Mathematics > Algebra > Permutations And Combinations

Let $A = \{1, 2, 3, \ldots, 7\}$ and let $P(A)$ denote the power set of $A$. If the number of functions $f: A \to P(A)$ such that $a \in f(a)$, $\forall\, a \in A$ is $m^n$, $m$ and $n \in \mathbb{N}$ and $m$ is least, then $m+n$ is equal to ____.