Problem Description

There are N points in 3D-space which make up a 3D-Convex hull*. How many faces does the 3D-convexhull have? It is guaranteed that all the points are not in the same plane.

In case you don’t know the definition of convex hull, here we give you a clarification from Wikipedia:
*Convex hull: In mathematics, the convex hull, for a set of points X in a real vector space V, is the minimal convex set containing X.

Input

There are several test cases. In each case the first line contains an integer N indicates the number of 3D-points (3< N <= 300), and then N lines follow, each line contains three numbers x, y, z (between -10000 and 10000) indicate the 3d-position of a point.

Output

Output the number of faces of the 3D-Convex hull.

7
1 1 0
1 -1 0
-1 1 0
-1 -1 0
0 0 1
0 0 0
0 0 -0.1
7
1 1 0
1 -1 0
-1 1 0
-1 -1 0
0 0 1
0 0 0
0 0 0.1

8
5