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.
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.
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.
1 0.0 0.0 2.0 0.0 2.0 2.0
1.000 1.000 1.414