1010

For every six numbers, the sum is equal to $-9$. Try grouping the first and fourth terms, second and fifth, and third and sixth and you'll see why. This cycle keeps occurring until we get to the end, which must consist of $...+2018+2019-2020-2021-2022$. We see that there are $337$ of these cycles, so the sum should be $-9(337)=-3033$. However, we counted $-2021$ and $-2022$, which we must add back. The answer is $-3033+2021+2022=\boxed{1010}$.