A certain function $$f$$ has the properties that $$f(3x) = 3f(x)$$ for all positive real values of $$x$$, and that $$f(x) = 1 - |x - 2|$$ for $$1\leq x \leq 3$$. Find the smallest $$x$$ for which $$f(x) = f(2001)$$.

(第十九届AIME2 2001 第8题)