Choosing Points

There are N distinct points on a two-dimensional plane. Choose some of the points so that all of the following conditions hold.

1. At least three points must be chosen.
2. For any two chosen points, consider the line passing through them. That line must contain at least one other chosen point besides those two.
3. The number of chosen points must be as large as possible.

Given the coordinates of all points, find the maximum number of points that can be chosen while satisfying the conditions.

The first line contains the number of points N (3 <= N <= 1,000).

Each of the next N lines contains two integers, the x-coordinate and y-coordinate of one point. The absolute value of every coordinate is at most 20,000. All given points are distinct.

Print the maximum number of points that can be chosen while satisfying the conditions. If no valid choice exists, print -1.