There are 20 towns on the bay of a circular island. Each town has 20 teams for a mathematical duel. No two of these teams are of equal strength. When two teams meet in a duel, the stronger one wins. For a given number $n\in \mathbb{N}$ one town $A$ can be called “n-stronger” than $B$, if there exist $n$ different duels between a team from $A$ and team from $B$, for which the team from $A$ wins. Find the maximum value of $n$, for which it is possible for each town to be n-stronger by its neighboring one clockwise.