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.

Input

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

Output

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 $10^{ - 6}$.

Note

The second sample has been drawn on the picture above.