Author: | Google Code Jam, World Finals 2009 | Time limit: | 10 sec | |

Input file: | input.txt | Memory limit: | 256 Mb | |

Output file: | output.txt |

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 contains one integer *N* — number of points.

Each of the next *N* lines contains two integer numbers *x*_{i}, *y*_{i} — coordinates of *i*-th point.

Output file should contain one real number — the minimum perimeter. Answers with a relative or absolute error of at most 10^{ − 7} will be considered correct. Degenerate triangles -— triangles with zero area -— are ok.

0 ≤ *n* ≤ 10^{6}

0 ≤ *x*_{i}, *y*_{i} ≤ 10^{9}