Fewest pirates with no mutual cannon aiming

There are $n$ pirates. Each pirate aims two cannons, at two different pirates other than himself. What is the smallest $n$ for which the aiming can be arranged so that no pair of pirates have cannons aimed at each other?

$5$. With $n\le 4$ there are $\binom n2$ pairs but $2n$ aimed cannons, and $2n>\binom n2$, so some pair must aim at each other. For $n=5$ there are exactly $10$ pairs and $10$ cannons, and pirate $i$ aiming at $i+1$ and $i+2$ (mod 5) uses each pair once.