# Cut the Cake

Time Limit: 5000/5000 MS (Java/Others)

Memory Limit: 102400/102400 K (Java/Others)

## Description

Mehmet is a nut cake seller. As the whole cake is too large and too heavy, a customer generally buys a specified part of it. The whole cake is a rectangle, while the specified part is a convex polygon region inside the rectangle. To get such specified part, Mehmet uses his sword to cut the cake. The only operation he can do is splitting a piece of cake into two parts by a straight cutting. As the cake is very solid, it cost as much as 1 unit energy to cut each length of cake. What's the minimum energy Mehmet has to consume to satisfy the customer?

## Input

There are multiple test cases. Process to the End of File.

The first line of each test cases contains three integers 3≤N≤100, 0<W≤5000, 0<H≤5000, where W and H are the width and height of the nut cake. The next N lines are the vertices of the specified part in clockwise or counterclockwise order. Each line contains two integers 0<Xi<W and 0<Yi<H.

## Output

For each test case, output the minimum energy with six digits after decimal point.

## Sample Input

4 100 100
10 10
20 10
20 20
10 20
5 40 30
12 25
28 25
32 20
20 8
8 20

## Sample Output

150.000000
109.494748

zhuyuanchen520

## Source

2013 Multi-University Training Contest 9