SP10231 AMR11D - Wizarding Duel

You are the organizer of a Wizarding Duel tournament at Hogwarts. N players participated in the tournament and each player played with every other player exactly once, and each such game resulted in a winner and a loser (no drawn games). It is now time to declare the results. Each player's score is the number of games the player won. However, you realize that something possibly went wrong with the scoring system, and the scores that you have noted down might be wrong. In fact, the scores you have noted down could simply not be possible. For example, suppose there are 3 players and the scores that you noted are 0,0 and 2. Clearly this is not possible as the game between the first two players must have had a winner and thus both the players cannot have score 0.

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