In a five-team tournament, each team plays one game with every other team. Each team has a $$50\%$$ chance of winning any game it plays. (There are no ties.) Let $$\frac{m}{n}$$ be the probability that the tournament will produce neither an undefeated team nor a winless team, where $$m$$ and $$n$$ are relatively prime integers. Find $$m+n$$.

(第十四届AIME1996 第6题)