ILL 1989 Problem 13

Let $n \leq 44, n \in \mathbb{N}.$ Prove that for any function $f$ defined over $\mathbb{N}^2$ whose images are in the set $\{1, 2, \ldots , n\},$ there are four ordered pairs $(i, j), (i, k), (l, j),$ and $(l, k)$ such that $$f(i, j) = f(i, k) = f(l, j) = f(l, k),$$ in which $i, j, k, l$ are chosen in such a way that there are natural numbers $m, p$ that satisfy $$1989m \leq i < l < 1989 + 1989m$$ and $$1989p \leq j < k < 1989 + 1989p.$$