Let \(P_1^{}\) be a regular \(r~\mbox{gon}\) and \(P_2^{}\) be a regular \(s~\mbox{gon}\) (\(r\geq s\geq 3\)) such that each interior angle of \(P_1^{}\) is \(\frac{59}{58}\) as large as each interior angle of \(P_2^{}\). What's the largest possible value of \(s_{}^{}\)?

(第八届AIME1990 第3题)