Cyclic monotonicity of sub-differential domain and convex property

Question

I am looking for hints/proof's overview/reference about this proposition :

Let $S\subset \mathbb{R}^d\times\mathbb{R}^d$. There exist a convex function $\phi$ such that $S\subset \partial\phi$ if and only if $S$ is cyclically monotone.

Here $\partial\phi$ denotes the sub-differential of $\phi$.