sol

General Donald has n soldiers on the battlefield. In order to know the layout of his soldiers exactly he received a map from the colonel, stating their positions. In order to receive new information from the enemy's camp he has sent a scout group. After a few hours this group returns with precious information: the enemy has a gun with which it can destroy any obstacle on the map on a straight line. Having this information, General Donald studies the map and notices that he has too many soldiers on a straight line.

Task

Determine the maximum number of soldiers that are located on the same straight line.

Input Data

Input file sol.in contains on the first line the number n, and on the following n lines the Cartesian map coordinates of each soldier. Such a line has format:
abscise ordinate (separated by a space).

Output Data

Output file sol.out will contain a single line with the maximum number of soldiers that are located on the same straight line.

Constraints and Statements

Example
sol.in sol.out Explanation
5
5 5
10 2
18 5
5 2
10 5

3

There are three soldiers located on a straight line.

Time limit: 0.2 seconds/test

prof. Doru Popescu Anastasiu
"Radu Greceanu" Slatina National High School
Contact:dopopan@yahoo.com