Selection and Training Session

Let $x_1,\dots ,x_{100}$ be nonnegative real numbers such that $x_i+x_{i+1}+x_{i+2}\le 1$ for all $i=1,\dots ,100$ (we put $x_{101}=x_1,x_{102}=x_2$). Find the maximal possible value of the sum $S={\sum }_{i=1}^{100}{x}_i{x}_{i+2}$.