In triangle $$ABC,\,$$ angle $$C$$ is a right angle and the altitude from $$C\,$$ meets $$\overline{AB}\,$$ at $$D.\,$$ The lengths of the sides of $$\triangle ABC\,$$ are integers, $$BD=29^3,\,$$ and $$\cos B=m/n\,$$, where $$m\,$$ and $$n\,$$ are relatively prime positive integers. Find $$m+n.\,$$

(第十二届AIME1994 第10题)