Problem
You will be given a set of points with integer coordinates. You are asked to compute the smallest perimeter of a triangle with distinct vertexes from this set of points.
Input
When you are ready to submit a solution, the file you will download will contain Java source code that produces the input data. You should compile and run that program (see details at the bottom of the problem statement), and it will print the input data for the problem to the standard output stream. The program is guaranteed to run within 30 seconds for the small input, and 90 seconds for the large input if you don't have other resourceintensive processes running.
The first line of the input data gives you the number of cases, T. T test cases follow. Each test case contains on the first line the integer n, the number of points in the set. n lines follow, each line containing two integer numbers x_{i}, y_{i}. These are the coordinates of the ith point. There may not be more than one point at the same coordinates.
Output
For each test case, output:Case #X: Ywhere X is the number of the test case and Y is the minimum perimeter. Answers with a relative or absolute error of at most 10^{9} will be considered correct. Degenerate triangles — triangles with zero area — are ok.
Limits
1 <= T <= 15Small dataset
3 <= n <= 10000Large dataset
3 <= n <= 1000000Sample
Input 
public class Input {

Output 
Case #1: 5.656854

How to compile and run downloaded Java program
Once you're ready to submit a solution, download the program, and run it using the following instructions to get the input file:/usr/lib/jvm/java6sun/bin/javac Input.javato compile the program.
/usr/lib/jvm/java6sun/bin/java Xmx512M Input >test.txtto run the program and save the results to a file named "test.txt". Now that file contains the testcase that you need to solve.
"C:\Program Files\Java\jdk1.6.0_16\bin\javac" Input.javato compile the program.
"C:\Program Files\Java\jdk1.6.0_16\bin\java" Xmx512M Input >test.txtto run the program and save the results to a file named "test.txt". Now that file contains the testcase that you need to solve.