Score: $500$ points

问题陈述

在二维平面上有$N$个不同的点。第$i$个点的坐标是$(x_i,y_i)$。

我们想使用这些点作为顶点，尽可能多地创建（非退化的）三角形。这里，同一个点不能用作多个三角形的顶点。

找出可以创建的三角形的最大数量。

什么是非退化三角形？非退化三角形是指其三个顶点不共线的三角形。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

There are $N$ distinct points on a two-dimensional plane. The coordinates of the $i$-th point are $(x_i,y_i)$.

We want to create as many (non-degenerate) triangles as possible using these points as the vertices. Here, the same point cannot be used as a vertex of multiple triangles.

Find the maximum number of triangles that can be created.

What is a non-degenerate triangle? A non-degenerate triangle is a triangle whose three vertices are not collinear.

Constraints

• $3 \leq N \leq 300$
• $-10^9 \leq x_i,y_i \leq 10^9$
• If $i \neq j$, then $(x_i,y_i) \neq (x_j,y_j)$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$N$

$x_1$ $y_1$

$x_2$ $y_2$

$\vdots$

$x_{N}$ $y_{N}$

Output

Print the answer.

Sample Input 1

7
0 0
1 1
0 3
5 2
3 4
2 0
2 2

Sample Output 1

2

For example, if we create a triangle from the first, third, and sixth points and another from the second, fourth, and fifth points, we can create two triangles.

The same point cannot be used as a vertex for multiple triangles, but the triangles may have overlapping areas.

Sample Input 2

3
0 0
0 1000000000
0 -1000000000

Sample Output 2

0