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.

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.