An algebra problem by Rohan K

Let $x_1, x_2, \ldots , x_{100}$ be non-negative real numbers such that $x_i + x_{i+1} + x_{i+2} \leq 1$ for all $i = 1,2,\ldots,100$ , where $x_{101} = x_1$ and $x_{102} = x_2$ .

Find the maximal possible value for the sum $\displaystyle S = \sum_{i=1}^{100} x_i x_{i+2}$ .