How to prove that $\mathcal{O}_{\sqrt{-11}}$ is a Euclidean domain?

Question

I want to prove that $\mathcal{O}_{\sqrt{-11}}$ is a Euclidean domain, which denotes the domain of algebraic integers in $\mathbb{Q}[\sqrt{d}]$. I know that it is $-11 \equiv 1\mod 4$, so I can write it as $a+b\sqrt{-11}$ where $a$ and $b$ are both integers or both half-integers. But I have no idea how to proceed such a question. Any help or hint is appreciated!