Corridor

2000ms

262144K

Description:

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.

$\text{[math]}$

Input:

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.

Output:

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.

Sample Input:

1 1 2
-1 1

Sample Output:

10.0000000000

Sample Input:

2 2 4
-1 0
1 2

Sample Output:

23.3333333333

Note:

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.

Informação

Provedor Codeforces

Código CF82E