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1143. Electric Path

Time limit: 1.0 second
Memory limit: 64 MB


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.


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


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).


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.


50.0 1.0
5.0 1.0
0.0 0.0
45.0 0.0
Problem Source: The competition for selecting the Vietnam IOI team