Straight Flight Bombing

Pilot klux is in trouble! He needs to perform a single bombing run with his damaged airplane, which can only fly in a straight line without turning. His goal is to bomb as many target locations as possible. The targets are given as points on a plane, and klux must choose a straight path that passes through the maximum number of these points.

Given a set of points, determine the maximum number of points that lie on the same straight line.

Note: Some points might be duplicate. Be sure to handle duplicates correctly.

inputFormat

The first line contains a single integer n (1 ≤ n ≤ 1000) representing the number of target points. Each of the following n lines contains two space-separated integers x and y (-10⁴ ≤ x, y ≤ 10⁴) specifying the coordinates of a target point.

outputFormat

Output a single integer representing the maximum number of points that lie on a single straight line.

sample

6
1 1
2 2
3 3
4 1
5 1
6 1

3