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.{readLine,readInt}
import scala.math.BigDecimal

object Main {
    def round(x:Double) =  {
      val y = x % 0.001
      if(y >= 0.0005) (x-y) + 0.001 else x-y
    }

    def main(args:Array[String]) = {
        val n = readInt
         for(i <- 0 until n) {
            val m = readLine.split(" ").map(_.toDouble)
            val (x12,y12,x13,y13) = (m(0)-m(2),m(1)-m(3),m(0)-m(4),m(1)-m(5))
            val (xx1,yy1,xx2,yy2,xx3,yy3) = (m(0)*m(0),m(1)*m(1),m(2)*m(2),m(3)*m(3),m(4)*m(4),m(5)*m(5))
            val g = 2*(x12*y13 - y12*x13)
            val x = (y13*(xx1 - xx2 + yy1 - yy2) - y12*(xx1 - xx3 + yy1 - yy3))/g
            val y = (x12*(xx1 - xx3 + yy1 - yy3) - x13*(xx1 - xx2 + yy1 - yy2))/g

            printf("%.3f %.3f %.3f\n",round(x),round(y),round(Math.sqrt(x*x+y*y)))
        }
    }
}