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)