### Problem Statement

Two people are within "shouting distance" if one can hear the other one shout. We have a group of identical people located across the countryside. We want to know how small the shouting distance can be and still allow a message to originate with anyone and be heard by everyone else by a sequence of shouts.

The locations of the people are given by int[]'s x and y, with the location of the i-th person given by the i-th element of x and the i-th element of y. Create a class Shouting that contains a method shout that is given x and y and that returns the smallest shouting distance that will allow complete communication.

### Definition

 Class: Shouting Method: shout Parameters: int[], int[] Returns: double Method signature: double shout(int[] x, int[] y) (be sure your method is public)

### Notes

-The returned value must be accurate to within a relative or absolute value of 1E-9.

### Constraints

-x and y will contain the same number of elements, between 1 and 50 inclusive.
-Each element of x and y will be between -10,000 and 10,000 inclusive.

### Examples

0)

 {-2000,-2000} {3000,3000}
Returns: 0.0
 These two people are standing in the same spot, so there is no need to shout.
1)

 {3,3,3,3,3,3,3} {2,3,4,3,9,8,1}
Returns: 4.0
 These people are standing in a line, and the biggest gap is between (3,4) and (3,8) which can be bridged by a shout of length 4.
2)

 {5,0,-5,0} {0,5,0,-5}
Returns: 7.0710678118654755
 These people are standing in a square. Shouting around the edges of the square is the best way to communicate, and each edge has a length of 5*sqrt(2)
3)

 {17} {1912}
Returns: 0.0

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=3950

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=6551&pm=3950

dgoodman

#### Testers:

PabloGilberto , lbackstrom , vorthys

#### Problem categories:

Brute Force, Graph Theory