Maximizing $\prod_{i=0}^n|x-\frac{i}{n}|$

Question

Let $x_i=\frac{i}{n}\;, i=0,1,...,n\;$ be $\;n+1$ equidistant points on the interval $[0,1]$. Prove: The maximum value of: $$\prod_{i=0}^n|x-\frac{i}{n}|$$ in the interval $[0,1]$ is achieved for $x\in (0,\frac{1}{n})$ or $x\in (\frac{n-1}{n},1)$ (i.e in the first or last subinterval).