You are given distinct points on a 2D plane. The -th point is located at .
For each integer , let be the maximum number of non-degenerate triangles you can place under the following conditions:
You add new points on the plane such that all points are distinct.
Each triangle has its vertices among the points.
No two triangles have an intersection with a positive area.
Compute .
输入格式
The input consists of a single test case in the following format.
The first line contains two integers and (, ), representing the number of points and the maximum value of . Each of the next lines contains two integers and (), representing the coordinates of the -th point. It is guaranteed that all points are distinct.
