SP2270 BALLOON - Balloons in a Box

You must write a program that simulates placing spherical balloons into a rectangular box. The simulation scenario is as follows. Imagine that you are given a rectangular box and a set of points. Each point represents a position where you might place a balloon. To place a balloon at a point, center it at the point and inflate the balloon until it touches a side of the box or a previously placed balloon. You may not use a point that is outside the box or inside a previously placed balloon. However, you may use the points in any order you like, and you need not use every point. Your objective is to place balloons in the box in an order that maximizes the total volume occupied by the balloons. You are required to calculate the volume within the box that is not enclosed by the balloons.

The input consists of several test cases. The first line of each test case contains a single integer n that indicates the number of points in the set (1

For each test case print one line of output consisting of the test case number followed by the volume of the box not occupied by balloons. Round the volume to the nearest integer. Follow the format in the sample output given below. Place a blank line after the output of each test case.