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
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.
For each test case, output
Case #X: dmin tminwhere X is the test case number, starting from 1. Any answer with absolute or relative error of at most 10-5 will be accepted.
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.
3 ≤ N ≤ 10
3 ≤ N ≤ 500
Given N points (xi, yi, zi), their center of the mass is the point (xc, yc, zc), where:
xc = (x1 + x2 + ... + xN) / N yc = (y1 + y2 + ... + yN) / N zc = (z1 + z2 + ... + zN) / N