Corridor

题目描述

Consider a house plan. Let the house be represented by an infinite horizontal strip defined by the inequality $ -h<=y<=h $ . Strictly outside the house there are two light sources at the points $ (0,f) $ and $ (0,-f) $ . Windows are located in the walls, the windows are represented by segments on the lines $ y=h $ and $ y=-h $ . Also, the windows are arranged symmetrically about the line $ y=0 $ . Your task is to find the area of the floor at the home, which will be lighted by the sources of light. 

输入输出格式

输入格式

The first line of the input file contains three integers $ n $ , $ h $ and $ f $ ( $ 1<=n<=500 $ , $ 1<=h<=10 $ , $ h&lt;f<=1000 $ ). Next, $ n $ lines contain two integers each $ l_{i} $ , $ r_{i} $ ( $ -5000<=l_{i}&lt;r_{i}<=5000 $ ), each entry indicates two segments. Endpoints of the first segment are $ (l_{i},h) $ - $ (r_{i},h) $ , and endpoints of the second segment are $ (l_{i},-h) $ - $ (r_{i},-h) $ . These segments describe location of windows. Numbers in the lines are space-separated. It is guaranteed that no two distinct segments have common points.

输出格式

Print the single real number — the area of the illuminated part of the floor with an absolute or relative error of no more than $ 10^{-4} $ .

输入输出样例

输入样例 #1

1 1 2
-1 1

输出样例 #1

10.0000000000

输入样例 #2

2 2 4
-1 0
1 2

输出样例 #2

23.3333333333

说明

The second sample test is shown on the figure. Green area is the desired area of the illuminated part of the floor. Violet segments indicate windows.