KöMaL 2007 B3971

The sum of the non-negative numbers $x$, $y$, $z$ is 1. Let $S= x^2y+y^2z+z^2x+xy^2+yz^2+zx^2 \text{and} C=x^2y+y^2z+z^2x.$ What are the maximum possible values of $S$ and $C$?