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.
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## 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.
[samples]
## 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.
考虑一个房屋平面图。
设房屋由不等式 $-h \leq y \leq h$ 定义的无限水平条带表示。在房屋外部严格之外，有两个光源位于点 $(0, f)$ 和 $(0, -f)$。窗户位于墙壁上，窗户由位于直线 $y = h$ 和 $y = -h$ 上的线段表示。此外，窗户关于直线 $y = 0$ 对称排列。
你的任务是求出房屋地板上被光源照亮的区域面积。
输入文件的第一行包含三个整数 $n$、$h$ 和 $f$（$1 \leq n \leq 500$，$1 \leq h \leq 10$，$h < f \leq 1000$）。接下来的 $n$ 行每行包含两个整数 $l_i$、$r_i$（$-5000 \leq l_i < r_i \leq 5000$），每条记录表示两个线段。第一个线段的端点为 $(l_i, h)$ 到 $(r_i, h)$，第二个线段的端点为 $(l_i, -h)$ 到 $(r_i, -h)$。这些线段描述了窗户的位置。行中的数字以空格分隔。保证任意两个不同的线段没有公共点。
输出一个实数——被照亮的地板部分的面积，绝对误差或相对误差不超过 $10^{-4}$。
第二个样例测试如图所示。绿色区域为所求的被照亮地板面积。紫色线段表示窗户。
## Input
输入文件的第一行包含三个整数 $n$、$h$ 和 $f$（$1 \leq n \leq 500$，$1 \leq h \leq 10$，$h < f \leq 1000$）。接下来的 $n$ 行每行包含两个整数 $l_i$、$r_i$（$-5000 \leq l_i < r_i \leq 5000$），每条记录表示两个线段。第一个线段的端点为 $(l_i, h)$ 到 $(r_i, h)$，第二个线段的端点为 $(l_i, -h)$ 到 $(r_i, -h)$。这些线段描述了窗户的位置。行中的数字以空格分隔。保证任意两个不同的线段没有公共点。
## Output
输出一个实数——被照亮的地板部分的面积，绝对误差或相对误差不超过 $10^{-4}$。
[samples]
## Note
第二个样例测试如图所示。绿色区域为所求的被照亮地板面积。紫色线段表示窗户。
**Definitions**
Let $ n, h, f \in \mathbb{Z} $ with $ 1 \leq n \leq 500 $, $ 1 \leq h \leq 10 $, $ h < f \leq 1000 $.
Let $ W = \{ (l_i, r_i) \mid i \in \{1, \dots, n\} \} $ be a set of $ n $ intervals, each defining a window segment on both top and bottom walls:
- Top window: segment from $ (l_i, h) $ to $ (r_i, h) $
- Bottom window: segment from $ (l_i, -h) $ to $ (r_i, -h) $
Two point light sources are located at $ (0, f) $ and $ (0, -f) $.
The house is the infinite horizontal strip $ \mathcal{H} = \{ (x, y) \in \mathbb{R}^2 \mid -h \leq y \leq h \} $.
**Constraints**
1. All $ l_i, r_i \in \mathbb{Z} $, $ -5000 \leq l_i < r_i \leq 5000 $
2. For all $ i \neq j $, intervals $ (l_i, r_i) $ and $ (l_j, r_j) $ are disjoint
3. $ h < f $
**Objective**
Compute the area of the region $ \mathcal{I} \subseteq \mathcal{H} $ illuminated by at least one of the two light sources, where illumination occurs via rays passing through the windows.
The illuminated region $ \mathcal{I} $ is the union of:
- The region illuminated by source $ (0, f) $ through the top windows:
$$
\mathcal{I}_+ = \bigcup_{i=1}^n \left\{ (x, y) \in \mathcal{H} \mid \exists t \in [0,1], \; (x, y) = (1-t)(l_i, h) + t(0, f) \text{ or } (x, y) = (1-t)(r_i, h) + t(0, f) \right\}
$$
(i.e., the convex hull of $ (l_i, h), (r_i, h), (0, f) $ intersected with $ \mathcal{H} $)
- The region illuminated by source $ (0, -f) $ through the bottom windows:
$$
\mathcal{I}_- = \bigcup_{i=1}^n \left\{ (x, y) \in \mathcal{H} \mid \exists t \in [0,1], \; (x, y) = (1-t)(l_i, -h) + t(0, -f) \text{ or } (x, y) = (1-t)(r_i, -h) + t(0, -f) \right\}
$$
Then:
$$
\mathcal{I} = \mathcal{I}_+ \cup \mathcal{I}_-
$$
Compute the area:
$$
\text{Area} = \iint_{\mathcal{I}} dx\,dy
$$