KöMaL 2008 A460

If $p$($x$) is a polynomial with degree less than 2$n$, show that $|p(n)| \le 2\sqrt{n} \cdot \max\big( |p(0)|, |p(1)|, \ldots, |p(n-1)|, |p(n+1)|, |p(n+2)|, \ldots, |p(2n)| \big).$