OMM 2004 Problem 4

At the end of a soccer tournament in which any pair of teams played between them exactly once, and in which there were not draws, it was observed that for any three teams $A, B$ and C, if $A$ defeated $B$ and $B$ defeated $C$ , then $A$ defeated $C$ . Any team calculated the difference (positive) between the number of games that it won and the number of games it lost. The sum of all these differences was $5000$ . How many teams played in the tournament? Find all possible answers.