Lower bound degree of approximating polynomial

Question

I am reading about quantum query lower bounds (polynomial method). They state that any polynomial such that $p(0) \in [0,1/3]$ and $p(t) \in [2/3, 1]$ for each $t \in \{1, 2, 3, \ldots, n\}$ has to have degree at least $\Omega(\sqrt{n})$. I fail to find an easy proof of this theorem.