CMO 1990 Problem 5

The function $f : \mathbb N \to \mathbb R$ satisfies $f(1) = 1, f(2) = 2$ and $$f (n+2) = f(n+2 - f(n+1) ) + f(n+1 - f(n) ).$$ Show that $0 \leq f(n+1) - f(n) \leq 1$ . Find all $n$ for which $f(n) = 1025$ .