Polygon

The military training ground has the shape of an n - gon. If one of the vertices is deleted, then the polygon becomes convex. Find the number of this vertex.

Input

The first line contains the number of vertices n (4 ≤ n ≤ 20) in polygon. Each of the next n lines contains two numbers - the coordinates of successive vertices of a polygon.

Output

Print the number of required vertex.

Examples