,4] [[5,4],[3]]=>[2,4] [[6,4],[4]]=>[2,4] [[3,3,1],[1]]=>[2,3,1] [[4,4,1],[2,1]]=>[2,3,1] [[4,3,1],[2]]=>[2,3,1] [[5,4,1],[3,1]]=>[2,3,1] [[5,3,1],[3]]=>[2,3,1] [[6,4,1],[4,1]]=>[2,3,1] [[2,2,2],[]]=>[2,2,2] [[3,3,2],[1,1]]=>[2,2,2] [[4,4,2],[2,2]]=>[2,2,2] [[3,2,2],[1]]=>[2,2,2] [[4,3,2],[2,1]]=>[2,2,2] [[5,4,2],[3,2]]=>[2,2,2] [[4,2,2],[2]]=>[2,2,2] [[5,3,2],[3,1]]=>[2,2,2] [[6,4,2],[4,2]]=>[2,2,2] [[2,2,1,1],[]]=>[2,2,1,1] [[3,3,2,1],[1,1,1]]=>[2,2,1,1] [[3,3,1,1],[1,1]]=>[2,2,1,1] [[4,4,2,1],[2,2,1]]=>[2,2,1,1] [[3,2,1,1],[1]]=>[2,2,1,1] [[4,3,2,1],[2,1,1]]=>[2,2,1,1] [[4,3,1,1],[2,1]]=>[2,2,1,1] [[5,4,2,1],[3,2,1]]=>[2,2,1,1] [[4,2,1,1],[2]]=>[2,2,1,1] [[5,3,2,1],[3,1,1]]=>[2,2,1,1] [[5,3,1,1],[3,1]]=>[2,2,1,1] [[6,4,2,1],[4,2,1]]=>[2,2,1,1] [[4,3,3],[2,2]]=>[2,1,3] [[5,4,3],[3,3]]=>[2,1,3] [[5,3,3],[3,2]]=>[2,1,3] [[6,4,3],[4,3]]=>[2,1,3] [[3,2,2,1],[1,1]]=>[2,1,2,1] [[4,3,3,1],[2,2,1]]=>[2,1,2,1] [[4,3,2,1],[2,2]]=>[2,1,2,1] [[5,4,3,1],[3,3,1]]=>[2,1,2,1] [[4,2,2,1],[2,1]]=>[2,1,2,1] [[5,3,3,1],[3,2,1]]=>[2,1,2,1] [[5,3,2,1],[3,2]]=>[2,1,2,1] [[6,4,3,1],[4,3,1]]=>[2,1,2,1] [[3,2,2,2],[1,1,1]]=>[2,1,1,2] [[4,3,3,2],[2,2,2]]=>[2,1,1,2] [[4,3,2,2],[2,2,1]]=>[2,1,1,2] [[5,4,3,2],[3,3,2]]=>[2,1,1,2] [[4,2,2,2],[2,1,1]]=>[2,1,1,2] [[5,3,3,2],[3,2,2]]=>[2,1,1,2] [[5,3,2,2],[3,2,1]]=>[2,1,1,2] [[6,4,3,2],[4,3,2]]=>[2,1,1,2] [[2,1,1,1,1],[]]=>[2,1,1,1,1] [[3,2,2,2,1],[1,1,1,1]]=>[2,1,1,1,1] [[3,2,2,1,1],[1,1,1]]=>[2,1,1,1,1] [[4,3,3,2,1],[2,2,2,1]]=>[2,1,1,1,1] [[3,2,1,1,1],[1,1]]=>[2,1,1,1,1] [[4,3,2,2,1],[2,2,1,1]]=>[2,1,1,1,1] [[4,3,2,1,1],[2,2,1]]=>[2,1,1,1,1] [[5,4,3,2,1],[3,3,2,1]]=>[2,1,1,1,1] [[3,1,1,1,1],[1]]=>[2,1,1,1,1] [[4,2,2,2,1],[2,1,1,1]]=>[2,1,1,1,1] [[4,2,2,1,1],[2,1,1]]=>[2,1,1,1,1] [[5,3,3,2,1],[3,2,2,1]]=>[2,1,1,1,1] [[4,2,1,1,1],[2,1]]=>[2,1,1,1,1] [[5,3,2,2,1],[3,2,1,1]]=>[2,1,1,1,1] [[5,3,2,1,1],[3,2,1]]=>[2,1,1,1,1] [[6,4,3,2,1],[4,3,2,1]]=>[2,1,1,1,1] [[5,5],[4]]=>[1,5] [[6,5],[5]]=>[1,5] [[4,4,1],[3]]=>[1,4,1] [[5,5,1],[4,1]]=>[1,4,1] [[5,4,1],[4]]=>[1,4,1] [[6,5,1],[5,1]]=>[1,4,1] [[3,3,2],[2]]=>[1,3,2] [[4,4,2],[3,1]]=>[1,3,2] [[5,5,2],[4,2]]=>[1,3,2] [[4,3,2],[3]]=>[1,3,2] [[5,4,2],[4,1]]=>[1,3,2] [[6,5,2],[5,2]]=>[1,3,2] [[3,3,1,1],[2]]=>[1,3,1,1] [[4,4,2,1],[3,1,1]]=>[1,3,1,1] [[4,4,1,1],[3,1]]=>[1,3,1,1] [[5,5,2,1],[4,2,1]]=>[1,3,1,1] [[4,3,1,1],[3]]=>[1,3,1,1] [[5,4,2,1],[4,1,1]]=>[1,3,1,1] [[5,4,1,1],[4,1]]=>[1,3,1,1] [[6,5,2,1],[5,2,1]]=>[1,3,1,1] [[3,3,3],[2,1]]=>[1,2,3] [[4,4,3],[3,2]]=>[1,2,3] [[5,5,3],[4,3]]=>[1,2,3] [[4,3,3],[3,1]]=>[1,2,3] [[5,4,3],[4,2]]=>[1,2,3] [[6,5,3],[5,3]]=>[1,2,3] [[2,2,2,1],[1]]=>[1,2,2,1] [[3,3,3,1],[2,1,1]]=>[1,2,2,1] [[3,3,2,1],[2,1]]=>[1,2,2,1] [[4,4,3,1],[3,2,1]]=>[1,2,2,1] [[4,4,2,1],[3,2]]=>[1,2,2,1] [[5,5,3,1],[4,3,1]]=>[1,2,2,1] [[3,2,2,1],[2]]=>[1,2,2,1] [[4,3,3,1],[3,1,1]]=>[1,2,2,1] [[4,3,2,1],[3,1]]=>[1,2,2,1] [[5,4,3,1],[4,2,1]]=>[1,2,2,1] [[5,4,2,1],[4,2]]=>[1,2,2,1] [[6,5,3,1],[5,3,1]]=>[1,2,2,1] [[3,3,2,2],[2,1,1]]=>[1,2,1,2] [[4,4,3,2],[3,2,2]]=>[1,2,1,2] [[4,4,2,2],[3,2,1]]=>[1,2,1,2] [[5,5,3,2],[4,3,2]]=>[1,2,1,2] [[4,3,2,2],[3,1,1]]=>[1,2,1,2] [[5,4,3,2],[4,2,2]]=>[1,2,1,2] [[5,4,2,2],[4,2,1]]=>[1,2,1,2] [[6,5,3,2],[5,3,2]]=>[1,2,1,2] [[2,2,1,1,1],[1]]=>[1,2,1,1,1] [[3,3,2,2,1],[2,1,1,1]]=>[1,2,1,1,1] [[3,3,2,1,1],[2,1,1]]=>[1,2,1,1,1] [[4,4,3,2,1],[3,2,2,1]]=>[1,2,1,1,1] [[3,3,1,1,1],[2,1]]=>[1,2,1,1,1] [[4,4,2,2,1],[3,2,1,1]]=>[1,2,1,1,1] [[4,4,2,1,1],[3,2,1]]=>[1,2,1,1,1] [[5,5,3,2,1],[4,3,2,1]]=>[1,2,1,1,1] [[3,2,1,1,1],[2]]=>[1,2,1,1,1] [[4,3,2,2,1],[3,1,1,1]]=>[1,2,1,1,1] [[4,3,2,1,1],[3,1,1]]=>[1,2,1,1,1] [[5,4,3,2,1],[4,2,2,1]]=>[1,2,1,1,1] [[4,3,1,1,1],[3,1]]=>[1,2,1,1,1] [[5,4,2,2,1],[4,2,1,1]]=>[1,2,1,1,1] [[5,4,2,1,1],[4,2,1]]=>[1,2,1,1,1] [[6,5,3,2,1],[5,3,2,1]]=>[1,2,1,1,1] [[4,4,4],[3,3]]=>[1,1,4] [[5,5,4],[4,4]]=>[1,1,4] [[5,4,4],[4,3]]=>[1,1,4] [[6,5,4],[5,4]]=>[1,1,4] [[3,3,3,1],[2,2]]=>[1,1,3,1] [[4,4,4,1],[3,3,1]]=>[1,1,3,1] [[4,4,3,1],[3,3]]=>[1,1,3,1] [[5,5,4,1],[4,4,1]]=>[1,1,3,1] [[4,3,3,1],[3,2]]=>[1,1,3,1] [[5,4,4,1],[4,3,1]]=>[1,1,3,1] [[5,4,3,1],[4,3]]=>[1,1,3,1] [[6,5,4,1],[5,4,1]]=>[1,1,3,1] [[2,2,2,2],[1,1]]=>[1,1,2,2] [[3,3,3,2],[2,2,1]]=>[1,1,2,2] [[4,4,4,2],[3,3,2]]=>[1,1,2,2] [[3,3,2,2],[2,2]]=>[1,1,2,2] [[4,4,3,2],[3,3,1]]=>[1,1,2,2] [[5,5,4,2],[4,4,2]]=>[1,1,2,2] [[3,2,2,2],[2,1]]=>[1,1,2,2] [[4,3,3,2],[3,2,1]]=>[1,1,2,2] [[5,4,4,2],[4,3,2]]=>[1,1,2,2] [[4,3,2,2],[3,2]]=>[1,1,2,2] [[5,4,3,2],[4,3,1]]=>[1,1,2,2] [[6,5,4,2],[5,4,2]]=>[1,1,2,2] [[2,2,2,1,1],[1,1]]=>[1,1,2,1,1] [[3,3,3,2,1],[2,2,1,1]]=>[1,1,2,1,1] [[3,3,3,1,1],[2,2,1]]=>[1,1,2,1,1] [[4,4,4,2,1],[3,3,2,1]]=>[1,1,2,1,1] [[3,3,2,1,1],[2,2]]=>[1,1,2,1,1] [[4,4,3,2,1],[3,3,1,1]]=>[1,1,2,1,1] [[4,4,3,1,1],[3,3,1]]=>[1,1,2,1,1] [[5,5,4,2,1],[4,4,2,1]]=>[1,1,2,1,1] [[3,2,2,1,1],[2,1]]=>[1,1,2,1,1] [[4,3,3,2,1],[3,2,1,1]]=>[1,1,2,1,1] [[4,3,3,1,1],[3,2,1]]=>[1,1,2,1,1] [[5,4,4,2,1],[4,3,2,1]]=>[1,1,2,1,1] [[4,3,2,1,1],[3,2]]=>[1,1,2,1,1] [[5,4,3,2,1],[4,3,1,1]]=>[1,1,2,1,1] [[5,4,3,1,1],[4,3,1]]=>[1,1,2,1,1] [[6,5,4,2,1],[5,4,2,1]]=>[1,1,2,1,1] [[3,3,3,3],[2,2,2]]=>[1,1,1,3] [[4,4,4,3],[3,3,3]]=>[1,1,1,3] [[4,4,3,3],[3,3,2]]=>[1,1,1,3] [[5,5,4,3],[4,4,3]]=>[1,1,1,3] [[4,3,3,3],[3,2,2]]=>[1,1,1,3] [[5,4,4,3],[4,3,3]]=>[1,1,1,3] [[5,4,3,3],[4,3,2]]=>[1,1,1,3] [[6,5,4,3],[5,4,3]]=>[1,1,1,3] [[2,2,2,2,1],[1,1,1]]=>[1,1,1,2,1] [[3,3,3,3,1],[2,2,2,1]]=>[1,1,1,2,1] [[3,3,3,2,1],[2,2,2]]=>[1,1,1,2,1] [[4,4,4,3,1],[3,3,3,1]]=>[1,1,1,2,1] [[3,3,2,2,1],[2,2,1]]=>[1,1,1,2,1] [[4,4,3,3,1],[3,3,2,1]]=>[1,1,1,2,1] [[4,4,3,2,1],[3,3,2]]=>[1,1,1,2,1] [[5,5,4,3,1],[4,4,3,1]]=>[1,1,1,2,1] [[3,2,2,2,1],[2,1,1]]=>[1,1,1,2,1] [[4,3,3,3,1],[3,2,2,1]]=>[1,1,1,2,1] [[4,3,3,2,1],[3,2,2]]=>[1,1,1,2,1] [[5,4,4,3,1],[4,3,3,1]]=>[1,1,1,2,1] [[4,3,2,2,1],[3,2,1]]=>[1,1,1,2,1] [[5,4,3,3,1],[4,3,2,1]]=>[1,1,1,2,1] [[5,4,3,2,1],[4,3,2]]=>[1,1,1,2,1] [[6,5,4,3,1],[5,4,3,1]]=>[1,1,1,2,1] [[2,2,2,2,2],[1,1,1,1]]=>[1,1,1,1,2] [[3,3,3,3,2],[2,2,2,2]]=>[1,1,1,1,2] [[3,3,3,2,2],[2,2,2,1]]=>[1,1,1,1,2] [[4,4,4,3,2],[3,3,3,2]]=>[1,1,1,1,2] [[3,3,2,2,2],[2,2,1,1]]=>[1,1,1,1,2] [[4,4,3,3,2],[3,3,2,2]]=>[1,1,1,1,2] [[4,4,3,2,2],[3,3,2,1]]=>[1,1,1,1,2] [[5,5,4,3,2],[4,4,3,2]]=>[1,1,1,1,2] [[3,2,2,2,2],[2,1,1,1]]=>[1,1,1,1,2] [[4,3,3,3,2],[3,2,2,2]]=>[1,1,1,1,2] [[4,3,3,2,2],[3,2,2,1]]=>[1,1,1,1,2] [[5,4,4,3,2],[4,3,3,2]]=>[1,1,1,1,2] [[4,3,2,2,2],[3,2,1,1]]=>[1,1,1,1,2] [[5,4,3,3,2],[4,3,2,2]]=>[1,1,1,1,2] [[5,4,3,2,2],[4,3,2,1]]=>[1,1,1,1,2] [[6,5,4,3,2],[5,4,3,2]]=>[1,1,1,1,2] [[1,1,1,1,1,1],[]]=>[1,1,1,1,1,1] [[2,2,2,2,2,1],[1,1,1,1,1]]=>[1,1,1,1,1,1] [[2,2,2,2,1,1],[1,1,1,1]]=>[1,1,1,1,1,1] [[3,3,3,3,2,1],[2,2,2,2,1]]=>[1,1,1,1,1,1] [[2,2,2,1,1,1],[1,1,1]]=>[1,1,1,1,1,1] [[3,3,3,2,2,1],[2,2,2,1,1]]=>[1,1,1,1,1,1] [[3,3,3,2,1,1],[2,2,2,1]]=>[1,1,1,1,1,1] [[4,4,4,3,2,1],[3,3,3,2,1]]=>[1,1,1,1,1,1] [[2,2,1,1,1,1],[1,1]]=>[1,1,1,1,1,1] [[3,3,2,2,2,1],[2,2,1,1,1]]=>[1,1,1,1,1,1] [[3,3,2,2,1,1],[2,2,1,1]]=>[1,1,1,1,1,1] [[4,4,3,3,2,1],[3,3,2,2,1]]=>[1,1,1,1,1,1] [[3,3,2,1,1,1],[2,2,1]]=>[1,1,1,1,1,1] [[4,4,3,2,2,1],[3,3,2,1,1]]=>[1,1,1,1,1,1] [[4,4,3,2,1,1],[3,3,2,1]]=>[1,1,1,1,1,1] [[5,5,4,3,2,1],[4,4,3,2,1]]=>[1,1,1,1,1,1] [[2,1,1,1,1,1],[1]]=>[1,1,1,1,1,1] [[3,2,2,2,2,1],[2,1,1,1,1]]=>[1,1,1,1,1,1] [[3,2,2,2,1,1],[2,1,1,1]]=>[1,1,1,1,1,1] [[4,3,3,3,2,1],[3,2,2,2,1]]=>[1,1,1,1,1,1] [[3,2,2,1,1,1],[2,1,1]]=>[1,1,1,1,1,1] [[4,3,3,2,2,1],[3,2,2,1,1]]=>[1,1,1,1,1,1] [[4,3,3,2,1,1],[3,2,2,1]]=>[1,1,1,1,1,1] [[5,4,4,3,2,1],[4,3,3,2,1]]=>[1,1,1,1,1,1] [[3,2,1,1,1,1],[2,1]]=>[1,1,1,1,1,1] [[4,3,2,2,2,1],[3,2,1,1,1]]=>[1,1,1,1,1,1] [[4,3,2,2,1,1],[3,2,1,1]]=>[1,1,1,1,1,1] [[5,4,3,3,2,1],[4,3,2,2,1]]=>[1,1,1,1,1,1] [[4,3,2,1,1,1],[3,2,1]]=>[1,1,1,1,1,1] [[5,4,3,2,2,1],[4,3,2,1,1]]=>[1,1,1,1,1,1] [[5,4,3,2,1,1],[4,3,2,1]]=>[1,1,1,1,1,1] [[6,5,4,3,2,1],[5,4,3,2,1]]=>[1,1,1,1,1,1] [[7],[]]=>[7] [[6,1],[]]=>[6,1] [[7,1],[1]]=>[6,1] [[5,2],[]]=>[5,2] [[6,2],[1]]=>[5,2] [[7,2],[2]]=>[5,2] [[5,1,1],[]]=>[5,1,1] [[6,2,1],[1,1]]=>[5,1,1] [[6,1,1],[1]]=>[5,1,1] [[7,2,1],[2,1]]=>[5,1,1] [[4,3],[]]=>[4,3] [[5,3],[1]]=>[4,3] [[6,3],[2]]=>[4,3] [[7,3],[3]]=>[4,3] [[4,2,1],[]]=>[4,2,1] [[5,3,1],[1,1]]=>[4,2,1] [[5,2,1],[1]]=>[4,2,1] [[6,3,1],[2,1]]=>[4,2,1] [[6,2,1],[2]]=>[4,2,1] [[7,3,1],[3,1]]=>[4,2,1] [[5,2,2],[1,1]]=>[4,1,2] [[6,3,2],[2,2]]=>[4,1,2] [[6,2,2],[2,1]]=>[4,1,2] [[7,3,2],[3,2]]=>[4,1,2] [[4,1,1,1],[]]=>[4,1,1,1] [[5,2,2,1],[1,1,1]]=>[4,1,1,1] [[5,2,1,1],[1,1]]=>[4,1,1,1] [[6,3,2,1],[2,2,1]]=>[4,1,1,1] [[5,1,1,1],[1]]=>[4,1,1,1] [[6,2,2,1],[2,1,1]]=>[4,1,1,1] [[6,2,1,1],[2,1]]=>[4,1,1,1] [[7,3,2,1],[3,2,1]]=>[4,1,1,1] [[4,4],[1]]=>[3,4] [[5,4],[2]]=>[3,4] [[6,4],[3]]=>[3,4] [[7,4],[4]]=>[3,4] [[3,3,1],[]]=>[3,3,1] [[4,4,1],[1,1]]=>[3,3,1] [[4,3,1],[1]]=>[3,3,1] [[5,4,1],[2,1]]=>[3,3,1] [[5,3,1],[2]]=>[3,3,1] [[6,4,1],[3,1]]=>[3,3,1] [[6,3,1],[3]]=>[3,3,1] [[7,4,1],[4,1]]=>[3,3,1] [[3,2,2],[]]=>[3,2,2] [[4,3,2],[1,1]]=>[3,2,2] [[5,4,2],[2,2]]=>[3,2,2] [[4,2,2],[1]]=>[3,2,2] [[5,3,2],[2,1]]=>[3,2,2] [[6,4,2],[3,2]]=>[3,2,2] [[5,2,2],[2]]=>[3,2,2] [[6,3,2],[3,1]]=>[3,2,2] [[7,4,2],[4,2]]=>[3,2,2] [[3,2,1,1],[]]=>[3,2,1,1] [[4,3,2,1],[1,1,1]]=>[3,2,1,1] [[4,3,1,1],[1,1]]=>[3,2,1,1] [[5,4,2,1],[2,2,1]]=>[3,2,1,1] [[4,2,1,1],[1]]=>[3,2,1,1] [[5,3,2,1],[2,1,1]]=>[3,2,1,1] [[5,3,1,1],[2,1]]=>[3,2,1,1] [[6,4,2,1],[3,2,1]]=>[3,2,1,1] [[5,2,1,1],[2]]=>[3,2,1,1] [[6,3,2,1],[3,1,1]]=>[3,2,1,1] [[6,3,1,1],[3,1]]=>[3,2,1,1] [[7,4,2,1],[4,2,1]]=>[3,2,1,1] [[5,3,3],[2,2]]=>[3,1,3] [[6,4,3],[3,3]]=>[3,1,3] [[6,3,3],[3,2]]=>[3,1,3] [[7,4,3],[4,3]]=>[3,1,3] [[4,2,2,1],[1,1]]=>[3,1,2,1] [[5,3,3,1],[2,2,1]]=>[3,1,2,1] [[5,3,2,1],[2,2]]=>[3,1,2,1] [[6,4,3,1],[3,3,1]]=>[3,1,2,1] [[5,2,2,1],[2,1]]=>[3,1,2,1] [[6,3,3,1],[3,2,1]]=>[3,1,2,1] [[6,3,2,1],[3,2]]=>[3,1,2,1] [[7,4,3,1],[4,3,1]]=>[3,1,2,1] [[4,2,2,2],[1,1,1]]=>[3,1,1,2] [[5,3,3,2],[2,2,2]]=>[3,1,1,2] [[5,3,2,2],[2,2,1]]=>[3,1,1,2] [[6,4,3,2],[3,3,2]]=>[3,1,1,2] [[5,2,2,2],[2,1,1]]=>[3,1,1,2] [[6,3,3,2],[3,2,2]]=>[3,1,1,2] [[6,3,2,2],[3,2,1]]=>[3,1,1,2] [[7,4,3,2],[4,3,2]]=>[3,1,1,2] [[3,1,1,1,1],[]]=>[3,1,1,1,1] [[4,2,2,2,1],[1,1,1,1]]=>[3,1,1,1,1] [[4,2,2,1,1],[1,1,1]]=>[3,1,1,1,1] [[5,3,3,2,1],[2,2,2,1]]=>[3,1,1,1,1] [[4,2,1,1,1],[1,1]]=>[3,1,1,1,1] [[5,3,2,2,1],[2,2,1,1]]=>[3,1,1,1,1] [[5,3,2,1,1],[2,2,1]]=>[3,1,1,1,1] [[6,4,3,2,1],[3,3,2,1]]=>[3,1,1,1,1] [[4,1,1,1,1],[1]]=>[3,1,1,1,1] [[5,2,2,2,1],[2,1,1,1]]=>[3,1,1,1,1] [[5,2,2,1,1],[2,1,1]]=>[3,1,1,1,1] [[6,3,3,2,1],[3,2,2,1]]=>[3,1,1,1,1] [[5,2,1,1,1],[2,1]]=>[3,1,1,1,1] [[6,3,2,2,1],[3,2,1,1]]=>[3,1,1,1,1] [[6,3,2,1,1],[3,2,1]]=>[3,1,1,1,1] [[7,4,3,2,1],[4,3,2,1]]=>[3,1,1,1,1] [[5,5],[3]]=>[2,5] [[6,5],[4]]=>[2,5] [[7,5],[5]]=>[2,5] [[4,4,1],[2]]=>[2,4,1] [[5,5,1],[3,1]]=>[2,4,1] [[5,4,1],[3]]=>[2,4,1] [[6,5,1],[4,1]]=>[2,4,1] [[6,4,1],[4]]=>[2,4,1] [[7,5,1],[5,1]]=>[2,4,1] [[3,3,2],[1]]=>[2,3,2] [[4,4,2],[2,1]]=>[2,3,2] [[5,5,2],[3,2]]=>[2,3,2] [[4,3,2],[2]]=>[2,3,2] [[5,4,2],[3,1]]=>[2,3,2] [[6,5,2],[4,2]]=>[2,3,2] [[5,3,2],[3]]=>[2,3,2] [[6,4,2],[4,1]]=>[2,3,2] [[7,5,2],[5,2]]=>[2,3,2] [[3,3,1,1],[1]]=>[2,3,1,1] [[4,4,2,1],[2,1,1]]=>[2,3,1,1] [[4,4,1,1],[2,1]]=>[2,3,1,1] [[5,5,2,1],[3,2,1]]=>[2,3,1,1] [[4,3,1,1],[2]]=>[2,3,1,1] [[5,4,2,1],[3,1,1]]=>[2,3,1,1] [[5,4,1,1],[3,1]]=>[2,3,1,1] [[6,5,2,1],[4,2,1]]=>[2,3,1,1] [[5,3,1,1],[3]]=>[2,3,1,1] [[6,4,2,1],[4,1,1]]=>[2,3,1,1] [[6,4,1,1],[4,1]]=>[2,3,1,1] [[7,5,2,1],[5,2,1]]=>[2,3,1,1] [[3,3,3],[1,1]]=>[2,2,3] [[4,4,3],[2,2]]=>[2,2,3] [[5,5,3],[3,3]]=>[2,2,3] [[4,3,3],[2,1]]=>[2,2,3] [[5,4,3],[3,2]]=>[2,2,3] [[6,5,3],[4,3]]=>[2,2,3] [[5,3,3],[3,1]]=>[2,2,3] [[6,4,3],[4,2]]=>[2,2,3] [[7,5,3],[5,3]]=>[2,2,3] [[2,2,2,1],[]]=>[2,2,2,1] [[3,3,3,1],[1,1,1]]=>[2,2,2,1] [[3,3,2,1],[1,1]]=>[2,2,2,1] [[4,4,3,1],[2,2,1]]=>[2,2,2,1] [[4,4,2,1],[2,2]]=>[2,2,2,1] [[5,5,3,1],[3,3,1]]=>[2,2,2,1] [[3,2,2,1],[1]]=>[2,2,2,1] [[4,3,3,1],[2,1,1]]=>[2,2,2,1] [[4,3,2,1],[2,1]]=>[2,2,2,1] [[5,4,3,1],[3,2,1]]=>[2,2,2,1] [[5,4,2,1],[3,2]]=>[2,2,2,1] [[6,5,3,1],[4,3,1]]=>[2,2,2,1] [[4,2,2,1],[2]]=>[2,2,2,1] [[5,3,3,1],[3,1,1]]=>[2,2,2,1] [[5,3,2,1],[3,1]]=>[2,2,2,1] [[6,4,3,1],[4,2,1]]=>[2,2,2,1] [[6,4,2,1],[4,2]]=>[2,2,2,1] [[7,5,3,1],[5,3,1]]=>[2,2,2,1] [[3,3,2,2],[1,1,1]]=>[2,2,1,2] [[4,4,3,2],[2,2,2]]=>[2,2,1,2] [[4,4,2,2],[2,2,1]]=>[2,2,1,2] [[5,5,3,2],[3,3,2]]=>[2,2,1,2] [[4,3,2,2],[2,1,1]]=>[2,2,1,2] [[5,4,3,2],[3,2,2]]=>[2,2,1,2] [[5,4,2,2],[3,2,1]]=>[2,2,1,2] [[6,5,3,2],[4,3,2]]=>[2,2,1,2] [[5,3,2,2],[3,1,1]]=>[2,2,1,2] [[6,4,3,2],[4,2,2]]=>[2,2,1,2] [[6,4,2,2],[4,2,1]]=>[2,2,1,2] [[7,5,3,2],[5,3,2]]=>[2,2,1,2] [[2,2,1,1,1],[]]=>[2,2,1,1,1] [[3,3,2,2,1],[1,1,1,1]]=>[2,2,1,1,1] [[3,3,2,1,1],[1,1,1]]=>[2,2,1,1,1] [[4,4,3,2,1],[2,2,2,1]]=>[2,2,1,1,1] [[3,3,1,1,1],[1,1]]=>[2,2,1,1,1] [[4,4,2,2,1],[2,2,1,1]]=>[2,2,1,1,1] [[4,4,2,1,1],[2,2,1]]=>[2,2,1,1,1] [[5,5,3,2,1],[3,3,2,1]]=>[2,2,1,1,1] [[3,2,1,1,1],[1]]=>[2,2,1,1,1] [[4,3,2,2,1],[2,1,1,1]]=>[2,2,1,1,1] [[4,3,2,1,1],[2,1,1]]=>[2,2,1,1,1] [[5,4,3,2,1],[3,2,2,1]]=>[2,2,1,1,1] [[4,3,1,1,1],[2,1]]=>[2,2,1,1,1] [[5,4,2,2,1],[3,2,1,1]]=>[2,2,1,1,1] [[5,4,2,1,1],[3,2,1]]=>[2,2,1,1,1] [[6,5,3,2,1],[4,3,2,1]]=>[2,2,1,1,1] [[4,2,1,1,1],[2]]=>[2,2,1,1,1] [[5,3,2,2,1],[3,1,1,1]]=>[2,2,1,1,1] [[5,3,2,1,1],[3,1,1]]=>[2,2,1,1,1] [[6,4,3,2,1],[4,2,2,1]]=>[2,2,1,1,1] [[5,3,1,1,1],[3,1]]=>[2,2,1,1,1] [[6,4,2,2,1],[4,2,1,1]]=>[2,2,1,1,1] [[6,4,2,1,1],[4,2,1]]=>[2,2,1,1,1] [[7,5,3,2,1],[5,3,2,1]]=>[2,2,1,1,1] [[5,4,4],[3,3]]=>[2,1,4] [[6,5,4],[4,4]]=>[2,1,4] [[6,4,4],[4,3]]=>[2,1,4] [[7,5,4],[5,4]]=>[2,1,4] [[4,3,3,1],[2,2]]=>[2,1,3,1] [[5,4,4,1],[3,3,1]]=>[2,1,3,1] [[5,4,3,1],[3,3]]=>[2,1,3,1] [[6,5,4,1],[4,4,1]]=>[2,1,3,1] [[5,3,3,1],[3,2]]=>[2,1,3,1] [[6,4,4,1],[4,3,1]]=>[2,1,3,1] [[6,4,3,1],[4,3]]=>[2,1,3,1] [[7,5,4,1],[5,4,1]]=>[2,1,3,1] [[3,2,2,2],[1,1]]=>[2,1,2,2] [[4,3,3,2],[2,2,1]]=>[2,1,2,2] [[5,4,4,2],[3,3,2]]=>[2,1,2,2] [[4,3,2,2],[2,2]]=>[2,1,2,2] [[5,4,3,2],[3,3,1]]=>[2,1,2,2] [[6,5,4,2],[4,4,2]]=>[2,1,2,2] [[4,2,2,2],[2,1]]=>[2,1,2,2] [[5,3,3,2],[3,2,1]]=>[2,1,2,2] [[6,4,4,2],[4,3,2]]=>[2,1,2,2] [[5,3,2,2],[3,2]]=>[2,1,2,2] [[6,4,3,2],[4,3,1]]=>[2,1,2,2] [[7,5,4,2],[5,4,2]]=>[2,1,2,2] [[3,2,2,1,1],[1,1]]=>[2,1,2,1,1] [[4,3,3,2,1],[2,2,1,1]]=>[2,1,2,1,1] [[4,3,3,1,1],[2,2,1]]=>[2,1,2,1,1] [[5,4,4,2,1],[3,3,2,1]]=>[2,1,2,1,1] [[4,3,2,1,1],[2,2]]=>[2,1,2,1,1] [[5,4,3,2,1],[3,3,1,1]]=>[2,1,2,1,1] [[5,4,3,1,1],[3,3,1]]=>[2,1,2,1,1] [[6,5,4,2,1],[4,4,2,1]]=>[2,1,2,1,1] [[4,2,2,1,1],[2,1]]=>[2,1,2,1,1] [[5,3,3,2,1],[3,2,1,1]]=>[2,1,2,1,1] [[5,3,3,1,1],[3,2,1]]=>[2,1,2,1,1] [[6,4,4,2,1],[4,3,2,1]]=>[2,1,2,1,1] [[5,3,2,1,1],[3,2]]=>[2,1,2,1,1] [[6,4,3,2,1],[4,3,1,1]]=>[2,1,2,1,1] [[6,4,3,1,1],[4,3,1]]=>[2,1,2,1,1] [[7,5,4,2,1],[5,4,2,1]]=>[2,1,2,1,1] [[4,3,3,3],[2,2,2]]=>[2,1,1,3] [[5,4,4,3],[3,3,3]]=>[2,1,1,3] [[5,4,3,3],[3,3,2]]=>[2,1,1,3] [[6,5,4,3],[4,4,3]]=>[2,1,1,3] [[5,3,3,3],[3,2,2]]=>[2,1,1,3] [[6,4,4,3],[4,3,3]]=>[2,1,1,3] [[6,4,3,3],[4,3,2]]=>[2,1,1,3] [[7,5,4,3],[5,4,3]]=>[2,1,1,3] [[3,2,2,2,1],[1,1,1]]=>[2,1,1,2,1] [[4,3,3,3,1],[2,2,2,1]]=>[2,1,1,2,1] [[4,3,3,2,1],[2,2,2]]=>[2,1,1,2,1] [[5,4,4,3,1],[3,3,3,1]]=>[2,1,1,2,1] [[4,3,2,2,1],[2,2,1]]=>[2,1,1,2,1] [[5,4,3,3,1],[3,3,2,1]]=>[2,1,1,2,1] [[5,4,3,2,1],[3,3,2]]=>[2,1,1,2,1] [[6,5,4,3,1],[4,4,3,1]]=>[2,1,1,2,1] [[4,2,2,2,1],[2,1,1]]=>[2,1,1,2,1] [[5,3,3,3,1],[3,2,2,1]]=>[2,1,1,2,1] [[5,3,3,2,1],[3,2,2]]=>[2,1,1,2,1] [[6,4,4,3,1],[4,3,3,1]]=>[2,1,1,2,1] [[5,3,2,2,1],[3,2,1]]=>[2,1,1,2,1] [[6,4,3,3,1],[4,3,2,1]]=>[2,1,1,2,1] [[6,4,3,2,1],[4,3,2]]=>[2,1,1,2,1] [[7,5,4,3,1],[5,4,3,1]]=>[2,1,1,2,1] [[3,2,2,2,2],[1,1,1,1]]=>[2,1,1,1,2] [[4,3,3,3,2],[2,2,2,2]]=>[2,1,1,1,2] [[4,3,3,2,2],[2,2,2,1]]=>[2,1,1,1,2] [[5,4,4,3,2],[3,3,3,2]]=>[2,1,1,1,2] [[4,3,2,2,2],[2,2,1,1]]=>[2,1,1,1,2] [[5,4,3,3,2],[3,3,2,2]]=>[2,1,1,1,2] [[5,4,3,2,2],[3,3,2,1]]=>[2,1,1,1,2] [[6,5,4,3,2],[4,4,3,2]]=>[2,1,1,1,2] [[4,2,2,2,2],[2,1,1,1]]=>[2,1,1,1,2] [[5,3,3,3,2],[3,2,2,2]]=>[2,1,1,1,2] [[5,3,3,2,2],[3,2,2,1]]=>[2,1,1,1,2] [[6,4,4,3,2],[4,3,3,2]]=>[2,1,1,1,2] [[5,3,2,2,2],[3,2,1,1]]=>[2,1,1,1,2] [[6,4,3,3,2],[4,3,2,2]]=>[2,1,1,1,2] [[6,4,3,2,2],[4,3,2,1]]=>[2,1,1,1,2] [[7,5,4,3,2],[5,4,3,2]]=>[2,1,1,1,2] [[2,1,1,1,1,1],[]]=>[2,1,1,1,1,1] [[3,2,2,2,2,1],[1,1,1,1,1]]=>[2,1,1,1,1,1] [[3,2,2,2,1,1],[1,1,1,1]]=>[2,1,1,1,1,1] [[4,3,3,3,2,1],[2,2,2,2,1]]=>[2,1,1,1,1,1] [[3,2,2,1,1,1],[1,1,1]]=>[2,1,1,1,1,1] [[4,3,3,2,2,1],[2,2,2,1,1]]=>[2,1,1,1,1,1] [[4,3,3,2,1,1],[2,2,2,1]]=>[2,1,1,1,1,1] [[5,4,4,3,2,1],[3,3,3,2,1]]=>[2,1,1,1,1,1] [[3,2,1,1,1,1],[1,1]]=>[2,1,1,1,1,1] [[4,3,2,2,2,1],[2,2,1,1,1]]=>[2,1,1,1,1,1] [[4,3,2,2,1,1],[2,2,1,1]]=>[2,1,1,1,1,1] [[5,4,3,3,2,1],[3,3,2,2,1]]=>[2,1,1,1,1,1] [[4,3,2,1,1,1],[2,2,1]]=>[2,1,1,1,1,1] [[5,4,3,2,2,1],[3,3,2,1,1]]=>[2,1,1,1,1,1] [[5,4,3,2,1,1],[3,3,2,1]]=>[2,1,1,1,1,1] [[6,5,4,3,2,1],[4,4,3,2,1]]=>[2,1,1,1,1,1] [[3,1,1,1,1,1],[1]]=>[2,1,1,1,1,1] [[4,2,2,2,2,1],[2,1,1,1,1]]=>[2,1,1,1,1,1] [[4,2,2,2,1,1],[2,1,1,1]]=>[2,1,1,1,1,1] [[5,3,3,3,2,1],[3,2,2,2,1]]=>[2,1,1,1,1,1] [[4,2,2,1,1,1],[2,1,1]]=>[2,1,1,1,1,1] [[5,3,3,2,2,1],[3,2,2,1,1]]=>[2,1,1,1,1,1] [[5,3,3,2,1,1],[3,2,2,1]]=>[2,1,1,1,1,1] [[6,4,4,3,2,1],[4,3,3,2,1]]=>[2,1,1,1,1,1] [[4,2,1,1,1,1],[2,1]]=>[2,1,1,1,1,1] [[5,3,2,2,2,1],[3,2,1,1,1]]=>[2,1,1,1,1,1] [[5,3,2,2,1,1],[3,2,1,1]]=>[2,1,1,1,1,1] [[6,4,3,3,2,1],[4,3,2,2,1]]=>[2,1,1,1,1,1] [[5,3,2,1,1,1],[3,2,1]]=>[2,1,1,1,1,1] [[6,4,3,2,2,1],[4,3,2,1,1]]=>[2,1,1,1,1,1] [[6,4,3,2,1,1],[4,3,2,1]]=>[2,1,1,1,1,1] [[7,5,4,3,2,1],[5,4,3,2,1]]=>[2,1,1,1,1,1] [[6,6],[5]]=>[1,6] [[7,6],[6]]=>[1,6] [[5,5,1],[4]]=>[1,5,1] [[6,6,1],[5,1]]=>[1,5,1] [[6,5,1],[5]]=>[1,5,1] [[7,6,1],[6,1]]=>[1,5,1] [[4,4,2],[3]]=>[1,4,2] [[5,5,2],[4,1]]=>[1,4,2] [[6,6,2],[5,2]]=>[1,4,2] [[5,4,2],[4]]=>[1,4,2] [[6,5,2],[5,1]]=>[1,4,2] [[7,6,2],[6,2]]=>[1,4,2] [[4,4,1,1],[3]]=>[1,4,1,1] [[5,5,2,1],[4,1,1]]=>[1,4,1,1] [[5,5,1,1],[4,1]]=>[1,4,1,1] [[6,6,2,1],[5,2,1]]=>[1,4,1,1] [[5,4,1,1],[4]]=>[1,4,1,1] [[6,5,2,1],[5,1,1]]=>[1,4,1,1] [[6,5,1,1],[5,1]]=>[1,4,1,1] [[7,6,2,1],[6,2,1]]=>[1,4,1,1] [[3,3,3],[2]]=>[1,3,3] [[4,4,3],[3,1]]=>[1,3,3] [[5,5,3],[4,2]]=>[1,3,3] [[6,6,3],[5,3]]=>[1,3,3] [[4,3,3],[3]]=>[1,3,3] [[5,4,3],[4,1]]=>[1,3,3] [[6,5,3],[5,2]]=>[1,3,3] [[7,6,3],[6,3]]=>[1,3,3] [[3,3,2,1],[2]]=>[1,3,2,1] [[4,4,3,1],[3,1,1]]=>[1,3,2,1] [[4,4,2,1],[3,1]]=>[1,3,2,1] [[5,5,3,1],[4,2,1]]=>[1,3,2,1] [[5,5,2,1],[4,2]]=>[1,3,2,1] [[6,6,3,1],[5,3,1]]=>[1,3,2,1] [[4,3,2,1],[3]]=>[1,3,2,1] [[5,4,3,1],[4,1,1]]=>[1,3,2,1] [[5,4,2,1],[4,1]]=>[1,3,2,1] [[6,5,3,1],[5,2,1]]=>[1,3,2,1] [[6,5,2,1],[5,2]]=>[1,3,2,1] [[7,6,3,1],[6,3,1]]=>[1,3,2,1] [[4,4,2,2],[3,1,1]]=>[1,3,1,2] [[5,5,3,2],[4,2,2]]=>[1,3,1,2] [[5,5,2,2],[4,2,1]]=>[1,3,1,2] [[6,6,3,2],[5,3,2]]=>[1,3,1,2] [[5,4,2,2],[4,1,1]]=>[1,3,1,2] [[6,5,3,2],[5,2,2]]=>[1,3,1,2] [[6,5,2,2],[5,2,1]]=>[1,3,1,2] [[7,6,3,2],[6,3,2]]=>[1,3,1,2] [[3,3,1,1,1],[2]]=>[1,3,1,1,1] [[4,4,2,2,1],[3,1,1,1]]=>[1,3,1,1,1] [[4,4,2,1,1],[3,1,1]]=>[1,3,1,1,1] [[5,5,3,2,1],[4,2,2,1]]=>[1,3,1,1,1] [[4,4,1,1,1],[3,1]]=>[1,3,1,1,1] [[5,5,2,2,1],[4,2,1,1]]=>[1,3,1,1,1] [[5,5,2,1,1],[4,2,1]]=>[1,3,1,1,1] [[6,6,3,2,1],[5,3,2,1]]=>[1,3,1,1,1] [[4,3,1,1,1],[3]]=>[1,3,1,1,1] [[5,4,2,2,1],[4,1,1,1]]=>[1,3,1,1,1] [[5,4,2,1,1],[4,1,1]]=>[1,3,1,1,1] [[6,5,3,2,1],[5,2,2,1]]=>[1,3,1,1,1] [[5,4,1,1,1],[4,1]]=>[1,3,1,1,1] [[6,5,2,2,1],[5,2,1,1]]=>[1,3,1,1,1] [[6,5,2,1,1],[5,2,1]]=>[1,3,1,1,1] [[7,6,3,2,1],[6,3,2,1]]=>[1,3,1,1,1] [[4,4,4],[3,2]]=>[1,2,4] [[5,5,4],[4,3]]=>[1,2,4] [[6,6,4],[5,4]]=>[1,2,4] [[5,4,4],[4,2]]=>[1,2,4] [[6,5,4],[5,3]]=>[1,2,4] [[7,6,4],[6,4]]=>[1,2,4] [[3,3,3,1],[2,1]]=>[1,2,3,1] [[4,4,4,1],[3,2,1]]=>[1,2,3,1] [[4,4,3,1],[3,2]]=>[1,2,3,1] [[5,5,4,1],[4,3,1]]=>[1,2,3,1] [[5,5,3,1],[4,3]]=>[1,2,3,1] [[6,6,4,1],[5,4,1]]=>[1,2,3,1] [[4,3,3,1],[3,1]]=>[1,2,3,1] [[5,4,4,1],[4,2,1]]=>[1,2,3,1] [[5,4,3,1],[4,2]]=>[1,2,3,1] [[6,5,4,1],[5,3,1]]=>[1,2,3,1] [[6,5,3,1],[5,3]]=>[1,2,3,1] [[7,6,4,1],[6,4,1]]=>[1,2,3,1] [[2,2,2,2],[1]]=>[1,2,2,2] [[3,3,3,2],[2,1,1]]=>[1,2,2,2] [[4,4,4,2],[3,2,2]]=>[1,2,2,2] [[3,3,2,2],[2,1]]=>[1,2,2,2] [[4,4,3,2],[3,2,1]]=>[1,2,2,2] [[5,5,4,2],[4,3,2]]=>[1,2,2,2] [[4,4,2,2],[3,2]]=>[1,2,2,2] [[5,5,3,2],[4,3,1]]=>[1,2,2,2] [[6,6,4,2],[5,4,2]]=>[1,2,2,2] [[3,2,2,2],[2]]=>[1,2,2,2] [[4,3,3,2],[3,1,1]]=>[1,2,2,2] [[5,4,4,2],[4,2,2]]=>[1,2,2,2] [[4,3,2,2],[3,1]]=>[1,2,2,2] [[5,4,3,2],[4,2,1]]=>[1,2,2,2] [[6,5,4,2],[5,3,2]]=>[1,2,2,2] [[5,4,2,2],[4,2]]=>[1,2,2,2] [[6,5,3,2],[5,3,1]]=>[1,2,2,2] [[7,6,4,2],[6,4,2]]=>[1,2,2,2] [[2,2,2,1,1],[1]]=>[1,2,2,1,1] [[3,3,3,2,1],[2,1,1,1]]=>[1,2,2,1,1] [[3,3,3,1,1],[2,1,1]]=>[1,2,2,1,1] [[4,4,4,2,1],[3,2,2,1]]=>[1,2,2,1,1] [[3,3,2,1,1],[2,1]]=>[1,2,2,1,1] [[4,4,3,2,1],[3,2,1,1]]=>[1,2,2,1,1] [[4,4,3,1,1],[3,2,1]]=>[1,2,2,1,1] [[5,5,4,2,1],[4,3,2,1]]=>[1,2,2,1,1] [[4,4,2,1,1],[3,2]]=>[1,2,2,1,1] [[5,5,3,2,1],[4,3,1,1]]=>[1,2,2,1,1] [[5,5,3,1,1],[4,3,1]]=>[1,2,2,1,1] [[6,6,4,2,1],[5,4,2,1]]=>[1,2,2,1,1] [[3,2,2,1,1],[2]]=>[1,2,2,1,1] [[4,3,3,2,1],[3,1,1,1]]=>[1,2,2,1,1] [[4,3,3,1,1],[3,1,1]]=>[1,2,2,1,1] [[5,4,4,2,1],[4,2,2,1]]=>[1,2,2,1,1] [[4,3,2,1,1],[3,1]]=>[1,2,2,1,1] [[5,4,3,2,1],[4,2,1,1]]=>[1,2,2,1,1] [[5,4,3,1,1],[4,2,1]]=>[1,2,2,1,1] [[6,5,4,2,1],[5,3,2,1]]=>[1,2,2,1,1] [[5,4,2,1,1],[4,2]]=>[1,2,2,1,1] [[6,5,3,2,1],[5,3,1,1]]=>[1,2,2,1,1] [[6,5,3,1,1],[5,3,1]]=>[1,2,2,1,1] [[7,6,4,2,1],[6,4,2,1]]=>[1,2,2,1,1] [[4,4,3,3],[3,2,2]]=>[1,2,1,3] [[5,5,4,3],[4,3,3]]=>[1,2,1,3] [[5,5,3,3],[4,3,2]]=>[1,2,1,3] [[6,6,4,3],[5,4,3]]=>[1,2,1,3] [[5,4,3,3],[4,2,2]]=>[1,2,1,3] [[6,5,4,3],[5,3,3]]=>[1,2,1,3] [[6,5,3,3],[5,3,2]]=>[1,2,1,3] [[7,6,4,3],[6,4,3]]=>[1,2,1,3] [[3,3,2,2,1],[2,1,1]]=>[1,2,1,2,1] [[4,4,3,3,1],[3,2,2,1]]=>[1,2,1,2,1] [[4,4,3,2,1],[3,2,2]]=>[1,2,1,2,1] [[5,5,4,3,1],[4,3,3,1]]=>[1,2,1,2,1] [[4,4,2,2,1],[3,2,1]]=>[1,2,1,2,1] [[5,5,3,3,1],[4,3,2,1]]=>[1,2,1,2,1] [[5,5,3,2,1],[4,3,2]]=>[1,2,1,2,1] [[6,6,4,3,1],[5,4,3,1]]=>[1,2,1,2,1] [[4,3,2,2,1],[3,1,1]]=>[1,2,1,2,1] [[5,4,3,3,1],[4,2,2,1]]=>[1,2,1,2,1] [[5,4,3,2,1],[4,2,2]]=>[1,2,1,2,1] [[6,5,4,3,1],[5,3,3,1]]=>[1,2,1,2,1] [[5,4,2,2,1],[4,2,1]]=>[1,2,1,2,1] [[6,5,3,3,1],[5,3,2,1]]=>[1,2,1,2,1] [[6,5,3,2,1],[5,3,2]]=>[1,2,1,2,1] [[7,6,4,3,1],[6,4,3,1]]=>[1,2,1,2,1] [[3,3,2,2,2],[2,1,1,1]]=>[1,2,1,1,2] [[4,4,3,3,2],[3,2,2,2]]=>[1,2,1,1,2] [[4,4,3,2,2],[3,2,2,1]]=>[1,2,1,1,2] [[5,5,4,3,2],[4,3,3,2]]=>[1,2,1,1,2] [[4,4,2,2,2],[3,2,1,1]]=>[1,2,1,1,2] [[5,5,3,3,2],[4,3,2,2]]=>[1,2,1,1,2] [[5,5,3,2,2],[4,3,2,1]]=>[1,2,1,1,2] [[6,6,4,3,2],[5,4,3,2]]=>[1,2,1,1,2] [[4,3,2,2,2],[3,1,1,1]]=>[1,2,1,1,2] [[5,4,3,3,2],[4,2,2,2]]=>[1,2,1,1,2] [[5,4,3,2,2],[4,2,2,1]]=>[1,2,1,1,2] [[6,5,4,3,2],[5,3,3,2]]=>[1,2,1,1,2] [[5,4,2,2,2],[4,2,1,1]]=>[1,2,1,1,2] [[6,5,3,3,2],[5,3,2,2]]=>[1,2,1,1,2] [[6,5,3,2,2],[5,3,2,1]]=>[1,2,1,1,2] [[7,6,4,3,2],[6,4,3,2]]=>[1,2,1,1,2] [[2,2,1,1,1,1],[1]]=>[1,2,1,1,1,1] [[3,3,2,2,2,1],[2,1,1,1,1]]=>[1,2,1,1,1,1] [[3,3,2,2,1,1],[2,1,1,1]]=>[1,2,1,1,1,1] [[4,4,3,3,2,1],[3,2,2,2,1]]=>[1,2,1,1,1,1] [[3,3,2,1,1,1],[2,1,1]]=>[1,2,1,1,1,1] [[4,4,3,2,2,1],[3,2,2,1,1]]=>[1,2,1,1,1,1] [[4,4,3,2,1,1],[3,2,2,1]]=>[1,2,1,1,1,1] [[5,5,4,3,2,1],[4,3,3,2,1]]=>[1,2,1,1,1,1] [[3,3,1,1,1,1],[2,1]]=>[1,2,1,1,1,1] [[4,4,2,2,2,1],[3,2,1,1,1]]=>[1,2,1,1,1,1] [[4,4,2,2,1,1],[3,2,1,1]]=>[1,2,1,1,1,1] [[5,5,3,3,2,1],[4,3,2,2,1]]=>[1,2,1,1,1,1] [[4,4,2,1,1,1],[3,2,1]]=>[1,2,1,1,1,1] [[5,5,3,2,2,1],[4,3,2,1,1]]=>[1,2,1,1,1,1] [[5,5,3,2,1,1],[4,3,2,1]]=>[1,2,1,1,1,1] [[6,6,4,3,2,1],[5,4,3,2,1]]=>[1,2,1,1,1,1] [[3,2,1,1,1,1],[2]]=>[1,2,1,1,1,1] [[4,3,2,2,2,1],[3,1,1,1,1]]=>[1,2,1,1,1,1] [[4,3,2,2,1,1],[3,1,1,1]]=>[1,2,1,1,1,1] [[5,4,3,3,2,1],[4,2,2,2,1]]=>[1,2,1,1,1,1] [[4,3,2,1,1,1],[3,1,1]]=>[1,2,1,1,1,1] [[5,4,3,2,2,1],[4,2,2,1,1]]=>[1,2,1,1,1,1] [[5,4,3,2,1,1],[4,2,2,1]]=>[1,2,1,1,1,1] [[6,5,4,3,2,1],[5,3,3,2,1]]=>[1,2,1,1,1,1] [[4,3,1,1,1,1],[3,1]]=>[1,2,1,1,1,1] [[5,4,2,2,2,1],[4,2,1,1,1]]=>[1,2,1,1,1,1] [[5,4,2,2,1,1],[4,2,1,1]]=>[1,2,1,1,1,1] [[6,5,3,3,2,1],[5,3,2,2,1]]=>[1,2,1,1,1,1] [[5,4,2,1,1,1],[4,2,1]]=>[1,2,1,1,1,1] [[6,5,3,2,2,1],[5,3,2,1,1]]=>[1,2,1,1,1,1] [[6,5,3,2,1,1],[5,3,2,1]]=>[1,2,1,1,1,1] [[7,6,4,3,2,1],[6,4,3,2,1]]=>[1,2,1,1,1,1] [[5,5,5],[4,4]]=>[1,1,5] [[6,6,5],[5,5]]=>[1,1,5] [[6,5,5],[5,4]]=>[1,1,5] [[7,6,5],[6,5]]=>[1,1,5] [[4,4,4,1],[3,3]]=>[1,1,4,1] [[5,5,5,1],[4,4,1]]=>[1,1,4,1] [[5,5,4,1],[4,4]]=>[1,1,4,1] [[6,6,5,1],[5,5,1]]=>[1,1,4,1] [[5,4,4,1],[4,3]]=>[1,1,4,1] [[6,5,5,1],[5,4,1]]=>[1,1,4,1] [[6,5,4,1],[5,4]]=>[1,1,4,1] [[7,6,5,1],[6,5,1]]=>[1,1,4,1] [[3,3,3,2],[2,2]]=>[1,1,3,2] [[4,4,4,2],[3,3,1]]=>[1,1,3,2] [[5,5,5,2],[4,4,2]]=>[1,1,3,2] [[4,4,3,2],[3,3]]=>[1,1,3,2] [[5,5,4,2],[4,4,1]]=>[1,1,3,2] [[6,6,5,2],[5,5,2]]=>[1,1,3,2] [[4,3,3,2],[3,2]]=>[1,1,3,2] [[5,4,4,2],[4,3,1]]=>[1,1,3,2] [[6,5,5,2],[5,4,2]]=>[1,1,3,2] [[5,4,3,2],[4,3]]=>[1,1,3,2] [[6,5,4,2],[5,4,1]]=>[1,1,3,2] [[7,6,5,2],[6,5,2]]=>[1,1,3,2] [[3,3,3,1,1],[2,2]]=>[1,1,3,1,1] [[4,4,4,2,1],[3,3,1,1]]=>[1,1,3,1,1] [[4,4,4,1,1],[3,3,1]]=>[1,1,3,1,1] [[5,5,5,2,1],[4,4,2,1]]=>[1,1,3,1,1] [[4,4,3,1,1],[3,3]]=>[1,1,3,1,1] [[5,5,4,2,1],[4,4,1,1]]=>[1,1,3,1,1] [[5,5,4,1,1],[4,4,1]]=>[1,1,3,1,1] [[6,6,5,2,1],[5,5,2,1]]=>[1,1,3,1,1] [[4,3,3,1,1],[3,2]]=>[1,1,3,1,1] [[5,4,4,2,1],[4,3,1,1]]=>[1,1,3,1,1] [[5,4,4,1,1],[4,3,1]]=>[1,1,3,1,1] [[6,5,5,2,1],[5,4,2,1]]=>[1,1,3,1,1] [[5,4,3,1,1],[4,3]]=>[1,1,3,1,1] [[6,5,4,2,1],[5,4,1,1]]=>[1,1,3,1,1] [[6,5,4,1,1],[5,4,1]]=>[1,1,3,1,1] [[7,6,5,2,1],[6,5,2,1]]=>[1,1,3,1,1] [[3,3,3,3],[2,2,1]]=>[1,1,2,3] [[4,4,4,3],[3,3,2]]=>[1,1,2,3] [[5,5,5,3],[4,4,3]]=>[1,1,2,3] [[4,4,3,3],[3,3,1]]=>[1,1,2,3] [[5,5,4,3],[4,4,2]]=>[1,1,2,3] [[6,6,5,3],[5,5,3]]=>[1,1,2,3] [[4,3,3,3],[3,2,1]]=>[1,1,2,3] [[5,4,4,3],[4,3,2]]=>[1,1,2,3] [[6,5,5,3],[5,4,3]]=>[1,1,2,3] [[5,4,3,3],[4,3,1]]=>[1,1,2,3] [[6,5,4,3],[5,4,2]]=>[1,1,2,3] [[7,6,5,3],[6,5,3]]=>[1,1,2,3] [[2,2,2,2,1],[1,1]]=>[1,1,2,2,1] [[3,3,3,3,1],[2,2,1,1]]=>[1,1,2,2,1] [[3,3,3,2,1],[2,2,1]]=>[1,1,2,2,1] [[4,4,4,3,1],[3,3,2,1]]=>[1,1,2,2,1] [[4,4,4,2,1],[3,3,2]]=>[1,1,2,2,1] [[5,5,5,3,1],[4,4,3,1]]=>[1,1,2,2,1] [[3,3,2,2,1],[2,2]]=>[1,1,2,2,1] [[4,4,3,3,1],[3,3,1,1]]=>[1,1,2,2,1] [[4,4,3,2,1],[3,3,1]]=>[1,1,2,2,1] [[5,5,4,3,1],[4,4,2,1]]=>[1,1,2,2,1] [[5,5,4,2,1],[4,4,2]]=>[1,1,2,2,1] [[6,6,5,3,1],[5,5,3,1]]=>[1,1,2,2,1] [[3,2,2,2,1],[2,1]]=>[1,1,2,2,1] [[4,3,3,3,1],[3,2,1,1]]=>[1,1,2,2,1] [[4,3,3,2,1],[3,2,1]]=>[1,1,2,2,1] [[5,4,4,3,1],[4,3,2,1]]=>[1,1,2,2,1] [[5,4,4,2,1],[4,3,2]]=>[1,1,2,2,1] [[6,5,5,3,1],[5,4,3,1]]=>[1,1,2,2,1] [[4,3,2,2,1],[3,2]]=>[1,1,2,2,1] [[5,4,3,3,1],[4,3,1,1]]=>[1,1,2,2,1] [[5,4,3,2,1],[4,3,1]]=>[1,1,2,2,1] [[6,5,4,3,1],[5,4,2,1]]=>[1,1,2,2,1] [[6,5,4,2,1],[5,4,2]]=>[1,1,2,2,1] [[7,6,5,3,1],[6,5,3,1]]=>[1,1,2,2,1] [[3,3,3,2,2],[2,2,1,1]]=>[1,1,2,1,2] [[4,4,4,3,2],[3,3,2,2]]=>[1,1,2,1,2] [[4,4,4,2,2],[3,3,2,1]]=>[1,1,2,1,2] [[5,5,5,3,2],[4,4,3,2]]=>[1,1,2,1,2] [[4,4,3,2,2],[3,3,1,1]]=>[1,1,2,1,2] [[5,5,4,3,2],[4,4,2,2]]=>[1,1,2,1,2] [[5,5,4,2,2],[4,4,2,1]]=>[1,1,2,1,2] [[6,6,5,3,2],[5,5,3,2]]=>[1,1,2,1,2] [[4,3,3,2,2],[3,2,1,1]]=>[1,1,2,1,2] [[5,4,4,3,2],[4,3,2,2]]=>[1,1,2,1,2] [[5,4,4,2,2],[4,3,2,1]]=>[1,1,2,1,2] [[6,5,5,3,2],[5,4,3,2]]=>[1,1,2,1,2] [[5,4,3,2,2],[4,3,1,1]]=>[1,1,2,1,2] [[6,5,4,3,2],[5,4,2,2]]=>[1,1,2,1,2] [[6,5,4,2,2],[5,4,2,1]]=>[1,1,2,1,2] [[7,6,5,3,2],[6,5,3,2]]=>[1,1,2,1,2] [[2,2,2,1,1,1],[1,1]]=>[1,1,2,1,1,1] [[3,3,3,2,2,1],[2,2,1,1,1]]=>[1,1,2,1,1,1] [[3,3,3,2,1,1],[2,2,1,1]]=>[1,1,2,1,1,1] [[4,4,4,3,2,1],[3,3,2,2,1]]=>[1,1,2,1,1,1] [[3,3,3,1,1,1],[2,2,1]]=>[1,1,2,1,1,1] [[4,4,4,2,2,1],[3,3,2,1,1]]=>[1,1,2,1,1,1] [[4,4,4,2,1,1],[3,3,2,1]]=>[1,1,2,1,1,1] [[5,5,5,3,2,1],[4,4,3,2,1]]=>[1,1,2,1,1,1] [[3,3,2,1,1,1],[2,2]]=>[1,1,2,1,1,1] [[4,4,3,2,2,1],[3,3,1,1,1]]=>[1,1,2,1,1,1] [[4,4,3,2,1,1],[3,3,1,1]]=>[1,1,2,1,1,1] [[5,5,4,3,2,1],[4,4,2,2,1]]=>[1,1,2,1,1,1] [[4,4,3,1,1,1],[3,3,1]]=>[1,1,2,1,1,1] [[5,5,4,2,2,1],[4,4,2,1,1]]=>[1,1,2,1,1,1] [[5,5,4,2,1,1],[4,4,2,1]]=>[1,1,2,1,1,1] [[6,6,5,3,2,1],[5,5,3,2,1]]=>[1,1,2,1,1,1] [[3,2,2,1,1,1],[2,1]]=>[1,1,2,1,1,1] [[4,3,3,2,2,1],[3,2,1,1,1]]=>[1,1,2,1,1,1] [[4,3,3,2,1,1],[3,2,1,1]]=>[1,1,2,1,1,1] [[5,4,4,3,2,1],[4,3,2,2,1]]=>[1,1,2,1,1,1] [[4,3,3,1,1,1],[3,2,1]]=>[1,1,2,1,1,1] [[5,4,4,2,2,1],[4,3,2,1,1]]=>[1,1,2,1,1,1] [[5,4,4,2,1,1],[4,3,2,1]]=>[1,1,2,1,1,1] [[6,5,5,3,2,1],[5,4,3,2,1]]=>[1,1,2,1,1,1] [[4,3,2,1,1,1],[3,2]]=>[1,1,2,1,1,1] [[5,4,3,2,2,1],[4,3,1,1,1]]=>[1,1,2,1,1,1] [[5,4,3,2,1,1],[4,3,1,1]]=>[1,1,2,1,1,1] [[6,5,4,3,2,1],[5,4,2,2,1]]=>[1,1,2,1,1,1] [[5,4,3,1,1,1],[4,3,1]]=>[1,1,2,1,1,1] [[6,5,4,2,2,1],[5,4,2,1,1]]=>[1,1,2,1,1,1] [[6,5,4,2,1,1],[5,4,2,1]]=>[1,1,2,1,1,1] [[7,6,5,3,2,1],[6,5,3,2,1]]=>[1,1,2,1,1,1] [[4,4,4,4],[3,3,3]]=>[1,1,1,4] [[5,5,5,4],[4,4,4]]=>[1,1,1,4] [[5,5,4,4],[4,4,3]]=>[1,1,1,4] [[6,6,5,4],[5,5,4]]=>[1,1,1,4] [[5,4,4,4],[4,3,3]]=>[1,1,1,4] [[6,5,5,4],[5,4,4]]=>[1,1,1,4] [[6,5,4,4],[5,4,3]]=>[1,1,1,4] [[7,6,5,4],[6,5,4]]=>[1,1,1,4] [[3,3,3,3,1],[2,2,2]]=>[1,1,1,3,1] [[4,4,4,4,1],[3,3,3,1]]=>[1,1,1,3,1] [[4,4,4,3,1],[3,3,3]]=>[1,1,1,3,1] [[5,5,5,4,1],[4,4,4,1]]=>[1,1,1,3,1] [[4,4,3,3,1],[3,3,2]]=>[1,1,1,3,1] [[5,5,4,4,1],[4,4,3,1]]=>[1,1,1,3,1] [[5,5,4,3,1],[4,4,3]]=>[1,1,1,3,1] [[6,6,5,4,1],[5,5,4,1]]=>[1,1,1,3,1] [[4,3,3,3,1],[3,2,2]]=>[1,1,1,3,1] [[5,4,4,4,1],[4,3,3,1]]=>[1,1,1,3,1] [[5,4,4,3,1],[4,3,3]]=>[1,1,1,3,1] [[6,5,5,4,1],[5,4,4,1]]=>[1,1,1,3,1] [[5,4,3,3,1],[4,3,2]]=>[1,1,1,3,1] [[6,5,4,4,1],[5,4,3,1]]=>[1,1,1,3,1] [[6,5,4,3,1],[5,4,3]]=>[1,1,1,3,1] [[7,6,5,4,1],[6,5,4,1]]=>[1,1,1,3,1] [[2,2,2,2,2],[1,1,1]]=>[1,1,1,2,2] [[3,3,3,3,2],[2,2,2,1]]=>[1,1,1,2,2] [[4,4,4,4,2],[3,3,3,2]]=>[1,1,1,2,2] [[3,3,3,2,2],[2,2,2]]=>[1,1,1,2,2] [[4,4,4,3,2],[3,3,3,1]]=>[1,1,1,2,2] [[5,5,5,4,2],[4,4,4,2]]=>[1,1,1,2,2] [[3,3,2,2,2],[2,2,1]]=>[1,1,1,2,2] [[4,4,3,3,2],[3,3,2,1]]=>[1,1,1,2,2] [[5,5,4,4,2],[4,4,3,2]]=>[1,1,1,2,2] [[4,4,3,2,2],[3,3,2]]=>[1,1,1,2,2] [[5,5,4,3,2],[4,4,3,1]]=>[1,1,1,2,2] [[6,6,5,4,2],[5,5,4,2]]=>[1,1,1,2,2] [[3,2,2,2,2],[2,1,1]]=>[1,1,1,2,2] [[4,3,3,3,2],[3,2,2,1]]=>[1,1,1,2,2] [[5,4,4,4,2],[4,3,3,2]]=>[1,1,1,2,2] [[4,3,3,2,2],[3,2,2]]=>[1,1,1,2,2] [[5,4,4,3,2],[4,3,3,1]]=>[1,1,1,2,2] [[6,5,5,4,2],[5,4,4,2]]=>[1,1,1,2,2] [[4,3,2,2,2],[3,2,1]]=>[1,1,1,2,2] [[5,4,3,3,2],[4,3,2,1]]=>[1,1,1,2,2] [[6,5,4,4,2],[5,4,3,2]]=>[1,1,1,2,2] [[5,4,3,2,2],[4,3,2]]=>[1,1,1,2,2] [[6,5,4,3,2],[5,4,3,1]]=>[1,1,1,2,2] [[7,6,5,4,2],[6,5,4,2]]=>[1,1,1,2,2] [[2,2,2,2,1,1],[1,1,1]]=>[1,1,1,2,1,1] [[3,3,3,3,2,1],[2,2,2,1,1]]=>[1,1,1,2,1,1] [[3,3,3,3,1,1],[2,2,2,1]]=>[1,1,1,2,1,1] [[4,4,4,4,2,1],[3,3,3,2,1]]=>[1,1,1,2,1,1] [[3,3,3,2,1,1],[2,2,2]]=>[1,1,1,2,1,1] [[4,4,4,3,2,1],[3,3,3,1,1]]=>[1,1,1,2,1,1] [[4,4,4,3,1,1],[3,3,3,1]]=>[1,1,1,2,1,1] [[5,5,5,4,2,1],[4,4,4,2,1]]=>[1,1,1,2,1,1] [[3,3,2,2,1,1],[2,2,1]]=>[1,1,1,2,1,1] [[4,4,3,3,2,1],[3,3,2,1,1]]=>[1,1,1,2,1,1] [[4,4,3,3,1,1],[3,3,2,1]]=>[1,1,1,2,1,1] [[5,5,4,4,2,1],[4,4,3,2,1]]=>[1,1,1,2,1,1] [[4,4,3,2,1,1],[3,3,2]]=>[1,1,1,2,1,1] [[5,5,4,3,2,1],[4,4,3,1,1]]=>[1,1,1,2,1,1] [[5,5,4,3,1,1],[4,4,3,1]]=>[1,1,1,2,1,1] [[6,6,5,4,2,1],[5,5,4,2,1]]=>[1,1,1,2,1,1] [[3,2,2,2,1,1],[2,1,1]]=>[1,1,1,2,1,1] [[4,3,3,3,2,1],[3,2,2,1,1]]=>[1,1,1,2,1,1] [[4,3,3,3,1,1],[3,2,2,1]]=>[1,1,1,2,1,1] [[5,4,4,4,2,1],[4,3,3,2,1]]=>[1,1,1,2,1,1] [[4,3,3,2,1,1],[3,2,2]]=>[1,1,1,2,1,1] [[5,4,4,3,2,1],[4,3,3,1,1]]=>[1,1,1,2,1,1] [[5,4,4,3,1,1],[4,3,3,1]]=>[1,1,1,2,1,1] [[6,5,5,4,2,1],[5,4,4,2,1]]=>[1,1,1,2,1,1] [[4,3,2,2,1,1],[3,2,1]]=>[1,1,1,2,1,1] [[5,4,3,3,2,1],[4,3,2,1,1]]=>[1,1,1,2,1,1] [[5,4,3,3,1,1],[4,3,2,1]]=>[1,1,1,2,1,1] [[6,5,4,4,2,1],[5,4,3,2,1]]=>[1,1,1,2,1,1] [[5,4,3,2,1,1],[4,3,2]]=>[1,1,1,2,1,1] [[6,5,4,3,2,1],[5,4,3,1,1]]=>[1,1,1,2,1,1] [[6,5,4,3,1,1],[5,4,3,1]]=>[1,1,1,2,1,1] [[7,6,5,4,2,1],[6,5,4,2,1]]=>[1,1,1,2,1,1] [[3,3,3,3,3],[2,2,2,2]]=>[1,1,1,1,3] [[4,4,4,4,3],[3,3,3,3]]=>[1,1,1,1,3] [[4,4,4,3,3],[3,3,3,2]]=>[1,1,1,1,3] [[5,5,5,4,3],[4,4,4,3]]=>[1,1,1,1,3] [[4,4,3,3,3],[3,3,2,2]]=>[1,1,1,1,3] [[5,5,4,4,3],[4,4,3,3]]=>[1,1,1,1,3] [[5,5,4,3,3],[4,4,3,2]]=>[1,1,1,1,3] [[6,6,5,4,3],[5,5,4,3]]=>[1,1,1,1,3] [[4,3,3,3,3],[3,2,2,2]]=>[1,1,1,1,3] [[5,4,4,4,3],[4,3,3,3]]=>[1,1,1,1,3] [[5,4,4,3,3],[4,3,3,2]]=>[1,1,1,1,3] [[6,5,5,4,3],[5,4,4,3]]=>[1,1,1,1,3] [[5,4,3,3,3],[4,3,2,2]]=>[1,1,1,1,3] [[6,5,4,4,3],[5,4,3,3]]=>[1,1,1,1,3] [[6,5,4,3,3],[5,4,3,2]]=>[1,1,1,1,3] [[7,6,5,4,3],[6,5,4,3]]=>[1,1,1,1,3] [[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1,2,1] [[3,3,3,3,3,1],[2,2,2,2,1]]=>[1,1,1,1,2,1] [[3,3,3,3,2,1],[2,2,2,2]]=>[1,1,1,1,2,1] [[4,4,4,4,3,1],[3,3,3,3,1]]=>[1,1,1,1,2,1] [[3,3,3,2,2,1],[2,2,2,1]]=>[1,1,1,1,2,1] [[4,4,4,3,3,1],[3,3,3,2,1]]=>[1,1,1,1,2,1] [[4,4,4,3,2,1],[3,3,3,2]]=>[1,1,1,1,2,1] [[5,5,5,4,3,1],[4,4,4,3,1]]=>[1,1,1,1,2,1] [[3,3,2,2,2,1],[2,2,1,1]]=>[1,1,1,1,2,1] [[4,4,3,3,3,1],[3,3,2,2,1]]=>[1,1,1,1,2,1] [[4,4,3,3,2,1],[3,3,2,2]]=>[1,1,1,1,2,1] [[5,5,4,4,3,1],[4,4,3,3,1]]=>[1,1,1,1,2,1] [[4,4,3,2,2,1],[3,3,2,1]]=>[1,1,1,1,2,1] [[5,5,4,3,3,1],[4,4,3,2,1]]=>[1,1,1,1,2,1] [[5,5,4,3,2,1],[4,4,3,2]]=>[1,1,1,1,2,1] [[6,6,5,4,3,1],[5,5,4,3,1]]=>[1,1,1,1,2,1] [[3,2,2,2,2,1],[2,1,1,1]]=>[1,1,1,1,2,1] [[4,3,3,3,3,1],[3,2,2,2,1]]=>[1,1,1,1,2,1] [[4,3,3,3,2,1],[3,2,2,2]]=>[1,1,1,1,2,1] [[5,4,4,4,3,1],[4,3,3,3,1]]=>[1,1,1,1,2,1] [[4,3,3,2,2,1],[3,2,2,1]]=>[1,1,1,1,2,1] [[5,4,4,3,3,1],[4,3,3,2,1]]=>[1,1,1,1,2,1] [[5,4,4,3,2,1],[4,3,3,2]]=>[1,1,1,1,2,1] [[6,5,5,4,3,1],[5,4,4,3,1]]=>[1,1,1,1,2,1] [[4,3,2,2,2,1],[3,2,1,1]]=>[1,1,1,1,2,1] [[5,4,3,3,3,1],[4,3,2,2,1]]=>[1,1,1,1,2,1] [[5,4,3,3,2,1],[4,3,2,2]]=>[1,1,1,1,2,1] [[6,5,4,4,3,1],[5,4,3,3,1]]=>[1,1,1,1,2,1] [[5,4,3,2,2,1],[4,3,2,1]]=>[1,1,1,1,2,1] [[6,5,4,3,3,1],[5,4,3,2,1]]=>[1,1,1,1,2,1] [[6,5,4,3,2,1],[5,4,3,2]]=>[1,1,1,1,2,1] [[7,6,5,4,3,1],[6,5,4,3,1]]=>[1,1,1,1,2,1] [[2,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1,2] [[3,3,3,3,3,2],[2,2,2,2,2]]=>[1,1,1,1,1,2] [[3,3,3,3,2,2],[2,2,2,2,1]]=>[1,1,1,1,1,2] [[4,4,4,4,3,2],[3,3,3,3,2]]=>[1,1,1,1,1,2] [[3,3,3,2,2,2],[2,2,2,1,1]]=>[1,1,1,1,1,2] [[4,4,4,3,3,2],[3,3,3,2,2]]=>[1,1,1,1,1,2] [[4,4,4,3,2,2],[3,3,3,2,1]]=>[1,1,1,1,1,2] [[5,5,5,4,3,2],[4,4,4,3,2]]=>[1,1,1,1,1,2] [[3,3,2,2,2,2],[2,2,1,1,1]]=>[1,1,1,1,1,2] [[4,4,3,3,3,2],[3,3,2,2,2]]=>[1,1,1,1,1,2] [[4,4,3,3,2,2],[3,3,2,2,1]]=>[1,1,1,1,1,2] [[5,5,4,4,3,2],[4,4,3,3,2]]=>[1,1,1,1,1,2] [[4,4,3,2,2,2],[3,3,2,1,1]]=>[1,1,1,1,1,2] [[5,5,4,3,3,2],[4,4,3,2,2]]=>[1,1,1,1,1,2] [[5,5,4,3,2,2],[4,4,3,2,1]]=>[1,1,1,1,1,2] [[6,6,5,4,3,2],[5,5,4,3,2]]=>[1,1,1,1,1,2] [[3,2,2,2,2,2],[2,1,1,1,1]]=>[1,1,1,1,1,2] [[4,3,3,3,3,2],[3,2,2,2,2]]=>[1,1,1,1,1,2] [[4,3,3,3,2,2],[3,2,2,2,1]]=>[1,1,1,1,1,2] [[5,4,4,4,3,2],[4,3,3,3,2]]=>[1,1,1,1,1,2] [[4,3,3,2,2,2],[3,2,2,1,1]]=>[1,1,1,1,1,2] [[5,4,4,3,3,2],[4,3,3,2,2]]=>[1,1,1,1,1,2] [[5,4,4,3,2,2],[4,3,3,2,1]]=>[1,1,1,1,1,2] [[6,5,5,4,3,2],[5,4,4,3,2]]=>[1,1,1,1,1,2] [[4,3,2,2,2,2],[3,2,1,1,1]]=>[1,1,1,1,1,2] [[5,4,3,3,3,2],[4,3,2,2,2]]=>[1,1,1,1,1,2] [[5,4,3,3,2,2],[4,3,2,2,1]]=>[1,1,1,1,1,2] [[6,5,4,4,3,2],[5,4,3,3,2]]=>[1,1,1,1,1,2] [[5,4,3,2,2,2],[4,3,2,1,1]]=>[1,1,1,1,1,2] [[6,5,4,3,3,2],[5,4,3,2,2]]=>[1,1,1,1,1,2] [[6,5,4,3,2,2],[5,4,3,2,1]]=>[1,1,1,1,1,2] [[7,6,5,4,3,2],[6,5,4,3,2]]=>[1,1,1,1,1,2] [[1,1,1,1,1,1,1],[]]=>[1,1,1,1,1,1,1] [[2,2,2,2,2,2,1],[1,1,1,1,1,1]]=>[1,1,1,1,1,1,1] [[2,2,2,2,2,1,1],[1,1,1,1,1]]=>[1,1,1,1,1,1,1] [[3,3,3,3,3,2,1],[2,2,2,2,2,1]]=>[1,1,1,1,1,1,1] [[2,2,2,2,1,1,1],[1,1,1,1]]=>[1,1,1,1,1,1,1] [[3,3,3,3,2,2,1],[2,2,2,2,1,1]]=>[1,1,1,1,1,1,1] [[3,3,3,3,2,1,1],[2,2,2,2,1]]=>[1,1,1,1,1,1,1] [[4,4,4,4,3,2,1],[3,3,3,3,2,1]]=>[1,1,1,1,1,1,1] [[2,2,2,1,1,1,1],[1,1,1]]=>[1,1,1,1,1,1,1] [[3,3,3,2,2,2,1],[2,2,2,1,1,1]]=>[1,1,1,1,1,1,1] [[3,3,3,2,2,1,1],[2,2,2,1,1]]=>[1,1,1,1,1,1,1] [[4,4,4,3,3,2,1],[3,3,3,2,2,1]]=>[1,1,1,1,1,1,1] [[3,3,3,2,1,1,1],[2,2,2,1]]=>[1,1,1,1,1,1,1] [[4,4,4,3,2,2,1],[3,3,3,2,1,1]]=>[1,1,1,1,1,1,1] [[4,4,4,3,2,1,1],[3,3,3,2,1]]=>[1,1,1,1,1,1,1] [[5,5,5,4,3,2,1],[4,4,4,3,2,1]]=>[1,1,1,1,1,1,1] [[2,2,1,1,1,1,1],[1,1]]=>[1,1,1,1,1,1,1] [[3,3,2,2,2,2,1],[2,2,1,1,1,1]]=>[1,1,1,1,1,1,1] [[3,3,2,2,2,1,1],[2,2,1,1,1]]=>[1,1,1,1,1,1,1] [[4,4,3,3,3,2,1],[3,3,2,2,2,1]]=>[1,1,1,1,1,1,1] [[3,3,2,2,1,1,1],[2,2,1,1]]=>[1,1,1,1,1,1,1] [[4,4,3,3,2,2,1],[3,3,2,2,1,1]]=>[1,1,1,1,1,1,1] [[4,4,3,3,2,1,1],[3,3,2,2,1]]=>[1,1,1,1,1,1,1] [[5,5,4,4,3,2,1],[4,4,3,3,2,1]]=>[1,1,1,1,1,1,1] [[3,3,2,1,1,1,1],[2,2,1]]=>[1,1,1,1,1,1,1] [[4,4,3,2,2,2,1],[3,3,2,1,1,1]]=>[1,1,1,1,1,1,1] [[4,4,3,2,2,1,1],[3,3,2,1,1]]=>[1,1,1,1,1,1,1] [[5,5,4,3,3,2,1],[4,4,3,2,2,1]]=>[1,1,1,1,1,1,1] [[4,4,3,2,1,1,1],[3,3,2,1]]=>[1,1,1,1,1,1,1] [[5,5,4,3,2,2,1],[4,4,3,2,1,1]]=>[1,1,1,1,1,1,1] [[5,5,4,3,2,1,1],[4,4,3,2,1]]=>[1,1,1,1,1,1,1] [[6,6,5,4,3,2,1],[5,5,4,3,2,1]]=>[1,1,1,1,1,1,1] [[2,1,1,1,1,1,1],[1]]=>[1,1,1,1,1,1,1] [[3,2,2,2,2,2,1],[2,1,1,1,1,1]]=>[1,1,1,1,1,1,1] [[3,2,2,2,2,1,1],[2,1,1,1,1]]=>[1,1,1,1,1,1,1] [[4,3,3,3,3,2,1],[3,2,2,2,2,1]]=>[1,1,1,1,1,1,1] [[3,2,2,2,1,1,1],[2,1,1,1]]=>[1,1,1,1,1,1,1] [[4,3,3,3,2,2,1],[3,2,2,2,1,1]]=>[1,1,1,1,1,1,1] [[4,3,3,3,2,1,1],[3,2,2,2,1]]=>[1,1,1,1,1,1,1] [[5,4,4,4,3,2,1],[4,3,3,3,2,1]]=>[1,1,1,1,1,1,1] [[3,2,2,1,1,1,1],[2,1,1]]=>[1,1,1,1,1,1,1] [[4,3,3,2,2,2,1],[3,2,2,1,1,1]]=>[1,1,1,1,1,1,1] [[4,3,3,2,2,1,1],[3,2,2,1,1]]=>[1,1,1,1,1,1,1] [[5,4,4,3,3,2,1],[4,3,3,2,2,1]]=>[1,1,1,1,1,1,1] [[4,3,3,2,1,1,1],[3,2,2,1]]=>[1,1,1,1,1,1,1] [[5,4,4,3,2,2,1],[4,3,3,2,1,1]]=>[1,1,1,1,1,1,1] [[5,4,4,3,2,1,1],[4,3,3,2,1]]=>[1,1,1,1,1,1,1] [[6,5,5,4,3,2,1],[5,4,4,3,2,1]]=>[1,1,1,1,1,1,1] [[3,2,1,1,1,1,1],[2,1]]=>[1,1,1,1,1,1,1] [[4,3,2,2,2,2,1],[3,2,1,1,1,1]]=>[1,1,1,1,1,1,1] [[4,3,2,2,2,1,1],[3,2,1,1,1]]=>[1,1,1,1,1,1,1] [[5,4,3,3,3,2,1],[4,3,2,2,2,1]]=>[1,1,1,1,1,1,1] [[4,3,2,2,1,1,1],[3,2,1,1]]=>[1,1,1,1,1,1,1] [[5,4,3,3,2,2,1],[4,3,2,2,1,1]]=>[1,1,1,1,1,1,1] [[5,4,3,3,2,1,1],[4,3,2,2,1]]=>[1,1,1,1,1,1,1] [[6,5,4,4,3,2,1],[5,4,3,3,2,1]]=>[1,1,1,1,1,1,1] [[4,3,2,1,1,1,1],[3,2,1]]=>[1,1,1,1,1,1,1] [[5,4,3,2,2,2,1],[4,3,2,1,1,1]]=>[1,1,1,1,1,1,1] [[5,4,3,2,2,1,1],[4,3,2,1,1]]=>[1,1,1,1,1,1,1] [[6,5,4,3,3,2,1],[5,4,3,2,2,1]]=>[1,1,1,1,1,1,1] [[5,4,3,2,1,1,1],[4,3,2,1]]=>[1,1,1,1,1,1,1] [[6,5,4,3,2,2,1],[5,4,3,2,1,1]]=>[1,1,1,1,1,1,1] [[6,5,4,3,2,1,1],[5,4,3,2,1]]=>[1,1,1,1,1,1,1] [[7,6,5,4,3,2,1],[6,5,4,3,2,1]]=>[1,1,1,1,1,1,1] [[8],[]]=>[8] [[7,1],[]]=>[7,1] [[6,2],[]]=>[6,2] [[6,1,1],[]]=>[6,1,1] [[5,3],[]]=>[5,3] [[5,2,1],[]]=>[5,2,1] [[5,1,1,1],[]]=>[5,1,1,1] [[4,4],[]]=>[4,4] [[4,3,1],[]]=>[4,3,1] [[4,2,2],[]]=>[4,2,2] [[4,2,1,1],[]]=>[4,2,1,1] [[4,1,1,1,1],[]]=>[4,1,1,1,1] [[3,3,2],[]]=>[3,3,2] [[3,3,1,1],[]]=>[3,3,1,1] [[3,2,2,1],[]]=>[3,2,2,1] [[3,2,1,1,1],[]]=>[3,2,1,1,1] [[3,1,1,1,1,1],[]]=>[3,1,1,1,1,1] [[2,2,2,2],[]]=>[2,2,2,2] [[2,2,2,1,1],[]]=>[2,2,2,1,1] [[2,2,1,1,1,1],[]]=>[2,2,1,1,1,1] [[2,1,1,1,1,1,1],[]]=>[2,1,1,1,1,1,1] [[1,1,1,1,1,1,1,1],[]]=>[1,1,1,1,1,1,1,1] [[3,3,3],[1]]=>[2,3,3] [[3,3,3,1],[1,1]]=>[2,2,3,1] [[4,4,1],[1]]=>[3,4,1] [[3,3,2,1],[1]]=>[2,3,2,1] [[2,2,2,2,1],[1]]=>[1,2,2,2,1] [[3,3,3,1],[2]]=>[1,3,3,1] [[3,3,3,2],[1,1,1]]=>[2,2,2,2] [[4,4,2],[1,1]]=>[3,3,2] [[4,4,4],[2,2]]=>[2,2,4] [[5,5],[2]]=>[3,5] [[4,4,3],[2,1]]=>[2,3,3] [[3,3,3,3],[2,1,1]]=>[1,2,2,3] [[4,3,3],[1,1]]=>[3,2,3] [[4,4,4],[3,1]]=>[1,3,4] [[5,4],[1]]=>[4,4] [[3,3,2,2],[1,1]]=>[2,2,2,2] [[4,4,2],[2]]=>[2,4,2] [[3,3,3,2],[2,1]]=>[1,2,3,2] [[4,3,2],[1]]=>[3,3,2] [[2,2,2,2,2],[1,1]]=>[1,1,2,2,2] [[3,2,2,2],[1]]=>[2,2,2,2] [[3,3,2,2],[2]]=>[1,3,2,2] [[3,3,3,3],[2,2]]=>[1,1,3,3] [[4,3,3],[2]]=>[2,3,3] [[4,4,3],[3]]=>[1,4,3] [[6,6],[4]]=>[2,6] [[6,5],[3]]=>[3,5] [[6,4],[2]]=>[4,4] [[6,3],[1]]=>[5,3] [[9],[]]=>[9] [[8,1],[]]=>[8,1] [[7,2],[]]=>[7,2] [[7,1,1],[]]=>[7,1,1] [[6,3],[]]=>[6,3] [[6,2,1],[]]=>[6,2,1] [[6,1,1,1],[]]=>[6,1,1,1] [[5,4],[]]=>[5,4] [[5,3,1],[]]=>[5,3,1] [[5,2,2],[]]=>[5,2,2] [[5,2,1,1],[]]=>[5,2,1,1] [[5,1,1,1,1],[]]=>[5,1,1,1,1] [[4,4,1],[]]=>[4,4,1] [[4,3,2],[]]=>[4,3,2] [[4,3,1,1],[]]=>[4,3,1,1] [[4,2,2,1],[]]=>[4,2,2,1] [[4,2,1,1,1],[]]=>[4,2,1,1,1] [[4,1,1,1,1,1],[]]=>[4,1,1,1,1,1] [[3,3,3],[]]=>[3,3,3] [[3,3,2,1],[]]=>[3,3,2,1] [[3,3,1,1,1],[]]=>[3,3,1,1,1] [[3,2,2,2],[]]=>[3,2,2,2] [[3,2,2,1,1],[]]=>[3,2,2,1,1] [[3,2,1,1,1,1],[]]=>[3,2,1,1,1,1] [[3,1,1,1,1,1,1],[]]=>[3,1,1,1,1,1,1] [[2,2,2,2,1],[]]=>[2,2,2,2,1] [[2,2,2,1,1,1],[]]=>[2,2,2,1,1,1] [[2,2,1,1,1,1,1],[]]=>[2,2,1,1,1,1,1] [[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],[]]=>[1,1,1,1,1,1,1,1,1] [[3,3,3,1],[1]]=>[2,3,3,1] [[3,3,3,3],[1,1,1]]=>[2,2,2,3] [[4,4,3],[1,1]]=>[3,3,3] [[4,4,4],[2,1]]=>[2,3,4] [[5,5],[1]]=>[4,5] [[3,3,3,2],[1,1]]=>[2,2,3,2] [[4,4,2],[1]]=>[3,4,2] [[3,3,2,2],[1]]=>[2,3,2,2] [[2,2,2,2,2],[1]]=>[1,2,2,2,2] [[3,3,3,2],[2]]=>[1,3,3,2] [[4,4,3],[2]]=>[2,4,3] [[3,3,3,3],[2,1]]=>[1,2,3,3] [[4,3,3],[1]]=>[3,3,3] [[4,4,4],[3]]=>[1,4,4] [[5,5,5],[3,3]]=>[2,2,5] [[6,6],[3]]=>[3,6] [[5,5,4],[3,2]]=>[2,3,4] [[5,4,4],[2,2]]=>[3,2,4] [[6,5],[2]]=>[4,5] [[5,5,3],[3,1]]=>[2,4,3] [[5,4,3],[2,1]]=>[3,3,3] [[5,3,3],[1,1]]=>[4,2,3] [[6,4],[1]]=>[5,4] [[5,5,2],[3]]=>[2,5,2] [[5,4,2],[2]]=>[3,4,2] [[5,3,2],[1]]=>[4,3,2] [[10],[]]=>[10] [[9,1],[]]=>[9,1] [[8,2],[]]=>[8,2] [[8,1,1],[]]=>[8,1,1] [[7,3],[]]=>[7,3] [[7,2,1],[]]=>[7,2,1] [[7,1,1,1],[]]=>[7,1,1,1] [[6,4],[]]=>[6,4] [[6,3,1],[]]=>[6,3,1] [[6,2,2],[]]=>[6,2,2] [[6,2,1,1],[]]=>[6,2,1,1] [[6,1,1,1,1],[]]=>[6,1,1,1,1] [[5,5],[]]=>[5,5] [[5,4,1],[]]=>[5,4,1] [[5,3,2],[]]=>[5,3,2] [[5,3,1,1],[]]=>[5,3,1,1] [[5,2,2,1],[]]=>[5,2,2,1] [[5,2,1,1,1],[]]=>[5,2,1,1,1] [[5,1,1,1,1,1],[]]=>[5,1,1,1,1,1] [[4,4,2],[]]=>[4,4,2] [[4,4,1,1],[]]=>[4,4,1,1] [[4,3,3],[]]=>[4,3,3] [[4,3,2,1],[]]=>[4,3,2,1] [[4,3,1,1,1],[]]=>[4,3,1,1,1] [[4,2,2,2],[]]=>[4,2,2,2] [[4,2,2,1,1],[]]=>[4,2,2,1,1] [[4,2,1,1,1,1],[]]=>[4,2,1,1,1,1] [[4,1,1,1,1,1,1],[]]=>[4,1,1,1,1,1,1] [[3,3,3,1],[]]=>[3,3,3,1] [[3,3,2,2],[]]=>[3,3,2,2] [[3,3,2,1,1],[]]=>[3,3,2,1,1] [[3,3,1,1,1,1],[]]=>[3,3,1,1,1,1] [[3,2,2,2,1],[]]=>[3,2,2,2,1] [[3,2,2,1,1,1],[]]=>[3,2,2,1,1,1] [[3,2,1,1,1,1,1],[]]=>[3,2,1,1,1,1,1] [[3,1,1,1,1,1,1,1],[]]=>[3,1,1,1,1,1,1,1] [[2,2,2,2,2],[]]=>[2,2,2,2,2] [[2,2,2,2,1,1],[]]=>[2,2,2,2,1,1] [[2,2,2,1,1,1,1],[]]=>[2,2,2,1,1,1,1] [[2,2,1,1,1,1,1,1],[]]=>[2,2,1,1,1,1,1,1] [[2,1,1,1,1,1,1,1,1],[]]=>[2,1,1,1,1,1,1,1,1] [[1,1,1,1,1,1,1,1,1,1],[]]=>[1,1,1,1,1,1,1,1,1,1] [[4,4,4],[1,1]]=>[3,3,4] [[3,3,3,2],[1]]=>[2,3,3,2] [[3,3,3,3],[1,1]]=>[2,2,3,3] [[4,4,3],[1]]=>[3,4,3] [[4,4,4],[2]]=>[2,4,4] [[3,3,3,3],[2]]=>[1,3,3,3] [[4,4,4,4],[2,2,2]]=>[2,2,2,4] [[5,5,4],[2,2]]=>[3,3,4] [[5,5,5],[3,2]]=>[2,3,5] [[6,6],[2]]=>[4,6] [[4,4,4,3],[2,2,1]]=>[2,2,3,3] [[5,5,3],[2,1]]=>[3,4,3] [[4,4,3,3],[2,1,1]]=>[2,3,2,3] [[4,3,3,3],[1,1,1]]=>[3,2,2,3] [[5,4,3],[1,1]]=>[4,3,3] [[5,5,4],[3,1]]=>[2,4,4] [[5,4,4],[2,1]]=>[3,3,4] [[6,5],[1]]=>[5,5] [[4,4,4,2],[2,2]]=>[2,2,4,2] [[5,5,2],[2]]=>[3,5,2] [[4,4,3,2],[2,1]]=>[2,3,3,2] [[4,3,3,2],[1,1]]=>[3,2,3,2] [[5,4,2],[1]]=>[4,4,2] [[4,4,2,2],[2]]=>[2,4,2,2] [[4,3,2,2],[1]]=>[3,3,2,2] [[5,5,3],[3]]=>[2,5,3] [[5,4,3],[2]]=>[3,4,3] [[5,3,3],[1]]=>[4,3,3] [[6,5],[]]=>[6,5] [[5,5,1],[]]=>[5,5,1] [[5,4,2],[]]=>[5,4,2] [[5,3,3],[]]=>[5,3,3] [[4,4,3],[]]=>[4,4,3] [[4,4,2,1],[]]=>[4,4,2,1] [[4,3,3,1],[]]=>[4,3,3,1] [[4,3,2,2],[]]=>[4,3,2,2] [[3,3,3,2],[]]=>[3,3,3,2] [[3,2,2,2,2],[]]=>[3,2,2,2,2] [[4,4,4],[1]]=>[3,4,4] [[3,3,3,3],[1]]=>[2,3,3,3] [[4,4,4,1],[1,1]]=>[3,3,4,1] [[4,4,3,1],[1]]=>[3,4,3,1] [[4,4,4,1],[2]]=>[2,4,4,1] [[4,4,4,2],[1,1,1]]=>[3,3,3,2] [[5,5,5],[2,2]]=>[3,3,5] [[3,3,3,3,3],[1,1,1,1]]=>[2,2,2,2,3] [[4,4,3,3],[1,1,1]]=>[3,3,2,3] [[4,4,4,3],[2,1,1]]=>[2,3,3,3] [[5,5,3],[1,1]]=>[4,4,3] [[4,4,4,4],[2,2,1]]=>[2,2,3,4] [[5,5,4],[2,1]]=>[3,4,4] [[5,5,5],[3,1]]=>[2,4,5] [[6,6],[1]]=>[5,6] [[4,4,4,4],[3,1,1]]=>[1,3,3,4] [[5,4,4],[1,1]]=>[4,3,4] [[3,3,3,3,2],[1,1,1]]=>[2,2,2,3,2] [[4,4,3,2],[1,1]]=>[3,3,3,2] [[4,4,4,2],[2,1]]=>[2,3,4,2] [[5,5,2],[1]]=>[4,5,2] [[3,3,3,2,2],[1,1]]=>[2,2,3,2,2] [[4,4,2,2],[1]]=>[3,4,2,2] [[3,3,2,2,2],[1]]=>[2,3,2,2,2] [[4,4,3,2],[2]]=>[2,4,3,2] [[4,3,3,2],[1]]=>[3,3,3,2] [[4,4,4,2],[3]]=>[1,4,4,2] [[4,4,4,3],[2,2]]=>[2,2,4,3] [[5,5,3],[2]]=>[3,5,3] [[4,4,3,3],[2,1]]=>[2,3,3,3] [[4,3,3,3],[1,1]]=>[3,2,3,3] [[4,4,4,3],[3,1]]=>[1,3,4,3] [[5,4,3],[1]]=>[4,4,3] [[5,5,4],[3]]=>[2,5,4] [[4,4,4,4],[3,2]]=>[1,2,4,4] [[5,4,4],[2]]=>[3,4,4] [[5,5,5],[4]]=>[1,5,5] [[4,3,3,3],[2]]=>[2,3,3,3] [[4,4,3,3],[3]]=>[1,4,3,3] [[6,6],[]]=>[6,6] [[5,5,2],[]]=>[5,5,2] [[5,4,3],[]]=>[5,4,3] [[4,4,4],[]]=>[4,4,4] [[4,4,3,1],[]]=>[4,4,3,1] [[4,4,2,2],[]]=>[4,4,2,2] [[4,3,3,2],[]]=>[4,3,3,2] [[3,3,3,3],[]]=>[3,3,3,3] [[3,3,3,2,1],[]]=>[3,3,3,2,1] [[3,3,2,2,2],[]]=>[3,3,2,2,2] [[2,2,2,2,2,2],[]]=>[2,2,2,2,2,2] [[4,4,4,1],[1]]=>[3,4,4,1] [[3,3,3,3,1],[1]]=>[2,3,3,3,1] [[4,4,4,3],[1,1,1]]=>[3,3,3,3] [[5,5,5],[2,1]]=>[3,4,5] [[4,4,4,4],[2,1,1]]=>[2,3,3,4] [[5,5,4],[1,1]]=>[4,4,4] [[4,4,4,2],[1,1]]=>[3,3,4,2] [[3,3,3,2,2],[1]]=>[2,3,3,2,2] [[3,3,3,3,2],[1,1]]=>[2,2,3,3,2] [[4,4,3,2],[1]]=>[3,4,3,2] [[4,4,4,2],[2]]=>[2,4,4,2] [[3,3,3,3,2],[2]]=>[1,3,3,3,2] [[3,3,3,3,3],[1,1,1]]=>[2,2,2,3,3] [[4,4,3,3],[1,1]]=>[3,3,3,3] [[4,4,4,3],[2,1]]=>[2,3,4,3] [[5,5,3],[1]]=>[4,5,3] [[4,4,4,4],[2,2]]=>[2,2,4,4] [[5,5,4],[2]]=>[3,5,4] [[5,5,5],[3]]=>[2,5,5] [[4,4,4,4],[3,1]]=>[1,3,4,4] [[5,4,4],[1]]=>[4,4,4] [[4,4,3,3],[2]]=>[2,4,3,3] [[3,3,3,3,3],[2,1]]=>[1,2,3,3,3] [[4,3,3,3],[1]]=>[3,3,3,3] [[4,4,4,3],[3]]=>[1,4,4,3] [[5,5,3],[]]=>[5,5,3] [[5,4,4],[]]=>[5,4,4] [[4,4,4,1],[]]=>[4,4,4,1] [[4,4,3,2],[]]=>[4,4,3,2] [[4,3,3,3],[]]=>[4,3,3,3] [[3,3,3,3,1],[]]=>[3,3,3,3,1] [[3,3,3,2,2],[]]=>[3,3,3,2,2] [[4,4,4,4],[1,1,1]]=>[3,3,3,4] [[5,5,5],[1,1]]=>[4,4,5] [[4,4,4,2],[1]]=>[3,4,4,2] [[3,3,3,3,2],[1]]=>[2,3,3,3,2] [[4,4,4,3],[1,1]]=>[3,3,4,3] [[5,5,5],[2]]=>[3,5,5] [[4,4,4,4],[2,1]]=>[2,3,4,4] [[5,5,4],[1]]=>[4,5,4] [[3,3,3,3,3],[1,1]]=>[2,2,3,3,3] [[4,4,3,3],[1]]=>[3,4,3,3] [[4,4,4,3],[2]]=>[2,4,4,3] [[3,3,3,3,3],[2]]=>[1,3,3,3,3] [[4,4,4,4],[3]]=>[1,4,4,4] [[5,5,4],[]]=>[5,5,4] [[4,4,4,2],[]]=>[4,4,4,2] [[4,4,3,3],[]]=>[4,4,3,3] [[3,3,3,3,2],[]]=>[3,3,3,3,2] [[4,4,4,4],[1,1]]=>[3,3,4,4] [[5,5,5],[1]]=>[4,5,5] [[4,4,4,3],[1]]=>[3,4,4,3] [[3,3,3,3,3],[1]]=>[2,3,3,3,3] [[4,4,4,4],[2]]=>[2,4,4,4] [[5,5,5],[]]=>[5,5,5] [[5,5,4,1],[]]=>[5,5,4,1] [[4,4,4,3],[]]=>[4,4,4,3] [[3,3,3,3,3],[]]=>[3,3,3,3,3] [[4,4,4,4],[1]]=>[3,4,4,4] [[5,5,5,1],[1]]=>[4,5,5,1] [[5,5,5,5],[4,1]]=>[1,4,5,5] [[5,5,5,4],[4]]=>[1,5,5,4] [[5,5,5,1],[]]=>[5,5,5,1] [[4,4,4,4],[]]=>[4,4,4,4] [[4,4,4,3,1],[]]=>[4,4,4,3,1] [[3,3,3,3,3,1],[]]=>[3,3,3,3,3,1] [[4,4,4,4,1],[1]]=>[3,4,4,4,1] [[3,3,3,3,3,3],[2]]=>[1,3,3,3,3,3] [[4,4,4,4,3],[3]]=>[1,4,4,4,3] [[4,4,4,4,4],[3,1]]=>[1,3,4,4,4] [[5,5,5,5],[4]]=>[1,5,5,5] [[4,4,4,4,1],[]]=>[4,4,4,4,1] [[4,4,4,4,4],[3]]=>[1,4,4,4,4] [[5,5,5,5,4],[4]]=>[1,5,5,5,4] [[5,5,5,5,5],[4,1]]=>[1,4,5,5,5] [[5,5,5,4,1],[]]=>[5,5,5,4,1] [[5,5,5,5,1],[1]]=>[4,5,5,5,1] [[5,5,5,5,5],[4]]=>[1,5,5,5,5] [[5,5,5,5,1],[]]=>[5,5,5,5,1] [[4,4,4,4,4,4],[3]]=>[1,4,4,4,4,4] [[4,4,4,4,4,1],[]]=>[4,4,4,4,4,1] [[6,6,6,6,6],[5]]=>[1,6,6,6,6] [[6,6,6,6,1],[]]=>[6,6,6,6,1] [[5,5,5,5,5,5],[4]]=>[1,5,5,5,5,5] [[5,5,5,5,5,1],[]]=>[5,5,5,5,5,1] [[6,6,6,6,6,6],[5]]=>[1,6,6,6,6,6] [[6,6,6,6,6,1],[]]=>[6,6,6,6,6,1]
click to show experimental identities (only identities of compositions of up to three maps are shown)
Description
The sequence of row lengths from top to bottom.
Properties
surjective, graded
Sage code
def mapping(mu):
    return Composition(mu.row_lengths())
Weight
26
Created
Sep 24, 2020 at 20:09 by Martin Rubey
Updated
Sep 24, 2020 at 20:09 by Martin Rubey