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)