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.

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.

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.

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

见题面 Input 部分

见题面 Output 部分