## Introduction

Let’s say that we have 2 circles in 2D space, as shown below:

Given the coordinates of centers of the circle and the length of the radii, find the area of the region that is covered by one or both circles.

**Input:**

The first line contains an integer D, the number of test cases. The following D lines each contain 6 positive integers: x_{1}, y_{1}, x_{2}, y_{2}, r_{1}, and r_{2}, respectively.

**Output:**

For each test case, output a line containing the area of the region described above to the nearest thousandth.

## Sample Input

```
2
0 0 5 5 10 10
31 67 50 20 50 50
```

## Sample Output

```
452.576
12697.102
```