Score : $300$ points

问题描述

在 $xy$ 平面上，我们有编号为 $1$ 到 $N$ 的 $N$ 个点。
第 $i$ 个点位于坐标 $(X_i,Y_i)$。任何两个不同的点都处于不同的位置。
找出从这 $N$ 个点中选择三个点的方法数，使得用线段连接所选的点构成一个具有正面积的三角形。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

In the $xy$-plane, we have $N$ points numbered $1$ through $N$.
Point $i$ is at the coordinates $(X_i,Y_i)$. Any two different points are at different positions.
Find the number of ways to choose three of these $N$ points so that connecting the chosen points with segments results in a triangle with a positive area.

Constraints

• All values in input are integers.
• $3 \le N \le 300$
• $-10^9 \le X_i,Y_i \le 10^9$
• $(X_i,Y_i) \neq (X_j,Y_j)$ if $i \neq j$.

Input

Input is given from Standard Input in the following format:

$N$

$X_1$ $Y_1$

$X_2$ $Y_2$

$\dots$

$X_N$ $Y_N$

Output

Print the answer as an integer.

Sample Input 1

4
0 1
1 3
1 1
-1 -1

Sample Output 1

3

The figure below illustrates the points.

There are three ways to choose points that form a triangle: $\{1,2,3\},\{1,3,4\},\{2,3,4\}$.

Sample Input 2

20
224 433
987654321 987654321
2 0
6 4
314159265 358979323
0 0
-123456789 123456789
-1000000000 1000000000
124 233
9 -6
-4 0
9 5
-7 3
333333333 -333333333
-9 -1
7 -10
-1 5
324 633
1000000000 -1000000000
20 0

Sample Output 2

1124

update @ 2024/3/10 09:50:59