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 x_i, y_i. 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 <= x_i, y_i <= 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