Karim Benzema likes to remember a small soccer tournament in which he participated many years ago. Karim remembers the following:
- There was a certain number $N$ of teams participating in the tournament. (But Karim does unfortunately not remember the value of $N$.)
- Each team played exactly one match against each of the other teams.
- For a win/draw/loss a team respectively scored 3/1/0 points.
- At the end of the tournament, Karim's team had gained more points than any of the other teams.
- At the end of the tournament, Karim's team had won fewer matches than any of the other teams.
Question: What is the smallest possible value $N\ge2$ that would be compatible with Karim's recollections?