VMO 1999 Problem 3

Let $S = \{0,1,2,\ldots,1999\}$ and $T = \{0,1,2,\ldots \}.$ Find all functions $f: T \mapsto S$ such that

(i) $f(s) = s \forall s \in S.$ (ii) $f(m+n) = f(f(m)+f(n)) \forall m,n \in T.$