Lining Up

Time Limit: 2000 ms Memory Limit: 65536 KiB

Problem Description

"How am I ever going to solve this problem?" said the pilot.

Indeed, the pilot was not facing an easy task. She had to drop
packages at specific points scattered in a dangerous area.
Furthermore, the pilot could only y over the area once in a straight
line, and she had to y over as many points as possible. All points
were given by means of integer coordinates in a two-dimensional space.
The pilot wanted to know the largest number of points from the given
set that all lie on one line. Can you write a program that calculates
this number? Your program has to be efficient!

Input

The input consists of N pairs of integers, where 1 < N < 700. Each
pair of integers is separated by one blank and ended by a new-line
character. The list of pairs is ended with an end-of-file character.
No pair will occur twice.

Output

The output consists of one integer representing the largest number of
points that all lie on one line.

Sample Input

1 1
2 2
3 3
9 10
10 11

Sample Output

3