Rectangle Puzzle

题意翻译

## 题目背景 一个平面上有两个矩形。 ## 题目描述 两个矩形的中心都位于坐标轴原点(即矩形对称的中心)。 第一个矩形的边与坐标轴平行,与$x$轴平行的边的长度等于$w$,与$y$轴平行的边的长度等于$h$。 第二个矩形可以通过用角度$α$相对于坐标原点旋转第一个矩形来获得。 请你求出两个矩形的重叠面积(图中阴影面积) ![](https://cdn.luogu.org/upload/vjudge_pic/CF280A/052b43ecd665cd6e4ffd3e118c46f92dcd4eb612.png)

题目描述

You are given two rectangles on a plane. The centers of both rectangles are located in the origin of coordinates (meaning the center of the rectangle's symmetry). The first rectangle's sides are parallel to the coordinate axes: the length of the side that is parallel to the $ Ox $ axis, equals $ w $ , the length of the side that is parallel to the $ Oy $ axis, equals $ h $ . The second rectangle can be obtained by rotating the first rectangle relative to the origin of coordinates by angle $ α $ . ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF280A/052b43ecd665cd6e4ffd3e118c46f92dcd4eb612.png)Your task is to find the area of the region which belongs to both given rectangles. This region is shaded in the picture.

输入输出格式

输入格式


The first line contains three integers $ w,h,α $ $ (1<=w,h<=10^{6}; 0<=α<=180) $ . Angle $ α $ is given in degrees.

输出格式


In a single line print a real number — the area of the region which belongs to both given rectangles. The answer will be considered correct if its relative or absolute error doesn't exceed $ 10^{-6} $ .

输入输出样例

输入样例 #1

1 1 45

输出样例 #1

0.828427125

输入样例 #2

6 4 30

输出样例 #2

19.668384925

说明

The second sample has been drawn on the picture above.