Let S={1,2,3,4,5,6,7}. Then the number of possible functions f: S → S such that f( m · n )=f( m ) · f( n ) for every m, n ∈ S and m · n ∈ S is equal…

Let $\displaystyle S=\{1,2,3,4,5,6,7\}$. Then the number of possible functions $\displaystyle f: S \rightarrow S$ such that $\displaystyle f(\mathrm{~m} \cdot \mathrm{n})=f(\mathrm{~m}) \cdot f(\mathrm{n})$ for every $\displaystyle \mathrm{m}, \mathrm{n} \in \mathrm{S}$ and $\displaystyle \mathrm{m} \cdot \mathrm{n} \in \mathrm{S}$ is equal to \_\_\_\_.