Suppose that a function f: R → R satisfies f(x+y)=f(x) f(y) for all x, y ∈ R and f(1)=3. If Σ_i=1^n f(i)=363, then n is equal to \ \ \ \.

Suppose that a function $\displaystyle f: \mathbf{R} \rightarrow \mathbf{R}$ satisfies $\displaystyle f(x+y)=f(x) f(y)$ for all $\displaystyle x, y \in \mathbf{R}$ and $\displaystyle f(1)=3$. If $\displaystyle \sum_{i=1}^{\mathrm{n}} f(i)=363$, then n is equal to \_\_\_\_.