Dividing the players into three teams as equally as possible can make the maximum number of games. So there are $4$, $4$, and $5$ players in the three teams and they will have $4\times4+4\times5+4\times5=56$ games in total. 
There are $13$ ping-pong players who will be divided into three teams, and they are going to have a men\textquotesingle s singles. The rule is that the players in the same team will not play with each other, and each of them only plays one game with each player in other teams. What is the maximum number of games happened in total? 
Options:
$$23$$ 
$$30$$ 
$$45$$ 
$$56$$ 
$$72$$ 