### Problem Statement

You have a large square box and some smaller triangular boxes (all two-dimensional). The triangular boxes all lie inside the square box. Triangular boxes may lie inside other triangular boxes, but they must not overlap. You randomly throw an object (represented as a point) into the square box, and you want to know if it lands inside exactly inBox triangular boxes.

You are given a String[] boxes, each element of which is formatted as "X1.Y1 X2.Y2 X3.Y3" (quotes for clarity only), representing the three corners of a triangular box. The large square box has sides parallel to the axes, and has corners at (0, 0) and (100, 100). Return the probability (between 0 and 1) that a random point within the square is contained in exactly inBox triangular boxes.

### Definition

 Class: SetOfBoxes Method: countThrow Parameters: String[], int Returns: double Method signature: double countThrow(String[] boxes, int inBox) (be sure your method is public)

### Notes

-Your return value must have an absolute or relative error less than 1e-9.

### Constraints

-boxes will contain between 0 and 50 elements, inclusive.
-Each element of boxes will be formatted as "X1.Y1 X2.Y2 X3.Y3" (quotes for clarity only).
-X1, Y1, X2, Y2, X3, Y3 will be integers with no leading zeros, each between 0 and 100, inclusive.
-Triangles represented by different elements of boxes will have no common points.
-inBox will be between 0 and 50, inclusive.

### Examples

0)

 `{"0.0 1.0 0.1"}` `1`
`Returns: 5.0E-5`
1)

 `{"0.0 20.0 0.10", "1.1 6.1 1.5"}` `1`
`Returns: 0.0090`
 Here it is the area of the first triangle minus the area of the second one.
2)

 `{"0.0 10.0 0.20", "0.100 0.90 20.100", "50.50 60.60 50.70", "51.55 55.60 51.65"}` `1`
`Returns: 0.028`
3)

 `{"0.0 10.0 0.20", "0.100 0.90 20.100", "50.50 60.60 50.70", "51.55 55.60 51.65"}` `0`
`Returns: 0.97`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=6596

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=10067&pm=6596

Vedensky

#### Testers:

PabloGilberto , brett1479 , Olexiy

#### Problem categories:

Geometry, Graph Theory, String Parsing