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 Scala (judge verdict: Wrong Answer)

import scala.io.StdIn.{readInt,readLine}

object Main{
    def main(args:Array[String]) = {
        val n = readInt
         for(i <- 0 until n) {
            val p = readLine.split(" ").map(_.toDouble)
            val (xa,ya) = (0,0)
            val (xb,yb) = (p(2)-p(0),p(3)-p(1))
            val (xc,yc) = (p(4)-p(0),p(5)-p(1))
            val d = 2*(xb*yc-yb*xc)
            val x = (yc*(xb*xb+yb*yb) - yb*(xc*xc+yc*yc))/d
            val y = (xb*(xc*xc+yc*yc) - xc*(xb*xb+yb*yb))/d
            printf("%.3f %.3f %.3f\n",x + xa,y + ya,Math.sqrt(x*x+y*y))

        }
    }
}