Given a set of n points in the two-dimensional plane, your task is to determine the convex hull of the points.
Input Format
First Line contains integer n, number of vertices of polygon. Next line contains x and y of that vertex
Output Format
Print the number of points in convex hull.
Constraints
|n|< 10^5
Example
Input
6 2 1 2 5 3 3 4 3 4 4 6 3
Output
4