Once an ACM programmer was driving along a highway. The road was very
smooth and straight, no pits, no bumps, no turns miles and miles forward.
In short, boring! So the programmer decided to view billboards along
the highway. One billboard was so interesting that the programmer wanted
to examine it properly. But without a computer he found it difficult to
determine the point with the maximal viewing angle.
We regard the billboard as a segment on a plane and assume that the road is represented by the abscissa axis. The input consists of four lines with numbers x1, y1, x2, y2, which are the coordinates of the billboard's edges. The numbers are integers in the range from −1000 to 1000. Billboard's edges are not coincide.
You should output the value (in radians) of the best viewing angle
of the billboard from the road within 6 digits after the decimal point.
Problem Author: Alexey Lakhtin
Problem Source: The 7th USU Open Personal Contest - February 25, 2006