## Task Description

You are given three circles, \( C_1, C_2 \), and \( C_3 \). The center of \( C_1 \) is at \( (x_1, y_1) \), and its radius is \( r_1 \). The centers and radius of \( C_2 \) and \( C_3 \) are defined similarly. A point $(x, y)$ is within a circle if its distance is less than or equal to the radius of the circle. For example, Both $(1, 0)$ and $(0, 0)$ are within the circle that centered at $(0, 0)$ and has radius 1. Now given the centers and radius of the three circles, please find the number of points $(x, y)$ where both $x$, and $y$ are integers, that are within odd number of circles. Note that the circles can overlap arbitrarily, however, the radius is no more than 10. As a result you must be careful about how to test points, so that your program will run fast, and without doing unnecessary testing.

## Input format

The first line of the input is the number of input cases. Each input case has three lines and each line has the $x$, $y$, coordinates of a circle, followed by the radius. The radius is no more than 10.

## Output format

For each test case output the number of points $(x, y)$ where both $x$, and $y$ are integers, that are within odd number of circles.

## Sample input

`2`

`0 0 1`

`0 0 2`

`2 0 1`

`0 0 1`

`1000000 0 1`

`0 1000000 1`

## Sample output

`11`

`15`