Let $X$ be a compact Riemann surface. Prove that if $X$ is isomorphic to $\mathbb{P}^1$, then $X$ admits a meromorphic function $f$ that has a single pole and that this pole has multiplicity one.
Since $X$ and $\mathbb{P}^1$ are isomorphic, then there exists a biholomorphic function $f$ between them. This $f$ happens to be meromorphic with only one pole. However, I can't seem to be able to prove that this pole must have multiplicity one. All I got so far is, assume that it has multiplicity greater than one, $n$, then every point in $\mathbb{P}^1$ must have multiplicity $n$. Can someone help me out with where to go next?
Hint: The integer $n$ is the number of points in $X$ (counting multiplicity) in the preimage of an arbitrary point in $\mathbf{P}^{1}$.