Preparando MOJI
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
Informação
Provedor Codeforces
Código CF1284E
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Submetido 0
BOUA! 0
Taxa de BOUA's 0%
Datas 09/05/2023 09:57:54
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