2707. Ground Works

单点时限: 5.0 sec

内存限制: 256 MB

The Hilbert Mole is a small and very rare mole. The first and only specimen was found by David Hilbert at his backyard. This mole lives in a huge burrow under the ground, and the border of this burrow forms a Hilbert curve of n-th order (Hn).

Hilbert curves can be defined as follows. H1 is a unit square with open top side (fig. 1a), Hn consists of four copies of Hn-1: bottom left and bottom right are copied without changes, top left is rotated 90 counter-clockwise and top right is rotated 90 clockwise. These small copies are connected by three segments of unit length (fig. 1b,c,d).

Trying to exterminate the mole, Mr. Hilbert fills the burrow with water (fig. 2). But air inside the burrow prevents water from filling it entirely. In this problem we suppose that air and water are incompressible and cannot leak throw the borders of the burrow. Your task is to find the total area of the burrow, filled with water.

Note that water can flow over the obstacle only when its level is strictly higher. See examples on fig. 3 for further clarification.

输入格式

The first line of the input file contains two integer numbers: n and α ― order of Hilbert curve and slope angle of surface in degrees (1 ≤ n ≤ 12, 0 ≤ α < 90).

输出格式

The first line of the output file must contain a single real number ― the total area of the burrow, filled with water. The relative error of the answer must not exceed 1e-7.

样例

Input
5 30
3 45
4 10
3 0
Output
190.803847577293
15.5
91.573591766702
26.0

2 人解决,2 人已尝试。

2 份提交通过,共有 61 份提交。

8.6 EMB 奖励。

创建: 12 年前.

修改: 2 年,10 月前.

最后提交: 13 小时前.

来源: NEERC 2008

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