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
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 xi, yi. These are the coordinates of the i-th point. There may not be more than one point at the same coordinates.
Output
For each test case, output:
Case #X: Y
where X is the number of the test case and Y is the minimum perimeter. Answers with a relative or absolute error of at most 10-5 will be considered correct. Degenerate triangles — triangles with zero area — are ok.
Limits
Memory limit: 1 GB.
1 <= T <= 15
0 <= xi, yi <= 109
Small dataset (5 Points)
Time limit: 60 12 seconds.
3 <= n <= 10000
Large dataset (15 Points)
Time limit: 120 20 seconds.
3 <= n <= 1000000
Sample
1 10 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9
Case #1: 5.656854