Entire function bounded by a polynomial is a polynomial with a less or equal degree- complex function

Question

There is an entire function $f$, that is bounded by polynomial $p(z)$ with degree $n$, meaning that

$|f(z)|≤|p(z)|$ for every $z\in\mathbb C$.

Show that $f$ is a polynomial of degree at most $n$ (less or equal to $n$).