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;

class Main {

	public static void main(String[] args) {

		Scanner sc = null;
		try {
			sc = new Scanner(System.in);
			int dataset = sc.nextInt();

			for (int i = 1; i <= dataset; i++) {

				// ??????(px,py)?????§?¨?????±?????????¢??°???????????????

				// ??????r????±?????????¢??°???????????????

				// ??????????????????????????????
			}

		} finally {
			sc.close();
		}
	}

	// ??????????±?????????¢??°
	public static double[] calcCircumcenter() {

		// AB
		// ??????????±???????
		// ??????????±???????

		// BC
		// ??????????±???????
		// ??????????±???????

		// AB??¨BC??§px????±???????
		// px????????£???py????±???????

		// ??§?¨?px,py?????????
		return null;

	}

	// ??????????±?????????¢??°
	public static double calcRadius() {

		// A?????§?¨????pxpy?????????
		// r?????????
		return 0.0;
	}

	// ??????????±?????????¢??°
	public static double calcMidpoint() {
		return 0.0;
	}

	// ??????????±?????????¢??°
	public static double calcSlope() {
		return 0.0;
	}

}