Along the palm beaches of Hawaii in the blazing summer are numerous umbrellas. When facing the ocean, the umbrellas appear to be isosceles triangles with one side on the x axis and the other sides will have equal length. Let's take a picture - but before we do that, can you estimate the area of all the umbrellas together?

For this problem, there are umbrellas each with one vertex at and another vertex at . For each umbrella, its third vertex is at . You are tasked with finding the area of the *union* of all the umbrellas (total area, where a region overlapped by *multiple* umbrellas should only be counted once in total).

#### Constraints

#### Input Specification

The first line contains , the number of umbrellas.

The next lines each contain 3 **integers**: , , and , describing the -th umbrella.

#### Output Specification

One *decimal* number, the area of the union of all umbrellas. Your answer will be regarded as correct if it has an absolute or relative error at most

#### Sample Input

```
2
1 5 2
3 11 2
```

#### Sample Output

`11.3333`

#### Sample Explanation

There is a triangle with vertices , and . There is another with vertices , , and . A diagram for the triangles is shown below

We wish to find this area:

Its area is . If you wish to find the area yourself, note that the two triangles intersect at .

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