Let $$S$$ be a set with six elements. Let $$P$$ be the set of all subsets of $$S.$$ Subsets $$A$$ and $$B$$ of $$S$$, not necessarily distinct, are chosen independently and at random from $$P$$. The probability that $$B$$ is contained in at least one of $$A$$ or $$S-A$$ is $$\frac{m}{n^{r}},$$ where $$m$$, $$n$$, and $$r$$ are positive integers, $$n$$ is prime, and $$m$$ and $$n$$ are relatively prime. Find $$m+n+r.$$ (The set $$S-A$$ is the set of all elements of $$S$$ which are not in $$A.$$)

(第二十五届AIME2 2007 第10题)