Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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', $n);
for ($count = 0; $count < $n; $count++) {
    fscanf(STDIN, '%f %f %f %f %f %f', $x1, $y1, $x2, $y2, $x3, $y3);
    $a = sqrt(($x1 - $x2) * ($x1 - $x2) + ($y1 - $y2) * ($y1 - $y2));
    $b = sqrt(($x3 - $x2) * ($x3 - $x2) + ($y3 - $y2) * ($y3 - $y2));
    $c = sqrt(($x1 - $x3) * ($x1 - $x3) + ($y1 - $y3) * ($y1 - $y3));
    $R = $a * $b * $c / sqrt(($a + $b + $c) * (- $a + $b + $c) * ($a - $b + $c) * ($a + $b - $c));
    $s = array();
    $s[] = $x2 - $x1;
    $s[] = $y2 - $y1;
    $s[] = ($x2 * $x2 - $x1 * $x1 + $y2 * $y2 - $y1 * $y1) / 2;
    $t = array();
    $t[] = $x3 - $x1;
    $t[] = $y3 - $y1;
    $t[] = ($x3 * $x3 - $x1 * $x1 + $y3 * $y3 - $y1 * $y1) / 2;

    if ($s[0] === 0) {
        $tmp = $s;
        $s = $t;
        $t = $tmp;
    }
    echo PHP_EOL;
}