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## 1143. Electric Path

Time limit: 1.0 second
Memory limit: 64 MB

### Background

At the team competition of the 10th national student informatics Olympic, which is organized at Hanoi National University, there are N teams participating. Each team is assigned to work in a camp. On the map, it can be seen that the camps are positioned on the vertices of a convex polygon with N vertices: P1, P2, …, PN (the vertices are enumerated around the polygon in counter-clockwise order.) In order to achieve absolute safety providing electricity to the camps, besides an electric supplying system, the host organization set up a path from a reserved electricity generator (which is placed in one of the camps) to every camp once, and the path's total length is minimum.

### Problem

Given the coordinates of the polygons' vertices (the camps' positions), determine the length of the electric path corresponding to the host organization's arrangement.

### Input

The first line contains the integer N (1 ≤ N ≤ 200). The i'th line of the next N lines contains two real numbers xi, yi, separated by a space, with no more than 3 digits after the decimal points, are vertex Pi's coordinates on the plane (with i = 1, 2, …, N). The length of the path connecting two vertex (xi, yi) and (xj, yj) is computed with the formula: sqrt((xixj)2 + (yiyj)2).

### Output

The only line should contain real number L (written in real number format, with 3 digits after the decimal point), which is the total length of the electric path.

### Sample

inputoutput
```4
50.0 1.0
5.0 1.0
0.0 0.0
45.0 0.0
```
```50.211
```
Problem Source: The competition for selecting the Vietnam IOI team
Tags: none