In the Faculty of Cybernetics football championship, \( n \geq 3 \) teams participated. The competition was held in a round-robin format, meaning that each team played against every other team exactly once. For a win, a team earns 3 points, for a loss no points are awarded, and for a draw, both teams receive 1 point each. It turned out that the winning team scored strictly more points than any other team and had at most as many wins as losses. What is the smallest \( n \) for which this could happen? Proposed by Bogdan Rublov