# 242. Three Circles

## I'm a slow walker, but I never walk backwards.

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

20 0 10 0 22 0 10 0 11000000 0 10 1000000 1


## Sample output

1115