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.