Laser Light

SCB-PA Inter School and C...
Limits 2s, 512 MB

A 2D grid consists of a lot of special lights bulbs, which turns on upon the incidence of a laser light. Each bulb has a specific coordinate and initially all of them are turned off. Now, you are given a super power, where you can place a laser light in the grid for once. Laser light goes in a straight line. You want to put the laser light in such a way, that you can turn on maximum number of light bulbs. The laser light must pass through $(0, 0)$ point. So, before placing the laser you want to write a program to find out the maximum number of lights that can be turned on.

Input

First line will have the number of bulbs, $L$ ($0 < L < 10^7$). Each of the next $L$ lines will contain two numbers $x$ ($-10^6 \le x \le 10^6$) and $y$ ($-10^6 \leq y \leq 10^6$), which represents the coordinate of a bulb.

Output

Print a number which is the maximum number of turned on bulbs.

Sample

InputOutput
5
1 1
2 2
3 3
5 3
-4 -3

3