# Crazy function

Let $$f$$ be a function from the set of positive integers to the set of positive integers such that $$f(x) \le x^2$$ for all positive integers $$x$$, and $$f(f(f(x))f(f(y))) = xy$$ for all positive integers $$x, y$$. Find the number of possible values of $$f(30)$$.

This problem is from the OMO.

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