Solve the programming task below in a Python markdown code block.
Write a program which prints the central coordinate $(p_x, p_y)$ and the radius $r$ of a circumscribed circle of a triangle which is constructed by three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$ on the plane surface.

Constraints

* $-100 \leq x_1, y_1, x_2, y_2, x_3, y_3 \leq 100$
* $ n \leq 20$

Input

Input consists of several datasets. In the first line, the number of datasets $n$ is given. Each dataset consists of:

$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$

in a line. All the input are real numbers.

Output

For each dataset, print $p_x$, $p_y$ and $r$ separated by a space in a line. Print the solution to three places of decimals. Round off the solution to three decimal places.

Example

Input

1
0.0 0.0 2.0 0.0 2.0 2.0


Output

1.000 1.000 1.414