Mines
UN peacekeepers in one of the world's hotspots neutralized a minefield using the following method. They had a map where each mine was marked by its Cartesian coordinates, and they observed that no 3 mines were collinear. They used a special cord to connect the mines, forming a convex polygon with the smallest possible perimeter, ensuring all other mines were inside this polygon. After neutralizing the mines along the cord, they repeated the process, forming a new polygon with the remaining mines. This continued until they could no longer form a polygon according to these rules.
Determine how many mines remain unneutralized and how many times the sappers had to stretch the cord.
Input
The first line of the input contains an integer N (3 ≤ N ≤ 1000) - the number of mines. The second line contains 2N integers (N pairs of x_i, y_i), representing the coordinates of each mine (−32000 ≤ x_i, y_i ≤ 32000).
Output
Output two integers separated by a space - the number of mines remaining and the number of cord stretching operations.