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.io.*;

public class Main {

    public static void main(String[] args){
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        try{
            String st = br.readLine();
            int n = Integer.parseInt(st);
            for(int i = 0;i<n;i++){
                st = br.readLine();
                String[] s = st.split(" ", 0);
                double x1=Double.parseDouble(s[0]);
                double y1=Double.parseDouble(s[1]);
                double x2=Double.parseDouble(s[2]);
                double y2=Double.parseDouble(s[3]);
                double x3=Double.parseDouble(s[4]);
                double y3=Double.parseDouble(s[5]);
                double A = 2*(x1-x2);
                double B = 2*(y1-y2);
                double C = (x1*x1-x2*x2)+(y1*y1-y2*y2);
                double D = 2*(x1-x3);
                double E = 2*(y1-y3);
                double F = (x1*x1-x3*x3)+(y1*y1-y3*y3);
                double px= Math.round(((B*F-C*E)/(B*D-A*E))*1000)/1000.0;
                double py= Math.round(((C*D-A*F)/(B*D-A*E))*1000)/1000.0;
                double r = Math.round((Math.sqrt(Math.pow(px-x1, 2)+Math.pow(py-y1, 2)))*1000)/1000.0;
                System.out.printf("%.3f %.3f %.3f",px,py,r);
            }
        }catch(IOException e){
            
        }
    }
}