# 1084. 一条直线上？

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 fly over the area once in a straight line, and she had to fly 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!

### 输入格式

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

### 输出格式

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

### 样例

Input
5
1 1
2 2
3 3
9 10
10 11
0

Output
3


61 人解决，82 人已尝试。

103 份提交通过，共有 266 份提交。

3.8 EMB 奖励。