Maximum-Vertex Convex Polygon

You are given N points in the plane whose coordinates are all natural numbers. Consider convex polygons whose vertices are the origin (0, 0) together with some of the given points; among all such polygons, we want the one with the greatest possible number of vertices. The origin (0, 0) must be one of the vertices of this polygon.

Write a program that determines the number of vertices of such a polygon.

A polygon is convex if, for every line segment whose endpoints lie inside the polygon, the whole segment also lies inside the polygon.

Two adjacent edges of the polygon may never be parallel; equivalently, no three consecutive vertices may be collinear.

The first line contains a natural number N ($2 \le N \le 100$), the number of given points.

Each of the next N lines contains two natural numbers X and Y ($1 \le X \le 100$, $1 \le Y \le 100$), separated by a single space, the coordinates of one point. All points are distinct.

Print a single line containing the number of vertices of the convex polygon that has the greatest number of vertices.

Note: the answer is always at least 3.