300434: CF82E. Corridor

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

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. ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF82E/d6b466d23d4cb893e131b9c90757dc6525b591d2.png)

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.

Input

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