MathNet 2011 Question 78

Let $x_1,\ldots,x_{100}$ be nonnegative reals with $x_i+x_{i+1}+x_{i+2}\le1$ for $i=1,\ldots,100$, where $x_{101}=x_1,x_{102}=x_2$. Find the maximum of $S=\sum_{i=1}^{100}x_ix_{i+2}$.