# Hello IMOment

We say that a set of positive integers $$S$$ is nice if it is a non-empty subsets of $$\left\{ 1,2,3,\ldots,2016 \right\}$$ and the product of numbers in $$S$$ is a perfect power of $$10$$.

For example, $$\{2,5,10\}$$ is a nice set because of $$2\cdot 5\cdot 10 = 10^2$$.

What is the size of the largest nice set?

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