Description

"What should I do?" pilot klux asks you for help.

In fact, klux is facing a very simple problem, but he is not good at it.

klux wants to bomb some locations in a certain area; they are points on a plane. However, he meets resistance, so he can fly only once, and because the plane is in poor condition, once it takes off it can only fly in a straight line and cannot turn. Now he wants to hit as many locations as possible in one flight.

Input Format

The first line contains an integer $n$.

Then $n$ lines follow, each containing a pair of integers that represent the coordinates of a point. No point appears twice.

Output Format

A single integer, the maximum number of points that a straight line can cover.

5
1 1
2 2
3 3
9 10
10 11

3

Hint

Constraints: For all testdata, it is guaranteed that $1\le n\le 700$.

This problem is translated and adapted from UVA 270; testdata and solution are provided by UVA.

Translated by ChatGPT 5