PL-OM 2012 Problem 4

$n$ players ( $n \ge 4$ ) took part in the tournament. Each player played exactly one match with every other player, there were no draws. There was no four players $(A, B, C, D)$ , such that $A$ won with $B$ , $B$ won with $C$ , $C$ won with $D$ and $D$ won with $A$ . Determine, depending on $n$ , maximum number of trios of players $(A, B, C)$ , such that $A$ won with $B$ , $B$ won with $C$ and $C$ won with $A$ . (Attention: Trios $(A, B, C)$ , $(B, C, A)$ and $(C, A, B)$ are the same trio.)