시간 제한 | 메모리 제한 | 제출 | 정답 | 맞은 사람 | 정답 비율 |
---|---|---|---|---|---|
3 초 (추가 시간 없음) | 512 MB | 14 | 14 | 14 | 100.000% |
Kiwon's favorite video game is now holding a new year event to motivate the users! The game is about building and defending a castle, which led Kiwon to think about the following puzzle.
In a 2-dimension plane, you have a set $s = \{(x_1, y_1), (x_2, y_2), \ldots, (x_n, y_n)\}$ consisting of $n$ distinct points. In the set $s$, no three distinct points lie on a single line. For a point $p \in s$, we can protect this point by building a castle. A castle is a simple quadrilateral (polygon with $4$ vertices) that strictly encloses the point $p$ (i.e. the point $p$ is strictly inside a quadrilateral).
Kiwon is interested in the number of $4$-point subsets of $s$ that can be used to build a castle protecting $p$. Note that, if a single subset can be connected in more than one way to enclose a point, it is counted only once.
Let $f(p)$ be the number of $4$-point subsets that can enclose the point $p$. Please compute the sum of $f(p)$ for all points $p \in s$.
The first line contains a single integer $n$ ($5 \le n \le 2\,500$).
In the next $n$ lines, two integers $x_i$ and $y_i$ ($-10^9 \le x_i, y_i \le 10^9$) denoting the position of points are given.
It is guaranteed that all points are distinct, and there are no three collinear points.
Print the sum of $f(p)$ for all points $p \in s$.
5 -1 0 1 0 -10 -1 10 -1 0 3
2
8 0 1 1 2 2 2 1 3 0 -1 -1 -2 -2 -2 -1 -3
40
10 588634631 265299215 -257682751 342279997 527377039 82412729 145077145 702473706 276067232 912883502 822614418 -514698233 280281434 -41461635 65985059 -827653144 188538640 592896147 -857422304 -529223472
213