Converse of Hurwitz theorem in several complex variables

Question

Let $\phi_{n}: \overline{\Omega} \to \mathbb{C}^{n}$ be e sequence of holomorphic map converges to a $\mathcal{C}^{2}$ smooth differmorphism $f: \overline{\Omega} \to f(\overline{\Omega})$, with $f \in Hol(\Omega) $ uniformly on $\overline{\Omega}$ in $\mathcal{C}^{2}$ topology. Then show that $\phi_{n}$ are injective on $\overline{\Omega}$ for large enough $n$.