Laser Shooting
There is a laser cannon at coordinates (0, 0) on the cartesian plane. There are also several targets on the plane. Each target is a vertical line segment, and the endpoints of the i-th target are at coordinates (x_i, y1_i) and (x_i, y2_i). A random angle between -PI/2 and PI/2, inclusive, is chosen, and a single shot is fired. The angle -PI/2 is straight down vertically, 0 is straight to the right horizontally, and PI/2 is straight up vertically. A shot is a straight ray of infinite length starting from the point (0, 0). A shot hits a target if there is a common point between them.
Find the expected number of targets that will be hit by the single shot. Hitting a target doesn't change the direction of the laser shot.
Input
Consists of multiple tests cases. The first line of each test case contains the number of targets n (1 ≤ n ≤ 50). Next thee line describe the targets coordinates. The i-th number of the second line of each test case contains the value of x_i, the i-th number of the third line contains the value of y1_i, the i-th number of the fourth line of each test case contains the value of y2_i. It is known that all the coordinates are integers, the values x_i are different, 1 ≤ x_i ≤ 1000, -1000 ≤ y1_i, y2_i ≤ 1000.
Output
For each test case print in a separate line with 4 digits after the decimal point the expected number of targets that will be hit by the single shot.