Let A ={1,2,3, …., 7} and let P ( A ) denote the power set of A. If the number of functions f: A → P ( A ) such that a ∈ f ( a ), ∀ a ∈ A is m^n, m…

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