CIIM 2009 Problem 3

Let $r > n$ be positive integers. A "good word" is an $n$ -tuple $\langle a_1,\dots, a_n \rangle$ of distinct positive integers between 1 and $r$ . A "play" consist of changing a integer $a_i$ of a good word, in such a way that the resulting word is still a good word. The distance between two good words $A= \langle a_1,\dots, a_n \rangle$ and $B = \langle b_1,\dots, b_n \rangle$ is the minimun number of plays needed to obtain B from A. Find the maximun posible distance between two good words.