Codeforces Round 172 (Div. 1)
A
Rectangle Puzzle
Codeforces
2000
原题
←B →
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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 $α$.

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image

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Your task is to find the area of the region which belongs to both given rectangles. This region is shaded in the picture.

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Input

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

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Output

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In a single line print a real number — the area of the region which belongs to both given rectangles.

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The answer will be considered correct if its relative or absolute error doesn't exceed $10^{ - 6}$.

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Note

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The second sample has been drawn on the picture above.

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样例

Input #1
1 1 45
Output #1
0.828427125
InputCopy OutputCopy
Input #2
6 4 30
Output #2
19.668384925
InputCopy OutputCopy
题目信息
题号
280A
时间限制
2 s
内存限制
256 MB
标签
计算几何

题面与样例版权归 Codeforces 及出题人所有;中文翻译由 AI 生成(CI 管线),如有出入请以原文为准。