A8928 | Rectangle Puzzle

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 $α$ .

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

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

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 $10^{-6}$ .