Problem:
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Circumscribed Circle of A Triangle.

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

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.

Constraints

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

$ n \leq 20$

Sample Input

1
0.0 0.0 2.0 0.0 2.0 2.0

Output for the Sample Input

1.000 1.000 1.414

Solution in PHP (judge verdict: Wrong Answer)

<?php

fscanf(STDIN, '%d', $n);
for ($i = 0; $i < $n; $i++) {
    fscanf(STDIN, '%f %f %f %f %f %f', $x1, $y1, $x2, $y2, $x3, $y3);
    $A1 = 2 * ($x2 - $x1);
    $B1 = 2 * ($y2 - $y1);
    $C1 = pow($x1, 2) - pow($x2, 2) + pow($y1, 2) - pow($y2, 2);
    $A2 = 2 * ($x3 - $x1);
    $B2 = 2 * ($y3 - $y1);
    $C2 = pow($x1, 2) - pow($x3, 2) + pow($y1, 2) - pow($y3, 2);

    $a = sqrt(pow($x2 - $x1, 2) + pow($y2 - $y1, 2));
    $b = sqrt(pow($x3 - $x2, 2) + pow($y3 - $y2, 2));
    $c = sqrt(pow($x1 - $x3, 2) + pow($y1 - $y3, 2));

    $x = ($B1 * $C2 - $B2 * $C1) / ($A1 * $B2 - $A2 * $B1);
    $y = ($C1 * $A2 - $C2 * $A1) / ($A1 * $B2 - $A2 * $B1);
    $r = $a / (2 * $b / $c);
    $x = round($x * 1000) / 1000;
    $y = round($y * 1000) / 1000;
    $r = round($r * 1000) / 1000;

    printf("%.3f %.3f %.3f\n", $x, $y, $r);
}