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 JAVA (judge verdict: Wrong Answer)

import java.util.*;

class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		for(int nn = 0; nn < n; nn++){
			double x1 = sc.nextDouble();
			double y1 = sc.nextDouble();
			double x2 = sc.nextDouble();
			double y2 = sc.nextDouble();
			double x3 = sc.nextDouble();
			double y3 = sc.nextDouble();
			double A = 2*(x2 - x1);
			double B = 2*(y2 - y1);
			double C = (x1*x1)-(x2*x2)+(y1*y1)-(y2*y2);
			double A2 = 2*(x3 - x1);
			double B2 = 2*(y3 - y1);
			double C2 = (x1*x1)-(x3*x3)+(y1*y1)-(y3*y3);
			double px = (B*C2-B2*C)/(A*B2-A2*B);
			double py = (C*A2-C2*A)/(A*B2-A2*B);
			double exe = Math.hypot(x1-px,y1-py);
			System.out.printf("%.3f %.3f %.3f",px,py,exe);
		}
	}
}