CF82E.Corridor

普及/提高-

通过率：0%

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题目描述

The first line of the input file contains three integers $n$ , $h$ and $f$ ( $1<=n<=500$ , $1<=h<=10$ , h<f<=1000 ). Next, $n$ lines contain two integers each $l_{i}$ , $r_{i}$ ( -5000<=l_{i}<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.

输入格式

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

输出格式

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.

输入输出样例

输入#1
```
1 1 2
-1 1
```
输出#1
```
10.0000000000
```
输入#2
```
2 2 4
-1 0
1 2
```
输出#2
```
23.3333333333
```

说明/提示

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.

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