Let S be a set with six elements. Let \mathcal{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 \mathcal{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 \operatorname{not} in A.)