Fishburg confectionery factory produces convex polygonshaped chocolates. Little Boy and Karlsson bought one and wanted to break it into two fragments. The areas of the fragments must be equal. Create a code to find out the length of breakageline of a minimal length using the given chocolate form.
Input
The first line of input contains an integer N — the number of polygon vertices (4 ≤ N ≤ 50). The other N lines contain coordinates of the vertices in the counterclockwise order. Coordinates are real numbers from −100 to 100 and given with at most 3 digits after decimal point.
Output
Output should contain the minimal length of breakageline with accuracy to 0.0001.
Sample
input  output 

4
0 0
4 0
4 3
0 3
 3

Problem Source: Rybinsk State Avia Academy