# Jorge's subset products

Let $$S=\{1,2,3,4,\ldots, 2013\}$$ and let $$n$$ be the smallest positive integer such that the product of any $$n$$ distinct elements in $$S$$ is divisible by $$2013$$. What are the last $$3$$ digits of $$n$$?

This problem is posed by Jorge T.

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