Homework

Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 413    Accepted Submission(s): 48

Problem Description

As this term is going to end, DRD needs to start his graphical homework.

In his homework, DRD needs to partition a point set S into two part. You can see that if one part has 100 points and the other has only 1 point, then this partition cannot be beautiful since it‘s too imbalanced. DRD wants to find a line to separate S, so that no points lie in the line and there are at least ⌊|S|3⌋ points in each side of the line. DRD finds it amazing that there may exist some points (no need to be in S) that if a line l passes it and does not pass any points in S, then l can be a separating line. Now, he wonders the area these points form.

Input

First line: a positive integer T≤10 indicating the number of test cases.
There are T cases following. In each case, the first line contains an positive integer n≤1000, and n lines follow. In each of these lines, there are 2 integers xi,yiindicating a point (xi,yi) in the plane. Note that |xi|,|yi|≤104
You can assume that no three points in S lies in the same line.

Output

For each test case: output ‘‘Case #x: ans‘‘ (without quotes), where x is the number of the cases, and ans is the area these points form.
Your answer is considered correct if and only if the absolute error or the relative error is smaller than 10−6.

Sample Input

2
4
1 1
1 -1
-1 -1
-1 1
8
-1 -1
-1 1
1 -1
1 1
-2 -2
-2 2
2 -2
2 2

Sample Output

Case #1: 4.000000
Case #2: 5.333333

Source