HDU4273 测试模板！ 求三维凸包，然后找重点，然后求重点到每个表面的距离。

# Rescue

**Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 326 Accepted Submission(s): 234**

Problem Description

I work at NASA outer space rescue team which needs much courage and patient. In daily life, I always receive a lot of mission, and I must complete it right now. Today, team leader announced me that there is a huge spaceship dropping anchor in the out space, and we should reach there for rescue. As a working principle, at first, we should check whether there are persons living in the spaceship. So we carry a kind of machine called life sensor which can sense the life phenomenon when the distance between the machine and the living is not farther than the sense radius. I have read the designing paper of the spaceship in advance. It has a form of a convex polyhedron, and we can assume it is isodense. For best control, control center of the whole ship is located at the center of the mass. It is sure that if someone is still alive, he will stay at the control center. It’s unfortunately that I find the door is stocked when I try to enter into the spaceship, so I can only sense the living out of the space ship. Now I have opened the machine and it’s time to set the sense radius of it. I wonder the minimal radius of the machine which can allowe me to check whether there are persons living in the spaceship.

Input

There are multiple test cases. The first line contains an integer n indicating the number of vertices of the polyhedron. (4 <= n <= 100) Each of the next n lines contains three integers xi, yi, zi, the coordinates of the polyhedron vertices (-10,000 <= xi, yi, zi <= 10,000). It guaranteed that the given points are vertices of the convex polyhedron, and the polyhedron is non-degenerate.

Output

For each test case, output a float number indicating the minimal radius of the machine. Your answer should accurate up to 0.001.

Sample Input

4 0 0 0 1 0 0 0 1 0 0 0 1 8 0 0 0 0 0 2 0 2 0 0 2 2 2 0 0 2 0 2 2 2 0 2 2 2

Sample Output

0.144 1.000

Source

2012 ACM/ICPC Asia Regional Changchun Online

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