Description

$n$ 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.

Input Format

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 Format

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

6
5 6 7 7 8 8

121

Hint

All testdata satisfy $n \le 8$.

Translated by ChatGPT 5