# Is This Even Possible?

For how many natural numbers $$n < 1000$$ are there, such that there exists a multiset of $$n$$ integers such that sum of $$n$$ of them is $$0$$, and the product of elements of that set is equal to $$n$$?

A multiset is a collection of objects where order doesn't matter (unlike a sequence) but multiplicities do matter (unlike a set). For example, $$\{1,1,2,3\} = \{2,1,3,1\} \neq \{1,2,3\}$$.

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