Near the planet Mars, in a faraway galaxy eerily similar to our own,
there is a fight to the death between the imperial forces and the
rebels. The rebel army has N ships which we will consider as points
If the cruiser is placed at
(|xi - x| + |yi - y| + |zi - z|) / pi
Your task is to find the position for the cruiser that minimizes the power required for its transmitter, and to output that power.
The first line of input gives the number of cases, T. T test cases follow.
Each test case contains on the first line the integer N, the number of ships in the test case.
N lines follow, each line containing four integer numbers xi, yi, zi and pi, separated by single spaces. These are the coordinates of the i-th ship, and the power of its receiver. There may be more than one ship at the same coordinates.
For each input case, you should output:
Case #X: Ywhere X is the number of the test case and Y is the minimal power that is enough to reach all the fleet's ships. Answers with a relative or absolute error of at most 10-6 will be considered correct.
1 ≤ T ≤ 10
0 ≤ xi, yi, zi ≤ 106
1 ≤ pi ≤ 106
1 ≤ N ≤ 10
1 ≤ N ≤ 1000
In the first test case, the four ships have coordinates (0, 0, 0), (1, 2, 0), (3, 4, 0), (2, 1, 0) and powers 1, 1, 1, 1 respectively. We can place a cruiser with the power 3.5 at the coordinates (1.5, 2, 0) which will be able to reach all the ships.
In the second case we can place the cruiser right on top of the ship, with transmitter power 0.