A8093 | Corridor

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.

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

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.