Laser Shooting#1582
There is a laser cannon located at on the Cartesian plane. There are also several targets on the plane. Each target is a vertical line segment, with endpoints at (x_i, y1_i) and (x_i, y2_i). A random angle between and , inclusive, is chosen, and a single shot is fired. The angle corresponds to shooting vertically downwards, is horizontally to the right, and is vertically upwards. The shot is a ray of infinite length starting from . A target is hit if the shot and the target segment have a common point. Hitting a target does not affect the path of the shot.
Find the expected number of targets that will be hit by a single shot.
The input consists of multiple test cases. The first line of each test case contains the number of targets (1 \leq n \leq 50). The next three lines describe the targets' coordinates. The -th number of the second line contains x_i, the -th number of the third line contains y1_i, and the -th number of the fourth line contains y2_i. All coordinates are integers, all x_i are distinct, 1 \leq x_i \leq 1000, -1000 \leq y1_i, y2_i \leq 1000.
For each test case, print on a separate line the expected number of targets that will be hit by a single shot, with digits after the decimal point.
Example 1