There is $N$ so that $\liminf S_n \leq S_n \leq \limsup S_n$ when $n > N$

Question

If $\liminf_{n\to\infty} S_n = -2$ and $\limsup_{n\to\infty} S_n = 1$, there exists $N$ so that $-2 \leq S_n \leq 1$ when $n > N$.

I think this is obvious. But how to prove it?