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------------------------------------------------------------------------
Map identifier: Mp00311
------------------------------------------------------------------------
Map name: to partition
------------------------------------------------------------------------
Domain: Plane partitions
------------------------------------------------------------------------
Codomain: Integer partitions
------------------------------------------------------------------------
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.
------------------------------------------------------------------------
References:
------------------------------------------------------------------------
Code:
def mapping(p):
return Partition(sum(row) for row in p)
------------------------------------------------------------------------
Map images:
[[1]] => [1]
[[1],[1]] => [1,1]
[[2]] => [2]
[[1,1]] => [2]
[[1],[1],[1]] => [1,1,1]
[[2],[1]] => [2,1]
[[1,1],[1]] => [2,1]
[[3]] => [3]
[[2,1]] => [3]
[[1,1,1]] => [3]
[[1],[1],[1],[1]] => [1,1,1,1]
[[2],[1],[1]] => [2,1,1]
[[2],[2]] => [2,2]
[[1,1],[1],[1]] => [2,1,1]
[[1,1],[1,1]] => [2,2]
[[3],[1]] => [3,1]
[[2,1],[1]] => [3,1]
[[1,1,1],[1]] => [3,1]
[[4]] => [4]
[[3,1]] => [4]
[[2,2]] => [4]
[[2,1,1]] => [4]
[[1,1,1,1]] => [4]
[[1],[1],[1],[1],[1]] => [1,1,1,1,1]
[[2],[1],[1],[1]] => [2,1,1,1]
[[2],[2],[1]] => [2,2,1]
[[1,1],[1],[1],[1]] => [2,1,1,1]
[[1,1],[1,1],[1]] => [2,2,1]
[[3],[1],[1]] => [3,1,1]
[[3],[2]] => [3,2]
[[2,1],[1],[1]] => [3,1,1]
[[2,1],[2]] => [3,2]
[[2,1],[1,1]] => [3,2]
[[1,1,1],[1],[1]] => [3,1,1]
[[1,1,1],[1,1]] => [3,2]
[[4],[1]] => [4,1]
[[3,1],[1]] => [4,1]
[[2,2],[1]] => [4,1]
[[2,1,1],[1]] => [4,1]
[[1,1,1,1],[1]] => [4,1]
[[5]] => [5]
[[4,1]] => [5]
[[3,2]] => [5]
[[3,1,1]] => [5]
[[2,2,1]] => [5]
[[2,1,1,1]] => [5]
[[1,1,1,1,1]] => [5]
[[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1]
[[2],[1],[1],[1],[1]] => [2,1,1,1,1]
[[2],[2],[1],[1]] => [2,2,1,1]
[[2],[2],[2]] => [2,2,2]
[[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],[1,1]] => [2,2,2]
[[3],[1],[1],[1]] => [3,1,1,1]
[[3],[2],[1]] => [3,2,1]
[[3],[3]] => [3,3]
[[2,1],[1],[1],[1]] => [3,1,1,1]
[[2,1],[2],[1]] => [3,2,1]
[[2,1],[1,1],[1]] => [3,2,1]
[[2,1],[2,1]] => [3,3]
[[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]] => [3,3]
[[4],[1],[1]] => [4,1,1]
[[4],[2]] => [4,2]
[[3,1],[1],[1]] => [4,1,1]
[[3,1],[2]] => [4,2]
[[3,1],[1,1]] => [4,2]
[[2,2],[1],[1]] => [4,1,1]
[[2,2],[2]] => [4,2]
[[2,2],[1,1]] => [4,2]
[[2,1,1],[1],[1]] => [4,1,1]
[[2,1,1],[2]] => [4,2]
[[2,1,1],[1,1]] => [4,2]
[[1,1,1,1],[1],[1]] => [4,1,1]
[[1,1,1,1],[1,1]] => [4,2]
[[5],[1]] => [5,1]
[[4,1],[1]] => [5,1]
[[3,2],[1]] => [5,1]
[[3,1,1],[1]] => [5,1]
[[2,2,1],[1]] => [5,1]
[[2,1,1,1],[1]] => [5,1]
[[1,1,1,1,1],[1]] => [5,1]
[[6]] => [6]
[[5,1]] => [6]
[[4,2]] => [6]
[[4,1,1]] => [6]
[[3,3]] => [6]
[[3,2,1]] => [6]
[[3,1,1,1]] => [6]
[[2,2,2]] => [6]
[[2,2,1,1]] => [6]
[[2,1,1,1,1]] => [6]
[[1,1,1,1,1,1]] => [6]
[[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]
[[2],[2],[1],[1],[1]] => [2,2,1,1,1]
[[2],[2],[2],[1]] => [2,2,2,1]
[[1,1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1]
[[1,1],[1,1],[1],[1],[1]] => [2,2,1,1,1]
[[1,1],[1,1],[1,1],[1]] => [2,2,2,1]
[[3],[1],[1],[1],[1]] => [3,1,1,1,1]
[[3],[2],[1],[1]] => [3,2,1,1]
[[3],[2],[2]] => [3,2,2]
[[3],[3],[1]] => [3,3,1]
[[2,1],[1],[1],[1],[1]] => [3,1,1,1,1]
[[2,1],[2],[1],[1]] => [3,2,1,1]
[[2,1],[2],[2]] => [3,2,2]
[[2,1],[1,1],[1],[1]] => [3,2,1,1]
[[2,1],[1,1],[1,1]] => [3,2,2]
[[2,1],[2,1],[1]] => [3,3,1]
[[1,1,1],[1],[1],[1],[1]] => [3,1,1,1,1]
[[1,1,1],[1,1],[1],[1]] => [3,2,1,1]
[[1,1,1],[1,1],[1,1]] => [3,2,2]
[[1,1,1],[1,1,1],[1]] => [3,3,1]
[[4],[1],[1],[1]] => [4,1,1,1]
[[4],[2],[1]] => [4,2,1]
[[4],[3]] => [4,3]
[[3,1],[1],[1],[1]] => [4,1,1,1]
[[3,1],[2],[1]] => [4,2,1]
[[3,1],[1,1],[1]] => [4,2,1]
[[3,1],[3]] => [4,3]
[[3,1],[2,1]] => [4,3]
[[2,2],[1],[1],[1]] => [4,1,1,1]
[[2,2],[2],[1]] => [4,2,1]
[[2,2],[1,1],[1]] => [4,2,1]
[[2,2],[2,1]] => [4,3]
[[2,1,1],[1],[1],[1]] => [4,1,1,1]
[[2,1,1],[2],[1]] => [4,2,1]
[[2,1,1],[1,1],[1]] => [4,2,1]
[[2,1,1],[2,1]] => [4,3]
[[2,1,1],[1,1,1]] => [4,3]
[[1,1,1,1],[1],[1],[1]] => [4,1,1,1]
[[1,1,1,1],[1,1],[1]] => [4,2,1]
[[1,1,1,1],[1,1,1]] => [4,3]
[[5],[1],[1]] => [5,1,1]
[[5],[2]] => [5,2]
[[4,1],[1],[1]] => [5,1,1]
[[4,1],[2]] => [5,2]
[[4,1],[1,1]] => [5,2]
[[3,2],[1],[1]] => [5,1,1]
[[3,2],[2]] => [5,2]
[[3,2],[1,1]] => [5,2]
[[3,1,1],[1],[1]] => [5,1,1]
[[3,1,1],[2]] => [5,2]
[[3,1,1],[1,1]] => [5,2]
[[2,2,1],[1],[1]] => [5,1,1]
[[2,2,1],[2]] => [5,2]
[[2,2,1],[1,1]] => [5,2]
[[2,1,1,1],[1],[1]] => [5,1,1]
[[2,1,1,1],[2]] => [5,2]
[[2,1,1,1],[1,1]] => [5,2]
[[1,1,1,1,1],[1],[1]] => [5,1,1]
[[1,1,1,1,1],[1,1]] => [5,2]
[[6],[1]] => [6,1]
[[5,1],[1]] => [6,1]
[[4,2],[1]] => [6,1]
[[4,1,1],[1]] => [6,1]
[[3,3],[1]] => [6,1]
[[3,2,1],[1]] => [6,1]
[[3,1,1,1],[1]] => [6,1]
[[2,2,2],[1]] => [6,1]
[[2,2,1,1],[1]] => [6,1]
[[2,1,1,1,1],[1]] => [6,1]
[[1,1,1,1,1,1],[1]] => [6,1]
[[7]] => [7]
[[6,1]] => [7]
[[5,2]] => [7]
[[5,1,1]] => [7]
[[4,3]] => [7]
[[4,2,1]] => [7]
[[4,1,1,1]] => [7]
[[3,3,1]] => [7]
[[3,2,2]] => [7]
[[3,2,1,1]] => [7]
[[3,1,1,1,1]] => [7]
[[2,2,2,1]] => [7]
[[2,2,1,1,1]] => [7]
[[2,1,1,1,1,1]] => [7]
[[1,1,1,1,1,1,1]] => [7]
[[1],[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1,1]
[[2],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1]
[[2],[2],[1],[1],[1],[1]] => [2,2,1,1,1,1]
[[2],[2],[2],[1],[1]] => [2,2,2,1,1]
[[2],[2],[2],[2]] => [2,2,2,2]
[[1,1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1]
[[1,1],[1,1],[1],[1],[1],[1]] => [2,2,1,1,1,1]
[[1,1],[1,1],[1,1],[1],[1]] => [2,2,2,1,1]
[[1,1],[1,1],[1,1],[1,1]] => [2,2,2,2]
[[3],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1]
[[3],[2],[1],[1],[1]] => [3,2,1,1,1]
[[3],[2],[2],[1]] => [3,2,2,1]
[[3],[3],[1],[1]] => [3,3,1,1]
[[3],[3],[2]] => [3,3,2]
[[2,1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1]
[[2,1],[2],[1],[1],[1]] => [3,2,1,1,1]
[[2,1],[2],[2],[1]] => [3,2,2,1]
[[2,1],[1,1],[1],[1],[1]] => [3,2,1,1,1]
[[2,1],[1,1],[1,1],[1]] => [3,2,2,1]
[[2,1],[2,1],[1],[1]] => [3,3,1,1]
[[2,1],[2,1],[2]] => [3,3,2]
[[2,1],[2,1],[1,1]] => [3,3,2]
[[1,1,1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1]
[[1,1,1],[1,1],[1],[1],[1]] => [3,2,1,1,1]
[[1,1,1],[1,1],[1,1],[1]] => [3,2,2,1]
[[1,1,1],[1,1,1],[1],[1]] => [3,3,1,1]
[[1,1,1],[1,1,1],[1,1]] => [3,3,2]
[[4],[1],[1],[1],[1]] => [4,1,1,1,1]
[[4],[2],[1],[1]] => [4,2,1,1]
[[4],[2],[2]] => [4,2,2]
[[4],[3],[1]] => [4,3,1]
[[4],[4]] => [4,4]
[[3,1],[1],[1],[1],[1]] => [4,1,1,1,1]
[[3,1],[2],[1],[1]] => [4,2,1,1]
[[3,1],[2],[2]] => [4,2,2]
[[3,1],[1,1],[1],[1]] => [4,2,1,1]
[[3,1],[1,1],[1,1]] => [4,2,2]
[[3,1],[3],[1]] => [4,3,1]
[[3,1],[2,1],[1]] => [4,3,1]
[[3,1],[3,1]] => [4,4]
[[2,2],[1],[1],[1],[1]] => [4,1,1,1,1]
[[2,2],[2],[1],[1]] => [4,2,1,1]
[[2,2],[2],[2]] => [4,2,2]
[[2,2],[1,1],[1],[1]] => [4,2,1,1]
[[2,2],[1,1],[1,1]] => [4,2,2]
[[2,2],[2,1],[1]] => [4,3,1]
[[2,2],[2,2]] => [4,4]
[[2,1,1],[1],[1],[1],[1]] => [4,1,1,1,1]
[[2,1,1],[2],[1],[1]] => [4,2,1,1]
[[2,1,1],[2],[2]] => [4,2,2]
[[2,1,1],[1,1],[1],[1]] => [4,2,1,1]
[[2,1,1],[1,1],[1,1]] => [4,2,2]
[[2,1,1],[2,1],[1]] => [4,3,1]
[[2,1,1],[1,1,1],[1]] => [4,3,1]
[[2,1,1],[2,1,1]] => [4,4]
[[1,1,1,1],[1],[1],[1],[1]] => [4,1,1,1,1]
[[1,1,1,1],[1,1],[1],[1]] => [4,2,1,1]
[[1,1,1,1],[1,1],[1,1]] => [4,2,2]
[[1,1,1,1],[1,1,1],[1]] => [4,3,1]
[[1,1,1,1],[1,1,1,1]] => [4,4]
[[5],[1],[1],[1]] => [5,1,1,1]
[[5],[2],[1]] => [5,2,1]
[[5],[3]] => [5,3]
[[4,1],[1],[1],[1]] => [5,1,1,1]
[[4,1],[2],[1]] => [5,2,1]
[[4,1],[1,1],[1]] => [5,2,1]
[[4,1],[3]] => [5,3]
[[4,1],[2,1]] => [5,3]
[[3,2],[1],[1],[1]] => [5,1,1,1]
[[3,2],[2],[1]] => [5,2,1]
[[3,2],[1,1],[1]] => [5,2,1]
[[3,2],[3]] => [5,3]
[[3,2],[2,1]] => [5,3]
[[3,1,1],[1],[1],[1]] => [5,1,1,1]
[[3,1,1],[2],[1]] => [5,2,1]
[[3,1,1],[1,1],[1]] => [5,2,1]
[[3,1,1],[3]] => [5,3]
[[3,1,1],[2,1]] => [5,3]
[[3,1,1],[1,1,1]] => [5,3]
[[2,2,1],[1],[1],[1]] => [5,1,1,1]
[[2,2,1],[2],[1]] => [5,2,1]
[[2,2,1],[1,1],[1]] => [5,2,1]
[[2,2,1],[2,1]] => [5,3]
[[2,2,1],[1,1,1]] => [5,3]
[[2,1,1,1],[1],[1],[1]] => [5,1,1,1]
[[2,1,1,1],[2],[1]] => [5,2,1]
[[2,1,1,1],[1,1],[1]] => [5,2,1]
[[2,1,1,1],[2,1]] => [5,3]
[[2,1,1,1],[1,1,1]] => [5,3]
[[1,1,1,1,1],[1],[1],[1]] => [5,1,1,1]
[[1,1,1,1,1],[1,1],[1]] => [5,2,1]
[[1,1,1,1,1],[1,1,1]] => [5,3]
[[6],[1],[1]] => [6,1,1]
[[6],[2]] => [6,2]
[[5,1],[1],[1]] => [6,1,1]
[[5,1],[2]] => [6,2]
[[5,1],[1,1]] => [6,2]
[[4,2],[1],[1]] => [6,1,1]
[[4,2],[2]] => [6,2]
[[4,2],[1,1]] => [6,2]
[[4,1,1],[1],[1]] => [6,1,1]
[[4,1,1],[2]] => [6,2]
[[4,1,1],[1,1]] => [6,2]
[[3,3],[1],[1]] => [6,1,1]
[[3,3],[2]] => [6,2]
[[3,3],[1,1]] => [6,2]
[[3,2,1],[1],[1]] => [6,1,1]
[[3,2,1],[2]] => [6,2]
[[3,2,1],[1,1]] => [6,2]
[[3,1,1,1],[1],[1]] => [6,1,1]
[[3,1,1,1],[2]] => [6,2]
[[3,1,1,1],[1,1]] => [6,2]
[[2,2,2],[1],[1]] => [6,1,1]
[[2,2,2],[2]] => [6,2]
[[2,2,2],[1,1]] => [6,2]
[[2,2,1,1],[1],[1]] => [6,1,1]
[[2,2,1,1],[2]] => [6,2]
[[2,2,1,1],[1,1]] => [6,2]
[[2,1,1,1,1],[1],[1]] => [6,1,1]
[[2,1,1,1,1],[2]] => [6,2]
[[2,1,1,1,1],[1,1]] => [6,2]
[[1,1,1,1,1,1],[1],[1]] => [6,1,1]
[[1,1,1,1,1,1],[1,1]] => [6,2]
[[7],[1]] => [7,1]
[[6,1],[1]] => [7,1]
[[5,2],[1]] => [7,1]
[[5,1,1],[1]] => [7,1]
[[4,3],[1]] => [7,1]
[[4,2,1],[1]] => [7,1]
[[4,1,1,1],[1]] => [7,1]
[[3,3,1],[1]] => [7,1]
[[3,2,2],[1]] => [7,1]
[[3,2,1,1],[1]] => [7,1]
[[3,1,1,1,1],[1]] => [7,1]
[[2,2,2,1],[1]] => [7,1]
[[2,2,1,1,1],[1]] => [7,1]
[[2,1,1,1,1,1],[1]] => [7,1]
[[1,1,1,1,1,1,1],[1]] => [7,1]
[[8]] => [8]
[[7,1]] => [8]
[[6,2]] => [8]
[[6,1,1]] => [8]
[[5,3]] => [8]
[[5,2,1]] => [8]
[[5,1,1,1]] => [8]
[[4,4]] => [8]
[[4,3,1]] => [8]
[[4,2,2]] => [8]
[[4,2,1,1]] => [8]
[[4,1,1,1,1]] => [8]
[[3,3,2]] => [8]
[[3,3,1,1]] => [8]
[[3,2,2,1]] => [8]
[[3,2,1,1,1]] => [8]
[[3,1,1,1,1,1]] => [8]
[[2,2,2,2]] => [8]
[[2,2,2,1,1]] => [8]
[[2,2,1,1,1,1]] => [8]
[[2,1,1,1,1,1,1]] => [8]
[[1,1,1,1,1,1,1,1]] => [8]
[[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]
[[2],[2],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1]
[[2],[2],[2],[1],[1],[1]] => [2,2,2,1,1,1]
[[2],[2],[2],[2],[1]] => [2,2,2,2,1]
[[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]] => [2,2,1,1,1,1,1]
[[1,1],[1,1],[1,1],[1],[1],[1]] => [2,2,2,1,1,1]
[[1,1],[1,1],[1,1],[1,1],[1]] => [2,2,2,2,1]
[[3],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1]
[[3],[2],[1],[1],[1],[1]] => [3,2,1,1,1,1]
[[3],[2],[2],[1],[1]] => [3,2,2,1,1]
[[3],[2],[2],[2]] => [3,2,2,2]
[[3],[3],[1],[1],[1]] => [3,3,1,1,1]
[[3],[3],[2],[1]] => [3,3,2,1]
[[3],[3],[3]] => [3,3,3]
[[2,1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1]
[[2,1],[2],[1],[1],[1],[1]] => [3,2,1,1,1,1]
[[2,1],[2],[2],[1],[1]] => [3,2,2,1,1]
[[2,1],[2],[2],[2]] => [3,2,2,2]
[[2,1],[1,1],[1],[1],[1],[1]] => [3,2,1,1,1,1]
[[2,1],[1,1],[1,1],[1],[1]] => [3,2,2,1,1]
[[2,1],[1,1],[1,1],[1,1]] => [3,2,2,2]
[[2,1],[2,1],[1],[1],[1]] => [3,3,1,1,1]
[[2,1],[2,1],[2],[1]] => [3,3,2,1]
[[2,1],[2,1],[1,1],[1]] => [3,3,2,1]
[[2,1],[2,1],[2,1]] => [3,3,3]
[[1,1,1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1]
[[1,1,1],[1,1],[1],[1],[1],[1]] => [3,2,1,1,1,1]
[[1,1,1],[1,1],[1,1],[1],[1]] => [3,2,2,1,1]
[[1,1,1],[1,1],[1,1],[1,1]] => [3,2,2,2]
[[1,1,1],[1,1,1],[1],[1],[1]] => [3,3,1,1,1]
[[1,1,1],[1,1,1],[1,1],[1]] => [3,3,2,1]
[[1,1,1],[1,1,1],[1,1,1]] => [3,3,3]
[[4],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1]
[[4],[2],[1],[1],[1]] => [4,2,1,1,1]
[[4],[2],[2],[1]] => [4,2,2,1]
[[4],[3],[1],[1]] => [4,3,1,1]
[[4],[3],[2]] => [4,3,2]
[[4],[4],[1]] => [4,4,1]
[[3,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1]
[[3,1],[2],[1],[1],[1]] => [4,2,1,1,1]
[[3,1],[2],[2],[1]] => [4,2,2,1]
[[3,1],[1,1],[1],[1],[1]] => [4,2,1,1,1]
[[3,1],[1,1],[1,1],[1]] => [4,2,2,1]
[[3,1],[3],[1],[1]] => [4,3,1,1]
[[3,1],[3],[2]] => [4,3,2]
[[3,1],[2,1],[1],[1]] => [4,3,1,1]
[[3,1],[2,1],[2]] => [4,3,2]
[[3,1],[2,1],[1,1]] => [4,3,2]
[[3,1],[3,1],[1]] => [4,4,1]
[[2,2],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1]
[[2,2],[2],[1],[1],[1]] => [4,2,1,1,1]
[[2,2],[2],[2],[1]] => [4,2,2,1]
[[2,2],[1,1],[1],[1],[1]] => [4,2,1,1,1]
[[2,2],[1,1],[1,1],[1]] => [4,2,2,1]
[[2,2],[2,1],[1],[1]] => [4,3,1,1]
[[2,2],[2,1],[2]] => [4,3,2]
[[2,2],[2,1],[1,1]] => [4,3,2]
[[2,2],[2,2],[1]] => [4,4,1]
[[2,1,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1]
[[2,1,1],[2],[1],[1],[1]] => [4,2,1,1,1]
[[2,1,1],[2],[2],[1]] => [4,2,2,1]
[[2,1,1],[1,1],[1],[1],[1]] => [4,2,1,1,1]
[[2,1,1],[1,1],[1,1],[1]] => [4,2,2,1]
[[2,1,1],[2,1],[1],[1]] => [4,3,1,1]
[[2,1,1],[2,1],[2]] => [4,3,2]
[[2,1,1],[2,1],[1,1]] => [4,3,2]
[[2,1,1],[1,1,1],[1],[1]] => [4,3,1,1]
[[2,1,1],[1,1,1],[1,1]] => [4,3,2]
[[2,1,1],[2,1,1],[1]] => [4,4,1]
[[1,1,1,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1]
[[1,1,1,1],[1,1],[1],[1],[1]] => [4,2,1,1,1]
[[1,1,1,1],[1,1],[1,1],[1]] => [4,2,2,1]
[[1,1,1,1],[1,1,1],[1],[1]] => [4,3,1,1]
[[1,1,1,1],[1,1,1],[1,1]] => [4,3,2]
[[1,1,1,1],[1,1,1,1],[1]] => [4,4,1]
[[5],[1],[1],[1],[1]] => [5,1,1,1,1]
[[5],[2],[1],[1]] => [5,2,1,1]
[[5],[2],[2]] => [5,2,2]
[[5],[3],[1]] => [5,3,1]
[[5],[4]] => [5,4]
[[4,1],[1],[1],[1],[1]] => [5,1,1,1,1]
[[4,1],[2],[1],[1]] => [5,2,1,1]
[[4,1],[2],[2]] => [5,2,2]
[[4,1],[1,1],[1],[1]] => [5,2,1,1]
[[4,1],[1,1],[1,1]] => [5,2,2]
[[4,1],[3],[1]] => [5,3,1]
[[4,1],[2,1],[1]] => [5,3,1]
[[4,1],[4]] => [5,4]
[[4,1],[3,1]] => [5,4]
[[3,2],[1],[1],[1],[1]] => [5,1,1,1,1]
[[3,2],[2],[1],[1]] => [5,2,1,1]
[[3,2],[2],[2]] => [5,2,2]
[[3,2],[1,1],[1],[1]] => [5,2,1,1]
[[3,2],[1,1],[1,1]] => [5,2,2]
[[3,2],[3],[1]] => [5,3,1]
[[3,2],[2,1],[1]] => [5,3,1]
[[3,2],[3,1]] => [5,4]
[[3,2],[2,2]] => [5,4]
[[3,1,1],[1],[1],[1],[1]] => [5,1,1,1,1]
[[3,1,1],[2],[1],[1]] => [5,2,1,1]
[[3,1,1],[2],[2]] => [5,2,2]
[[3,1,1],[1,1],[1],[1]] => [5,2,1,1]
[[3,1,1],[1,1],[1,1]] => [5,2,2]
[[3,1,1],[3],[1]] => [5,3,1]
[[3,1,1],[2,1],[1]] => [5,3,1]
[[3,1,1],[1,1,1],[1]] => [5,3,1]
[[3,1,1],[3,1]] => [5,4]
[[3,1,1],[2,1,1]] => [5,4]
[[2,2,1],[1],[1],[1],[1]] => [5,1,1,1,1]
[[2,2,1],[2],[1],[1]] => [5,2,1,1]
[[2,2,1],[2],[2]] => [5,2,2]
[[2,2,1],[1,1],[1],[1]] => [5,2,1,1]
[[2,2,1],[1,1],[1,1]] => [5,2,2]
[[2,2,1],[2,1],[1]] => [5,3,1]
[[2,2,1],[1,1,1],[1]] => [5,3,1]
[[2,2,1],[2,2]] => [5,4]
[[2,2,1],[2,1,1]] => [5,4]
[[2,1,1,1],[1],[1],[1],[1]] => [5,1,1,1,1]
[[2,1,1,1],[2],[1],[1]] => [5,2,1,1]
[[2,1,1,1],[2],[2]] => [5,2,2]
[[2,1,1,1],[1,1],[1],[1]] => [5,2,1,1]
[[2,1,1,1],[1,1],[1,1]] => [5,2,2]
[[2,1,1,1],[2,1],[1]] => [5,3,1]
[[2,1,1,1],[1,1,1],[1]] => [5,3,1]
[[2,1,1,1],[2,1,1]] => [5,4]
[[2,1,1,1],[1,1,1,1]] => [5,4]
[[1,1,1,1,1],[1],[1],[1],[1]] => [5,1,1,1,1]
[[1,1,1,1,1],[1,1],[1],[1]] => [5,2,1,1]
[[1,1,1,1,1],[1,1],[1,1]] => [5,2,2]
[[1,1,1,1,1],[1,1,1],[1]] => [5,3,1]
[[1,1,1,1,1],[1,1,1,1]] => [5,4]
[[6],[1],[1],[1]] => [6,1,1,1]
[[6],[2],[1]] => [6,2,1]
[[6],[3]] => [6,3]
[[5,1],[1],[1],[1]] => [6,1,1,1]
[[5,1],[2],[1]] => [6,2,1]
[[5,1],[1,1],[1]] => [6,2,1]
[[5,1],[3]] => [6,3]
[[5,1],[2,1]] => [6,3]
[[4,2],[1],[1],[1]] => [6,1,1,1]
[[4,2],[2],[1]] => [6,2,1]
[[4,2],[1,1],[1]] => [6,2,1]
[[4,2],[3]] => [6,3]
[[4,2],[2,1]] => [6,3]
[[4,1,1],[1],[1],[1]] => [6,1,1,1]
[[4,1,1],[2],[1]] => [6,2,1]
[[4,1,1],[1,1],[1]] => [6,2,1]
[[4,1,1],[3]] => [6,3]
[[4,1,1],[2,1]] => [6,3]
[[4,1,1],[1,1,1]] => [6,3]
[[3,3],[1],[1],[1]] => [6,1,1,1]
[[3,3],[2],[1]] => [6,2,1]
[[3,3],[1,1],[1]] => [6,2,1]
[[3,3],[3]] => [6,3]
[[3,3],[2,1]] => [6,3]
[[3,2,1],[1],[1],[1]] => [6,1,1,1]
[[3,2,1],[2],[1]] => [6,2,1]
[[3,2,1],[1,1],[1]] => [6,2,1]
[[3,2,1],[3]] => [6,3]
[[3,2,1],[2,1]] => [6,3]
[[3,2,1],[1,1,1]] => [6,3]
[[3,1,1,1],[1],[1],[1]] => [6,1,1,1]
[[3,1,1,1],[2],[1]] => [6,2,1]
[[3,1,1,1],[1,1],[1]] => [6,2,1]
[[3,1,1,1],[3]] => [6,3]
[[3,1,1,1],[2,1]] => [6,3]
[[3,1,1,1],[1,1,1]] => [6,3]
[[2,2,2],[1],[1],[1]] => [6,1,1,1]
[[2,2,2],[2],[1]] => [6,2,1]
[[2,2,2],[1,1],[1]] => [6,2,1]
[[2,2,2],[2,1]] => [6,3]
[[2,2,2],[1,1,1]] => [6,3]
[[2,2,1,1],[1],[1],[1]] => [6,1,1,1]
[[2,2,1,1],[2],[1]] => [6,2,1]
[[2,2,1,1],[1,1],[1]] => [6,2,1]
[[2,2,1,1],[2,1]] => [6,3]
[[2,2,1,1],[1,1,1]] => [6,3]
[[2,1,1,1,1],[1],[1],[1]] => [6,1,1,1]
[[2,1,1,1,1],[2],[1]] => [6,2,1]
[[2,1,1,1,1],[1,1],[1]] => [6,2,1]
[[2,1,1,1,1],[2,1]] => [6,3]
[[2,1,1,1,1],[1,1,1]] => [6,3]
[[1,1,1,1,1,1],[1],[1],[1]] => [6,1,1,1]
[[1,1,1,1,1,1],[1,1],[1]] => [6,2,1]
[[1,1,1,1,1,1],[1,1,1]] => [6,3]
[[7],[1],[1]] => [7,1,1]
[[7],[2]] => [7,2]
[[6,1],[1],[1]] => [7,1,1]
[[6,1],[2]] => [7,2]
[[6,1],[1,1]] => [7,2]
[[5,2],[1],[1]] => [7,1,1]
[[5,2],[2]] => [7,2]
[[5,2],[1,1]] => [7,2]
[[5,1,1],[1],[1]] => [7,1,1]
[[5,1,1],[2]] => [7,2]
[[5,1,1],[1,1]] => [7,2]
[[4,3],[1],[1]] => [7,1,1]
[[4,3],[2]] => [7,2]
[[4,3],[1,1]] => [7,2]
[[4,2,1],[1],[1]] => [7,1,1]
[[4,2,1],[2]] => [7,2]
[[4,2,1],[1,1]] => [7,2]
[[4,1,1,1],[1],[1]] => [7,1,1]
[[4,1,1,1],[2]] => [7,2]
[[4,1,1,1],[1,1]] => [7,2]
[[3,3,1],[1],[1]] => [7,1,1]
[[3,3,1],[2]] => [7,2]
[[3,3,1],[1,1]] => [7,2]
[[3,2,2],[1],[1]] => [7,1,1]
[[3,2,2],[2]] => [7,2]
[[3,2,2],[1,1]] => [7,2]
[[3,2,1,1],[1],[1]] => [7,1,1]
[[3,2,1,1],[2]] => [7,2]
[[3,2,1,1],[1,1]] => [7,2]
[[3,1,1,1,1],[1],[1]] => [7,1,1]
[[3,1,1,1,1],[2]] => [7,2]
[[3,1,1,1,1],[1,1]] => [7,2]
[[2,2,2,1],[1],[1]] => [7,1,1]
[[2,2,2,1],[2]] => [7,2]
[[2,2,2,1],[1,1]] => [7,2]
[[2,2,1,1,1],[1],[1]] => [7,1,1]
[[2,2,1,1,1],[2]] => [7,2]
[[2,2,1,1,1],[1,1]] => [7,2]
[[2,1,1,1,1,1],[1],[1]] => [7,1,1]
[[2,1,1,1,1,1],[2]] => [7,2]
[[2,1,1,1,1,1],[1,1]] => [7,2]
[[1,1,1,1,1,1,1],[1],[1]] => [7,1,1]
[[1,1,1,1,1,1,1],[1,1]] => [7,2]
[[8],[1]] => [8,1]
[[7,1],[1]] => [8,1]
[[6,2],[1]] => [8,1]
[[6,1,1],[1]] => [8,1]
[[5,3],[1]] => [8,1]
[[5,2,1],[1]] => [8,1]
[[5,1,1,1],[1]] => [8,1]
[[4,4],[1]] => [8,1]
[[4,3,1],[1]] => [8,1]
[[4,2,2],[1]] => [8,1]
[[4,2,1,1],[1]] => [8,1]
[[4,1,1,1,1],[1]] => [8,1]
[[3,3,2],[1]] => [8,1]
[[3,3,1,1],[1]] => [8,1]
[[3,2,2,1],[1]] => [8,1]
[[3,2,1,1,1],[1]] => [8,1]
[[3,1,1,1,1,1],[1]] => [8,1]
[[2,2,2,2],[1]] => [8,1]
[[2,2,2,1,1],[1]] => [8,1]
[[2,2,1,1,1,1],[1]] => [8,1]
[[2,1,1,1,1,1,1],[1]] => [8,1]
[[1,1,1,1,1,1,1,1],[1]] => [8,1]
[[9]] => [9]
[[8,1]] => [9]
[[7,2]] => [9]
[[7,1,1]] => [9]
[[6,3]] => [9]
[[6,2,1]] => [9]
[[6,1,1,1]] => [9]
[[5,4]] => [9]
[[5,3,1]] => [9]
[[5,2,2]] => [9]
[[5,2,1,1]] => [9]
[[5,1,1,1,1]] => [9]
[[4,4,1]] => [9]
[[4,3,2]] => [9]
[[4,3,1,1]] => [9]
[[4,2,2,1]] => [9]
[[4,2,1,1,1]] => [9]
[[4,1,1,1,1,1]] => [9]
[[3,3,3]] => [9]
[[3,3,2,1]] => [9]
[[3,3,1,1,1]] => [9]
[[3,2,2,2]] => [9]
[[3,2,2,1,1]] => [9]
[[3,2,1,1,1,1]] => [9]
[[3,1,1,1,1,1,1]] => [9]
[[2,2,2,2,1]] => [9]
[[2,2,2,1,1,1]] => [9]
[[2,2,1,1,1,1,1]] => [9]
[[2,1,1,1,1,1,1,1]] => [9]
[[1,1,1,1,1,1,1,1,1]] => [9]
[[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1,1,1,1]
[[2],[1],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1,1]
[[2],[2],[1],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1,1]
[[2],[2],[2],[1],[1],[1],[1]] => [2,2,2,1,1,1,1]
[[2],[2],[2],[2],[1],[1]] => [2,2,2,2,1,1]
[[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]
[[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],[1]] => [2,2,2,1,1,1,1]
[[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]] => [2,2,2,2,2]
[[3],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1]
[[3],[2],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1]
[[3],[2],[2],[1],[1],[1]] => [3,2,2,1,1,1]
[[3],[2],[2],[2],[1]] => [3,2,2,2,1]
[[3],[3],[1],[1],[1],[1]] => [3,3,1,1,1,1]
[[3],[3],[2],[1],[1]] => [3,3,2,1,1]
[[3],[3],[2],[2]] => [3,3,2,2]
[[3],[3],[3],[1]] => [3,3,3,1]
[[2,1],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1]
[[2,1],[2],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1]
[[2,1],[2],[2],[1],[1],[1]] => [3,2,2,1,1,1]
[[2,1],[2],[2],[2],[1]] => [3,2,2,2,1]
[[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]] => [3,2,2,1,1,1]
[[2,1],[1,1],[1,1],[1,1],[1]] => [3,2,2,2,1]
[[2,1],[2,1],[1],[1],[1],[1]] => [3,3,1,1,1,1]
[[2,1],[2,1],[2],[1],[1]] => [3,3,2,1,1]
[[2,1],[2,1],[2],[2]] => [3,3,2,2]
[[2,1],[2,1],[1,1],[1],[1]] => [3,3,2,1,1]
[[2,1],[2,1],[1,1],[1,1]] => [3,3,2,2]
[[2,1],[2,1],[2,1],[1]] => [3,3,3,1]
[[1,1,1],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1]
[[1,1,1],[1,1],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1]
[[1,1,1],[1,1],[1,1],[1],[1],[1]] => [3,2,2,1,1,1]
[[1,1,1],[1,1],[1,1],[1,1],[1]] => [3,2,2,2,1]
[[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],[1]] => [3,3,2,1,1]
[[1,1,1],[1,1,1],[1,1],[1,1]] => [3,3,2,2]
[[1,1,1],[1,1,1],[1,1,1],[1]] => [3,3,3,1]
[[4],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1]
[[4],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1]
[[4],[2],[2],[1],[1]] => [4,2,2,1,1]
[[4],[2],[2],[2]] => [4,2,2,2]
[[4],[3],[1],[1],[1]] => [4,3,1,1,1]
[[4],[3],[2],[1]] => [4,3,2,1]
[[4],[3],[3]] => [4,3,3]
[[4],[4],[1],[1]] => [4,4,1,1]
[[4],[4],[2]] => [4,4,2]
[[3,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1]
[[3,1],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1]
[[3,1],[2],[2],[1],[1]] => [4,2,2,1,1]
[[3,1],[2],[2],[2]] => [4,2,2,2]
[[3,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1]
[[3,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1]
[[3,1],[1,1],[1,1],[1,1]] => [4,2,2,2]
[[3,1],[3],[1],[1],[1]] => [4,3,1,1,1]
[[3,1],[3],[2],[1]] => [4,3,2,1]
[[3,1],[3],[3]] => [4,3,3]
[[3,1],[2,1],[1],[1],[1]] => [4,3,1,1,1]
[[3,1],[2,1],[2],[1]] => [4,3,2,1]
[[3,1],[2,1],[1,1],[1]] => [4,3,2,1]
[[3,1],[2,1],[2,1]] => [4,3,3]
[[3,1],[3,1],[1],[1]] => [4,4,1,1]
[[3,1],[3,1],[2]] => [4,4,2]
[[3,1],[3,1],[1,1]] => [4,4,2]
[[2,2],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1]
[[2,2],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1]
[[2,2],[2],[2],[1],[1]] => [4,2,2,1,1]
[[2,2],[2],[2],[2]] => [4,2,2,2]
[[2,2],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1]
[[2,2],[1,1],[1,1],[1],[1]] => [4,2,2,1,1]
[[2,2],[1,1],[1,1],[1,1]] => [4,2,2,2]
[[2,2],[2,1],[1],[1],[1]] => [4,3,1,1,1]
[[2,2],[2,1],[2],[1]] => [4,3,2,1]
[[2,2],[2,1],[1,1],[1]] => [4,3,2,1]
[[2,2],[2,1],[2,1]] => [4,3,3]
[[2,2],[2,2],[1],[1]] => [4,4,1,1]
[[2,2],[2,2],[2]] => [4,4,2]
[[2,2],[2,2],[1,1]] => [4,4,2]
[[2,1,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1]
[[2,1,1],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1]
[[2,1,1],[2],[2],[1],[1]] => [4,2,2,1,1]
[[2,1,1],[2],[2],[2]] => [4,2,2,2]
[[2,1,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1]
[[2,1,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1]
[[2,1,1],[1,1],[1,1],[1,1]] => [4,2,2,2]
[[2,1,1],[2,1],[1],[1],[1]] => [4,3,1,1,1]
[[2,1,1],[2,1],[2],[1]] => [4,3,2,1]
[[2,1,1],[2,1],[1,1],[1]] => [4,3,2,1]
[[2,1,1],[2,1],[2,1]] => [4,3,3]
[[2,1,1],[1,1,1],[1],[1],[1]] => [4,3,1,1,1]
[[2,1,1],[1,1,1],[1,1],[1]] => [4,3,2,1]
[[2,1,1],[1,1,1],[1,1,1]] => [4,3,3]
[[2,1,1],[2,1,1],[1],[1]] => [4,4,1,1]
[[2,1,1],[2,1,1],[2]] => [4,4,2]
[[2,1,1],[2,1,1],[1,1]] => [4,4,2]
[[1,1,1,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1]
[[1,1,1,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1]
[[1,1,1,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1]
[[1,1,1,1],[1,1],[1,1],[1,1]] => [4,2,2,2]
[[1,1,1,1],[1,1,1],[1],[1],[1]] => [4,3,1,1,1]
[[1,1,1,1],[1,1,1],[1,1],[1]] => [4,3,2,1]
[[1,1,1,1],[1,1,1],[1,1,1]] => [4,3,3]
[[1,1,1,1],[1,1,1,1],[1],[1]] => [4,4,1,1]
[[1,1,1,1],[1,1,1,1],[1,1]] => [4,4,2]
[[5],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1]
[[5],[2],[1],[1],[1]] => [5,2,1,1,1]
[[5],[2],[2],[1]] => [5,2,2,1]
[[5],[3],[1],[1]] => [5,3,1,1]
[[5],[3],[2]] => [5,3,2]
[[5],[4],[1]] => [5,4,1]
[[5],[5]] => [5,5]
[[4,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1]
[[4,1],[2],[1],[1],[1]] => [5,2,1,1,1]
[[4,1],[2],[2],[1]] => [5,2,2,1]
[[4,1],[1,1],[1],[1],[1]] => [5,2,1,1,1]
[[4,1],[1,1],[1,1],[1]] => [5,2,2,1]
[[4,1],[3],[1],[1]] => [5,3,1,1]
[[4,1],[3],[2]] => [5,3,2]
[[4,1],[2,1],[1],[1]] => [5,3,1,1]
[[4,1],[2,1],[2]] => [5,3,2]
[[4,1],[2,1],[1,1]] => [5,3,2]
[[4,1],[4],[1]] => [5,4,1]
[[4,1],[3,1],[1]] => [5,4,1]
[[4,1],[4,1]] => [5,5]
[[3,2],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1]
[[3,2],[2],[1],[1],[1]] => [5,2,1,1,1]
[[3,2],[2],[2],[1]] => [5,2,2,1]
[[3,2],[1,1],[1],[1],[1]] => [5,2,1,1,1]
[[3,2],[1,1],[1,1],[1]] => [5,2,2,1]
[[3,2],[3],[1],[1]] => [5,3,1,1]
[[3,2],[3],[2]] => [5,3,2]
[[3,2],[2,1],[1],[1]] => [5,3,1,1]
[[3,2],[2,1],[2]] => [5,3,2]
[[3,2],[2,1],[1,1]] => [5,3,2]
[[3,2],[3,1],[1]] => [5,4,1]
[[3,2],[2,2],[1]] => [5,4,1]
[[3,2],[3,2]] => [5,5]
[[3,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1]
[[3,1,1],[2],[1],[1],[1]] => [5,2,1,1,1]
[[3,1,1],[2],[2],[1]] => [5,2,2,1]
[[3,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1]
[[3,1,1],[1,1],[1,1],[1]] => [5,2,2,1]
[[3,1,1],[3],[1],[1]] => [5,3,1,1]
[[3,1,1],[3],[2]] => [5,3,2]
[[3,1,1],[2,1],[1],[1]] => [5,3,1,1]
[[3,1,1],[2,1],[2]] => [5,3,2]
[[3,1,1],[2,1],[1,1]] => [5,3,2]
[[3,1,1],[1,1,1],[1],[1]] => [5,3,1,1]
[[3,1,1],[1,1,1],[1,1]] => [5,3,2]
[[3,1,1],[3,1],[1]] => [5,4,1]
[[3,1,1],[2,1,1],[1]] => [5,4,1]
[[3,1,1],[3,1,1]] => [5,5]
[[2,2,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1]
[[2,2,1],[2],[1],[1],[1]] => [5,2,1,1,1]
[[2,2,1],[2],[2],[1]] => [5,2,2,1]
[[2,2,1],[1,1],[1],[1],[1]] => [5,2,1,1,1]
[[2,2,1],[1,1],[1,1],[1]] => [5,2,2,1]
[[2,2,1],[2,1],[1],[1]] => [5,3,1,1]
[[2,2,1],[2,1],[2]] => [5,3,2]
[[2,2,1],[2,1],[1,1]] => [5,3,2]
[[2,2,1],[1,1,1],[1],[1]] => [5,3,1,1]
[[2,2,1],[1,1,1],[1,1]] => [5,3,2]
[[2,2,1],[2,2],[1]] => [5,4,1]
[[2,2,1],[2,1,1],[1]] => [5,4,1]
[[2,2,1],[2,2,1]] => [5,5]
[[2,1,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1]
[[2,1,1,1],[2],[1],[1],[1]] => [5,2,1,1,1]
[[2,1,1,1],[2],[2],[1]] => [5,2,2,1]
[[2,1,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1]
[[2,1,1,1],[1,1],[1,1],[1]] => [5,2,2,1]
[[2,1,1,1],[2,1],[1],[1]] => [5,3,1,1]
[[2,1,1,1],[2,1],[2]] => [5,3,2]
[[2,1,1,1],[2,1],[1,1]] => [5,3,2]
[[2,1,1,1],[1,1,1],[1],[1]] => [5,3,1,1]
[[2,1,1,1],[1,1,1],[1,1]] => [5,3,2]
[[2,1,1,1],[2,1,1],[1]] => [5,4,1]
[[2,1,1,1],[1,1,1,1],[1]] => [5,4,1]
[[2,1,1,1],[2,1,1,1]] => [5,5]
[[1,1,1,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1]
[[1,1,1,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1]
[[1,1,1,1,1],[1,1],[1,1],[1]] => [5,2,2,1]
[[1,1,1,1,1],[1,1,1],[1],[1]] => [5,3,1,1]
[[1,1,1,1,1],[1,1,1],[1,1]] => [5,3,2]
[[1,1,1,1,1],[1,1,1,1],[1]] => [5,4,1]
[[1,1,1,1,1],[1,1,1,1,1]] => [5,5]
[[6],[1],[1],[1],[1]] => [6,1,1,1,1]
[[6],[2],[1],[1]] => [6,2,1,1]
[[6],[2],[2]] => [6,2,2]
[[6],[3],[1]] => [6,3,1]
[[6],[4]] => [6,4]
[[5,1],[1],[1],[1],[1]] => [6,1,1,1,1]
[[5,1],[2],[1],[1]] => [6,2,1,1]
[[5,1],[2],[2]] => [6,2,2]
[[5,1],[1,1],[1],[1]] => [6,2,1,1]
[[5,1],[1,1],[1,1]] => [6,2,2]
[[5,1],[3],[1]] => [6,3,1]
[[5,1],[2,1],[1]] => [6,3,1]
[[5,1],[4]] => [6,4]
[[5,1],[3,1]] => [6,4]
[[4,2],[1],[1],[1],[1]] => [6,1,1,1,1]
[[4,2],[2],[1],[1]] => [6,2,1,1]
[[4,2],[2],[2]] => [6,2,2]
[[4,2],[1,1],[1],[1]] => [6,2,1,1]
[[4,2],[1,1],[1,1]] => [6,2,2]
[[4,2],[3],[1]] => [6,3,1]
[[4,2],[2,1],[1]] => [6,3,1]
[[4,2],[4]] => [6,4]
[[4,2],[3,1]] => [6,4]
[[4,2],[2,2]] => [6,4]
[[4,1,1],[1],[1],[1],[1]] => [6,1,1,1,1]
[[4,1,1],[2],[1],[1]] => [6,2,1,1]
[[4,1,1],[2],[2]] => [6,2,2]
[[4,1,1],[1,1],[1],[1]] => [6,2,1,1]
[[4,1,1],[1,1],[1,1]] => [6,2,2]
[[4,1,1],[3],[1]] => [6,3,1]
[[4,1,1],[2,1],[1]] => [6,3,1]
[[4,1,1],[1,1,1],[1]] => [6,3,1]
[[4,1,1],[4]] => [6,4]
[[4,1,1],[3,1]] => [6,4]
[[4,1,1],[2,1,1]] => [6,4]
[[3,3],[1],[1],[1],[1]] => [6,1,1,1,1]
[[3,3],[2],[1],[1]] => [6,2,1,1]
[[3,3],[2],[2]] => [6,2,2]
[[3,3],[1,1],[1],[1]] => [6,2,1,1]
[[3,3],[1,1],[1,1]] => [6,2,2]
[[3,3],[3],[1]] => [6,3,1]
[[3,3],[2,1],[1]] => [6,3,1]
[[3,3],[3,1]] => [6,4]
[[3,3],[2,2]] => [6,4]
[[3,2,1],[1],[1],[1],[1]] => [6,1,1,1,1]
[[3,2,1],[2],[1],[1]] => [6,2,1,1]
[[3,2,1],[2],[2]] => [6,2,2]
[[3,2,1],[1,1],[1],[1]] => [6,2,1,1]
[[3,2,1],[1,1],[1,1]] => [6,2,2]
[[3,2,1],[3],[1]] => [6,3,1]
[[3,2,1],[2,1],[1]] => [6,3,1]
[[3,2,1],[1,1,1],[1]] => [6,3,1]
[[3,2,1],[3,1]] => [6,4]
[[3,2,1],[2,2]] => [6,4]
[[3,2,1],[2,1,1]] => [6,4]
[[3,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1]
[[3,1,1,1],[2],[1],[1]] => [6,2,1,1]
[[3,1,1,1],[2],[2]] => [6,2,2]
[[3,1,1,1],[1,1],[1],[1]] => [6,2,1,1]
[[3,1,1,1],[1,1],[1,1]] => [6,2,2]
[[3,1,1,1],[3],[1]] => [6,3,1]
[[3,1,1,1],[2,1],[1]] => [6,3,1]
[[3,1,1,1],[1,1,1],[1]] => [6,3,1]
[[3,1,1,1],[3,1]] => [6,4]
[[3,1,1,1],[2,1,1]] => [6,4]
[[3,1,1,1],[1,1,1,1]] => [6,4]
[[2,2,2],[1],[1],[1],[1]] => [6,1,1,1,1]
[[2,2,2],[2],[1],[1]] => [6,2,1,1]
[[2,2,2],[2],[2]] => [6,2,2]
[[2,2,2],[1,1],[1],[1]] => [6,2,1,1]
[[2,2,2],[1,1],[1,1]] => [6,2,2]
[[2,2,2],[2,1],[1]] => [6,3,1]
[[2,2,2],[1,1,1],[1]] => [6,3,1]
[[2,2,2],[2,2]] => [6,4]
[[2,2,2],[2,1,1]] => [6,4]
[[2,2,1,1],[1],[1],[1],[1]] => [6,1,1,1,1]
[[2,2,1,1],[2],[1],[1]] => [6,2,1,1]
[[2,2,1,1],[2],[2]] => [6,2,2]
[[2,2,1,1],[1,1],[1],[1]] => [6,2,1,1]
[[2,2,1,1],[1,1],[1,1]] => [6,2,2]
[[2,2,1,1],[2,1],[1]] => [6,3,1]
[[2,2,1,1],[1,1,1],[1]] => [6,3,1]
[[2,2,1,1],[2,2]] => [6,4]
[[2,2,1,1],[2,1,1]] => [6,4]
[[2,2,1,1],[1,1,1,1]] => [6,4]
[[2,1,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1]
[[2,1,1,1,1],[2],[1],[1]] => [6,2,1,1]
[[2,1,1,1,1],[2],[2]] => [6,2,2]
[[2,1,1,1,1],[1,1],[1],[1]] => [6,2,1,1]
[[2,1,1,1,1],[1,1],[1,1]] => [6,2,2]
[[2,1,1,1,1],[2,1],[1]] => [6,3,1]
[[2,1,1,1,1],[1,1,1],[1]] => [6,3,1]
[[2,1,1,1,1],[2,1,1]] => [6,4]
[[2,1,1,1,1],[1,1,1,1]] => [6,4]
[[1,1,1,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1]
[[1,1,1,1,1,1],[1,1],[1],[1]] => [6,2,1,1]
[[1,1,1,1,1,1],[1,1],[1,1]] => [6,2,2]
[[1,1,1,1,1,1],[1,1,1],[1]] => [6,3,1]
[[1,1,1,1,1,1],[1,1,1,1]] => [6,4]
[[7],[1],[1],[1]] => [7,1,1,1]
[[7],[2],[1]] => [7,2,1]
[[7],[3]] => [7,3]
[[6,1],[1],[1],[1]] => [7,1,1,1]
[[6,1],[2],[1]] => [7,2,1]
[[6,1],[1,1],[1]] => [7,2,1]
[[6,1],[3]] => [7,3]
[[6,1],[2,1]] => [7,3]
[[5,2],[1],[1],[1]] => [7,1,1,1]
[[5,2],[2],[1]] => [7,2,1]
[[5,2],[1,1],[1]] => [7,2,1]
[[5,2],[3]] => [7,3]
[[5,2],[2,1]] => [7,3]
[[5,1,1],[1],[1],[1]] => [7,1,1,1]
[[5,1,1],[2],[1]] => [7,2,1]
[[5,1,1],[1,1],[1]] => [7,2,1]
[[5,1,1],[3]] => [7,3]
[[5,1,1],[2,1]] => [7,3]
[[5,1,1],[1,1,1]] => [7,3]
[[4,3],[1],[1],[1]] => [7,1,1,1]
[[4,3],[2],[1]] => [7,2,1]
[[4,3],[1,1],[1]] => [7,2,1]
[[4,3],[3]] => [7,3]
[[4,3],[2,1]] => [7,3]
[[4,2,1],[1],[1],[1]] => [7,1,1,1]
[[4,2,1],[2],[1]] => [7,2,1]
[[4,2,1],[1,1],[1]] => [7,2,1]
[[4,2,1],[3]] => [7,3]
[[4,2,1],[2,1]] => [7,3]
[[4,2,1],[1,1,1]] => [7,3]
[[4,1,1,1],[1],[1],[1]] => [7,1,1,1]
[[4,1,1,1],[2],[1]] => [7,2,1]
[[4,1,1,1],[1,1],[1]] => [7,2,1]
[[4,1,1,1],[3]] => [7,3]
[[4,1,1,1],[2,1]] => [7,3]
[[4,1,1,1],[1,1,1]] => [7,3]
[[3,3,1],[1],[1],[1]] => [7,1,1,1]
[[3,3,1],[2],[1]] => [7,2,1]
[[3,3,1],[1,1],[1]] => [7,2,1]
[[3,3,1],[3]] => [7,3]
[[3,3,1],[2,1]] => [7,3]
[[3,3,1],[1,1,1]] => [7,3]
[[3,2,2],[1],[1],[1]] => [7,1,1,1]
[[3,2,2],[2],[1]] => [7,2,1]
[[3,2,2],[1,1],[1]] => [7,2,1]
[[3,2,2],[3]] => [7,3]
[[3,2,2],[2,1]] => [7,3]
[[3,2,2],[1,1,1]] => [7,3]
[[3,2,1,1],[1],[1],[1]] => [7,1,1,1]
[[3,2,1,1],[2],[1]] => [7,2,1]
[[3,2,1,1],[1,1],[1]] => [7,2,1]
[[3,2,1,1],[3]] => [7,3]
[[3,2,1,1],[2,1]] => [7,3]
[[3,2,1,1],[1,1,1]] => [7,3]
[[3,1,1,1,1],[1],[1],[1]] => [7,1,1,1]
[[3,1,1,1,1],[2],[1]] => [7,2,1]
[[3,1,1,1,1],[1,1],[1]] => [7,2,1]
[[3,1,1,1,1],[3]] => [7,3]
[[3,1,1,1,1],[2,1]] => [7,3]
[[3,1,1,1,1],[1,1,1]] => [7,3]
[[2,2,2,1],[1],[1],[1]] => [7,1,1,1]
[[2,2,2,1],[2],[1]] => [7,2,1]
[[2,2,2,1],[1,1],[1]] => [7,2,1]
[[2,2,2,1],[2,1]] => [7,3]
[[2,2,2,1],[1,1,1]] => [7,3]
[[2,2,1,1,1],[1],[1],[1]] => [7,1,1,1]
[[2,2,1,1,1],[2],[1]] => [7,2,1]
[[2,2,1,1,1],[1,1],[1]] => [7,2,1]
[[2,2,1,1,1],[2,1]] => [7,3]
[[2,2,1,1,1],[1,1,1]] => [7,3]
[[2,1,1,1,1,1],[1],[1],[1]] => [7,1,1,1]
[[2,1,1,1,1,1],[2],[1]] => [7,2,1]
[[2,1,1,1,1,1],[1,1],[1]] => [7,2,1]
[[2,1,1,1,1,1],[2,1]] => [7,3]
[[2,1,1,1,1,1],[1,1,1]] => [7,3]
[[1,1,1,1,1,1,1],[1],[1],[1]] => [7,1,1,1]
[[1,1,1,1,1,1,1],[1,1],[1]] => [7,2,1]
[[1,1,1,1,1,1,1],[1,1,1]] => [7,3]
[[8],[1],[1]] => [8,1,1]
[[8],[2]] => [8,2]
[[7,1],[1],[1]] => [8,1,1]
[[7,1],[2]] => [8,2]
[[7,1],[1,1]] => [8,2]
[[6,2],[1],[1]] => [8,1,1]
[[6,2],[2]] => [8,2]
[[6,2],[1,1]] => [8,2]
[[6,1,1],[1],[1]] => [8,1,1]
[[6,1,1],[2]] => [8,2]
[[6,1,1],[1,1]] => [8,2]
[[5,3],[1],[1]] => [8,1,1]
[[5,3],[2]] => [8,2]
[[5,3],[1,1]] => [8,2]
[[5,2,1],[1],[1]] => [8,1,1]
[[5,2,1],[2]] => [8,2]
[[5,2,1],[1,1]] => [8,2]
[[5,1,1,1],[1],[1]] => [8,1,1]
[[5,1,1,1],[2]] => [8,2]
[[5,1,1,1],[1,1]] => [8,2]
[[4,4],[1],[1]] => [8,1,1]
[[4,4],[2]] => [8,2]
[[4,4],[1,1]] => [8,2]
[[4,3,1],[1],[1]] => [8,1,1]
[[4,3,1],[2]] => [8,2]
[[4,3,1],[1,1]] => [8,2]
[[4,2,2],[1],[1]] => [8,1,1]
[[4,2,2],[2]] => [8,2]
[[4,2,2],[1,1]] => [8,2]
[[4,2,1,1],[1],[1]] => [8,1,1]
[[4,2,1,1],[2]] => [8,2]
[[4,2,1,1],[1,1]] => [8,2]
[[4,1,1,1,1],[1],[1]] => [8,1,1]
[[4,1,1,1,1],[2]] => [8,2]
[[4,1,1,1,1],[1,1]] => [8,2]
[[3,3,2],[1],[1]] => [8,1,1]
[[3,3,2],[2]] => [8,2]
[[3,3,2],[1,1]] => [8,2]
[[3,3,1,1],[1],[1]] => [8,1,1]
[[3,3,1,1],[2]] => [8,2]
[[3,3,1,1],[1,1]] => [8,2]
[[3,2,2,1],[1],[1]] => [8,1,1]
[[3,2,2,1],[2]] => [8,2]
[[3,2,2,1],[1,1]] => [8,2]
[[3,2,1,1,1],[1],[1]] => [8,1,1]
[[3,2,1,1,1],[2]] => [8,2]
[[3,2,1,1,1],[1,1]] => [8,2]
[[3,1,1,1,1,1],[1],[1]] => [8,1,1]
[[3,1,1,1,1,1],[2]] => [8,2]
[[3,1,1,1,1,1],[1,1]] => [8,2]
[[2,2,2,2],[1],[1]] => [8,1,1]
[[2,2,2,2],[2]] => [8,2]
[[2,2,2,2],[1,1]] => [8,2]
[[2,2,2,1,1],[1],[1]] => [8,1,1]
[[2,2,2,1,1],[2]] => [8,2]
[[2,2,2,1,1],[1,1]] => [8,2]
[[2,2,1,1,1,1],[1],[1]] => [8,1,1]
[[2,2,1,1,1,1],[2]] => [8,2]
[[2,2,1,1,1,1],[1,1]] => [8,2]
[[2,1,1,1,1,1,1],[1],[1]] => [8,1,1]
[[2,1,1,1,1,1,1],[2]] => [8,2]
[[2,1,1,1,1,1,1],[1,1]] => [8,2]
[[1,1,1,1,1,1,1,1],[1],[1]] => [8,1,1]
[[1,1,1,1,1,1,1,1],[1,1]] => [8,2]
[[9],[1]] => [9,1]
[[8,1],[1]] => [9,1]
[[7,2],[1]] => [9,1]
[[7,1,1],[1]] => [9,1]
[[6,3],[1]] => [9,1]
[[6,2,1],[1]] => [9,1]
[[6,1,1,1],[1]] => [9,1]
[[5,4],[1]] => [9,1]
[[5,3,1],[1]] => [9,1]
[[5,2,2],[1]] => [9,1]
[[5,2,1,1],[1]] => [9,1]
[[5,1,1,1,1],[1]] => [9,1]
[[4,4,1],[1]] => [9,1]
[[4,3,2],[1]] => [9,1]
[[4,3,1,1],[1]] => [9,1]
[[4,2,2,1],[1]] => [9,1]
[[4,2,1,1,1],[1]] => [9,1]
[[4,1,1,1,1,1],[1]] => [9,1]
[[3,3,3],[1]] => [9,1]
[[3,3,2,1],[1]] => [9,1]
[[3,3,1,1,1],[1]] => [9,1]
[[3,2,2,2],[1]] => [9,1]
[[3,2,2,1,1],[1]] => [9,1]
[[3,2,1,1,1,1],[1]] => [9,1]
[[3,1,1,1,1,1,1],[1]] => [9,1]
[[2,2,2,2,1],[1]] => [9,1]
[[2,2,2,1,1,1],[1]] => [9,1]
[[2,2,1,1,1,1,1],[1]] => [9,1]
[[2,1,1,1,1,1,1,1],[1]] => [9,1]
[[1,1,1,1,1,1,1,1,1],[1]] => [9,1]
[[10]] => [10]
[[9,1]] => [10]
[[8,2]] => [10]
[[8,1,1]] => [10]
[[7,3]] => [10]
[[7,2,1]] => [10]
[[7,1,1,1]] => [10]
[[6,4]] => [10]
[[6,3,1]] => [10]
[[6,2,2]] => [10]
[[6,2,1,1]] => [10]
[[6,1,1,1,1]] => [10]
[[5,5]] => [10]
[[5,4,1]] => [10]
[[5,3,2]] => [10]
[[5,3,1,1]] => [10]
[[5,2,2,1]] => [10]
[[5,2,1,1,1]] => [10]
[[5,1,1,1,1,1]] => [10]
[[4,4,2]] => [10]
[[4,4,1,1]] => [10]
[[4,3,3]] => [10]
[[4,3,2,1]] => [10]
[[4,3,1,1,1]] => [10]
[[4,2,2,2]] => [10]
[[4,2,2,1,1]] => [10]
[[4,2,1,1,1,1]] => [10]
[[4,1,1,1,1,1,1]] => [10]
[[3,3,3,1]] => [10]
[[3,3,2,2]] => [10]
[[3,3,2,1,1]] => [10]
[[3,3,1,1,1,1]] => [10]
[[3,2,2,2,1]] => [10]
[[3,2,2,1,1,1]] => [10]
[[3,2,1,1,1,1,1]] => [10]
[[3,1,1,1,1,1,1,1]] => [10]
[[2,2,2,2,2]] => [10]
[[2,2,2,2,1,1]] => [10]
[[2,2,2,1,1,1,1]] => [10]
[[2,2,1,1,1,1,1,1]] => [10]
[[2,1,1,1,1,1,1,1,1]] => [10]
[[1,1,1,1,1,1,1,1,1,1]] => [10]
-----------------------------------------------------------------------------
Created: Aug 28, 2023 at 10:00 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Aug 28, 2023 at 10:00 by Martin Rubey