SE-SKOLORNAS 2011 Problem 6

How many functions $f:\mathbb N \to \mathbb N$ are there such that $f(0)=2011$ , $f(1) = 111$ , and $$f\left(\max \{x + y + 2, xy\}\right) = \min \{f (x + y), f (xy + 2)\}$$ for all non-negative integers $x$ , $y$ ?