Let $$S^{}_{}$$ be the set of all rational numbers $$r^{}_{}$$，$$0< r< 1$$, that have a repeating decimal expansion in the form $$0.abcabcabc\ldots=0.\overline{abc}$$, where the digits $$a^{}_{}$$, $$b^{}_{}$$, and $$c^{}_{}$$ are not necessarily distinct. To write the elements of $$S^{}_{}$$ as fractions in lowest terms, how many different numerators are required?

(第一十届AIME1992 第5题)