Extending biholomorhpic functions on $S^2$ has a Riemann surface

Question

Let $A = \{ \alpha_1,\alpha_2, \alpha_3, \alpha_4\}$ and $B = \{\beta_1,\beta_2,\beta_3,\beta_4\}$ be sets of four distinct points in $S^2$ and $f : S^2 \setminus A \rightarrow S ^2\setminus B$ is a biholomorphic map. I need to show that f extends to a biholomorphic map of $S^2$ onto itself.