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3D Convex Hull

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 2030    Accepted Submission(s): 1071


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 doní»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.
 

Sample Input
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
 

Sample Output
8 5
 

Source
 

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