Problem Statement 
 You wish to build three watchtowers to overlook several points of interest. The points of interest are given in the int[]s x and y, where each element of x and the corresponding element of y represent the coordinates of a single point of interest.
Each of the three watchtowers has a field of view that is the same in all directions. The viewing distance of each of the three watchtowers is given in the int[] view, so the ith watchtower can see all points which are located not further than view[i] units from it. Assuming optimal placement, return the maximum number of points of interest that are within view of at least one of the watchtowers.


Definition 
 Class:  ThreeWatchtowers  Method:  maximumCoverage  Parameters:  int[], int[], int[]  Returns:  int  Method signature:  int maximumCoverage(int[] x, int[] y, int[] view)  (be sure your method is public) 




Notes 
  Even though points of interest are restricted to a given area, the watchtowers themselves may be located outside of that area, and do not necessarily have to be placed on lattice points. 
  A watchtower can see a point exactly on the edge of its field of view. Thus, a watchtower at (0, 0) with a radius of 2 could see a point at (0, 2). 

Constraints 
  x and y will each contain between 1 and 20 elements, inclusive. 
  x and y will each contain the same number of elements. 
  Each element of x and y will be between 0 and 20, inclusive. 
  view will contain exactly 3 elements. 
  Each element of view will be between 1 and 20, inclusive. 

Examples 
0)  
 {0, 10, 20}  {15, 16, 20}  {1, 1, 1} 
 Returns: 3  Even though the watchtowers can't see very far, with only three points of interest, it is trivial to cover them all. 


1)  
 {0, 1, 10, 20, 15, 14}  {1, 0, 10, 20, 18, 12}  {2, 2, 2} 
 Returns: 4  The first two points are close enough together to be covered by a single watchtower. The other points are too spread out, so the other two towers can each only see a single point. 


2)  
 {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}  {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}  {1, 1, 13} 
 Returns: 10  The first two watchtowers are not really needed, since the last one has a wide enough range to see all 10 points at once. 


3)  
 {0, 5, 6, 16, 18, 20}  {0, 6, 7, 20, 20, 20}  {1, 3, 5} 
 Returns: 6  The first watchtower covers the first point. The second watchtower can cover the next two points. The last three points can be covered by the final tower. 


4)  
 {1, 2, 0, 3, 1}  {0, 3, 2, 1, 0}  {1, 1, 1} 
 Returns: 4  

5)  
 {10, 18, 16, 9, 17, 20, 4, 3, 11, 9}  {4, 17, 6, 14, 14, 14, 12, 12, 13, 16}  {1, 1, 2} 
 Returns: 7  
