SAUDI ARABIAN MATHEMATICAL COMPETITIONS

There are totally $16$ teams participating in a football tournament; each team playing with every other exactly $1$ time. In each match, the winner gains $3$ points, the loser gains $0$ point and each team gains $1$ point for the tie match. Suppose that at the end of the tournament, each team gains the same number of points. Prove that there are at least $4$ teams that have the same number of winning matches, the same number of losing matches and the same number of tie matches.