### Problem Statement

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. Return 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.

### Definition

 Class: LaserShooting Method: numberOfHits Parameters: int[], int[], int[] Returns: double Method signature: double numberOfHits(int[] x, int[] y1, int[] y2) (be sure your method is public)

### Notes

-A return value with either an absolute or relative error of less than 1.0e-9 is considered correct.

### Constraints

-x will contain between 1 and 50 elements, inclusive.
-All elements of x will be distinct.
-x, y1 and y2 will contain the same number of elements.
-Each element of x will be between 1 and 1,000, inclusive.
-Each element of y1 and y2 will be between -1,000 and 1,000, inclusive.
-All targets will have positive lengths.

### Examples

0)

 `{1}` `{-1}` `{1}`
`Returns: 0.5`
 The only one target will be hit with probability 1/2.
1)

 `{1,2}` `{-1,-2}` `{1,2}`
`Returns: 1.0`
 Both targets will be hit with probability 1/2.
2)

 `{3,4,7,1}` `{1,2,3,4}` `{4,3,2,1}`
`Returns: 0.4623163952488826`
3)

 `{134,298,151,942}` `{-753,-76,19,568}` `{440,689,-39,672}`
`Returns: 1.444210260641501`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=10258

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=13522&pm=10258

Gluk

#### Testers:

PabloGilberto , Olexiy , ivan_metelsky

Brute Force