### Problem Statement

You are given the coordinates of several vertices in space. Each vertex is colored 'R', 'G' or 'B'. You are to determine the maximum possible area of a triangle such that all three of its vertices are the same color, or all three of its vertices are different colors.

You are given a String[] points describing the vertices. Each element of points will be in the form "color x y z", where color is 'R', 'G', or 'B', and x, y, z are integers with no leading zeroes.

### Definition

 Class: FindTriangle Method: largestArea Parameters: String[] Returns: double Method signature: double largestArea(String[] points) (be sure your method is public)

### Notes

-A triangle with all three vertices colinear, or two vertices overlapping, has area 0.
-Returned value must be within 1.0e-9 absolute or relative error.

### Constraints

-points will have between 5 and 50 elements, inclusive.
-Each element of points will be formatted as "color x y z" (quotes added for clarity).
-Each color will be 'R', 'G', or 'B'.
-Each x, y and z will be an integer between 0 and 999, inclusive, with no leading zeros.

### Examples

0)

 ```{"R 0 0 0", "R 0 4 0", "R 0 0 3", "G 92 14 7", "G 12 16 8"}```
`Returns: 6.0`
 The coloring restrictions mean that we can only consider the first three points, which form a classic 3-4-5 triangle with an area of 6.
1)

 ```{"R 0 0 0", "R 0 4 0", "R 0 0 3", "G 0 5 0", "B 0 0 12"}```
`Returns: 30.0`
 Our bet here is to take the red point at the origin, the green point, and the blue point. These actually form a 5-12-13 triangle. Area = 30.
2)

 ```{"R 0 0 0", "R 0 4 0", "R 0 0 3", "R 90 0 3", "G 2 14 7", "G 2 18 7", "G 29 14 3", "B 12 16 8"}```
`Returns: 225.0`
 We have a lot more choices here.
3)

 ```{"R 0 0 0", "R 1 1 0", "R 4 4 0", "G 10 10 10", "G 0 1 2"} ```
`Returns: 0.0`
 All three red points are colinear.

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=5943

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=9809&pm=5943

timmac

#### Testers:

PabloGilberto , brett1479 , Olexiy

#### Problem categories:

Brute Force, Geometry, Math