P13449 [GCJ 2009 Finals] Min Perimeter

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.

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.

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** - $1 \leq T \leq 15$ - $0 \leq x_i, y_i \leq 10^9$ **Small dataset(5 Pts)** - Time limit: ~~60~~ 15 seconds. - $3 \leq n \leq 10000$ **Large dataset(15 Pts)** - Time limit: ~~120~~ 30 seconds. - $3 \leq n \leq 1000000$