### 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 i-th 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`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=8265

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=10807&pm=8265

timmac

#### Testers:

PabloGilberto , brett1479 , Olexiy , ivan_metelsky

#### Problem categories:

Brute Force, Geometry