Functions

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