Let \(S^{}_{}\) be a subset of \(\{1,2,3^{}_{},\ldots,1989\}\) such that no two members of \(S^{}_{}\) differ by \(4^{}_{}\) or \(7^{}_{}\). What is the largest number of elements \(S^{}_{}\) can have?

(第七届AIME1989 第13题)