AQT is studying circles and he has encountered the following problem. Two circles and have their centres located at on a coordinate plane. Circle and have radii and , respectively. AQT decides to add another circle with radius and a centre that is located at , where and are real numbers. The location of circle is random but it follows the condition that it is completely inside circle . Formally, . A position of circle is called valid if the circumference of circle has intersection points with the circumference of circle . AQT wants to know the probability that the position of circle is valid. AQT is given of these problems. Can you help AQT solve all of them?

#### Constraints

In all subtasks,

It is guaranteed that , , and are integers.

##### Subtask 1 [10%]

##### Subtask 2 [15%]

##### Subtask 3 [75%]

No additional constraints.

#### Input Specification

The first line contains , the number of problems you need to help AQT solve.

The next lines each contain the radii of the three circles: , , and .

#### Output Specification

Output lines. In the -th line, output the answer to the -th problem. Your answer will be considered correct if it differs from the correct answer by at most .

#### Sample Input

```
2
2 3 1
5 10 2
```

#### Sample Output

```
0.25
0.375
```

#### Explanation

For the first test case, circle and are represented by the blue circle and the red circle, respectively. The green circles represent possible valid positions for circle .

**valid**centres for circle and has an area of

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