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.Scanner;
public class Main {

	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		for(int i = 0; i < n; i++) {
			double x1 = s.nextDouble();
			double y1 = s.nextDouble();
			double x2 = s.nextDouble();
			double y2 = s.nextDouble();
			double x3 = s.nextDouble();
			double y3 = s.nextDouble();
			
			double a1 = 2 * (x2 - x1);
			double b1 = 2 * (y2 - y1);
			double c1 = 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 x = (b1*c2 - b2*c1)/(a1*b2 - a2*b1);
			double y = (c1*a2 - c2*a1)/(a1*b2 - a2*b1);
			
			double l = Math.sqrt((x - x1) * (x - x1) + (y - y1) * (y - y1));
			if(x == -0.0) {
				x = 0.0;
			}
			if(y == -0.0) {
				y = 0.0;
			}
			if(l == -0.0) {
				l = 0.0;
			}
			
			System.out.printf("%.3f %.3f %.3f",x,y,l);
		}
	}
}