SE-SKOLORNAS 1968 Problem 4

For $n\ne 0$ , let f(n) be the largest $k$ such that $3^k$ divides $n$ . If $M$ is a set of $n > 1$ integers, show that the number of possible values for $f(m-n)$ , where $m, n$ belong to $M$ cannot exceed $n-1$ .