Problem
You are studying a swarm of N fireflies. Each firefly is moving
in a straight line at a constant speed. You are standing at the center
of the universe, at position
You know the position and velocity of each firefly at t = 0, and are only interested in
Input
The first line of input contains a single integer T, the number of test cases. Each test case starts with a line that contains an integer N, the number of fireflies, followed by N lines of the form
x y z vx vy vzEach of these lines describes one firefly: (x, y, z) is its initial position at time t = 0, and (vx, vy, vz) is its velocity.
Output
For each test case, output
Case #X: d_{min} t_{min}where X is the test case number, starting from 1. Any answer with absolute or relative error of at most 10^{5} will be accepted.
Limits
All the numbers in the input will be integers.
1 ≤ T ≤ 100
The values of x, y, z, vx, vy and vz will be between 5000 and 5000, inclusive.
Small dataset
3 ≤ N ≤ 10
Large dataset
3 ≤ N ≤ 500
Sample
Input 
Output 
3

Case #1: 0.00000000 1.00000000

Notes
Given N points (x_{i}, y_{i}, z_{i}), their center of the mass is the point (x_{c}, y_{c}, z_{c}), where:
x_{c} = (x_{1} + x_{2} + ... + x_{N}) / N y_{c} = (y_{1} + y_{2} + ... + y_{N}) / N z_{c} = (z_{1} + z_{2} + ... + z_{N}) / N
Points  Correct  Attempted 

10pt  823  1428 
17pt  737  913 