Lining Up

Source : ACM ICPC East Central North America 1994
Time limit : 3 sec Memory limit : 32 M

Submitted : 1307, Accepted : 376

"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!


There are multiple test cases!
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.
The input ends with a case which N is equal to zero


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: