ISL 2013 A5

Let $\mathbb{Z}_{\geqslant 0}$ be the set of all nonnegative integers. Find all the functions $f: \mathbb{Z}_{\geqslant 0} \rightarrow \mathbb{Z}_{\geqslant 0}$ satisfying the relation $$f(f(f(n)))=f(n+1)+1$$ for all $n \in \mathbb{Z}_{\geqslant 0}$. (Serbia)