Is there a function satisfying the following conditions? [closed]

Let $\Omega$ be a bounded smooth open set of $\mathbb R^N$.

Is there a function $\psi \in C^2(\overline \Omega)$ satisfying the following conditions:

$\frac{\partial \psi}{\partial n} = n \cdot D\psi = 1$ on $\partial \Omega$, $\psi = 0$ on $\partial \Omega$, and $\psi > 0$ in $\Omega$,where $n$ is the unit outward normal to $\partial \Omega$.