CF82E.Corridor

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.

考虑一个房屋的平面图。

设该房屋由满足不等式 $-h \le y \le h$ 的无限水平条带表示。房屋外部（严格在条带之外）有两个光源，分别位于点 $(0, f)$ 和 $(0, -f)$。窗户位于墙壁上，即分别位于直线 $y = h$ 和 $y = -h$ 上的线段；此外，这些窗户关于直线 $y = 0$ 对称。

你的任务是求出房屋地板（即条带内部区域）中被光源照亮部分的面积。

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.

输入文件的第一行包含三个整数 $n$、$h$ 和 $f$（$1 ≤ n ≤ 500$，$1 ≤ h ≤ 10$，$h < f ≤ 1000$）。接下来的 $n$ 行每行包含两个整数 $l_i$、$r_i$（$-5000 ≤ l_i < r_i ≤ 5000$），每对数表示两条线段：第一条线段的端点为 $(l_i,\,h)$–$(r_i,\,h)$，第二条线段的端点为 $(l_i,\,-h)$–$(r_i,\,-h)$。这些线段描述了窗户的位置。每行中的数字以空格分隔。保证任意两条不同的线段之间没有公共点。

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.

输出一个实数——地板被照亮部分的面积，要求绝对或相对误差不超过 $10^{-4}$。

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.

第二个样例测试如图所示。绿色区域为地板上被照亮部分的期望面积。紫色线段表示窗户。