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> Prove that the no of solutions of the equation $f(z)=w$, counted with Multiplicities for $w$ varying in $D\_2$, is constant on $D\_2$.
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**Def**: A map $f\colon X \to Y$ is said to be proper if $f^{-1}(K)$ is compact for every compact set $K$ in $Y$. 

**Domain**: Open connected Set.

Let $D\_1$ and $D\_2$ be domains in $ \mathbb C$. Suppose $f\colon D\_1 \to D\_2 $ is a proper holomorphic mapping. Prove that the number of solutions of the equation $f(z)=w$, counted with multiplicities, for $w$ varying in $D\_2$ is constant on $D\_2$.

Can someone please give some hints/ideas?