P3154 [CQOI2009] Round-robin Tournament

$n$ teams play a round-robin: every pair of teams plays exactly once, and a draw gives $1$, a win $3$, and a loss $0$ points. Given the teams’ final scores, find how many possible scoreboards there are. ```平1胜3负0``` means: - If two teams draw, each receives $1$ point. - Otherwise, the winner receives $3$ points, and the defeated team receives $0$ points.

The first line contains a positive integer $n$, the number of teams. The second line contains $n$ non-negative integers, the score of each team.

Output a single line: the number of possible scoreboards. It is guaranteed that at least one possible scoreboard exists.

All testdata satisfy $n \le 8$. Translated by ChatGPT 5