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)