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 Ruby (judge verdict: Accepted)

require 'scanf'

n = gets.to_i
n.times{
    x1, y1, x2, y2, x3, y3 = gets.scanf("%f %f %f %f %f %f ")
    
    dnm = (2*x2*y3-2*x1*y3+(2*x1-2*x3)*y2+(2*x3-2*x2)*y1)
    numx = -(y2*(y3**2-y1**2+x3**2-x1**2)+y1*((-y3**2)-x3**2+x2**2)+y1**2*y3-x2**2*y3+x1**2*y3+y2**2*(y1-y3))
    numy = (x2*(y3**2+x3**2-x1**2)+x1*((-y3**2)-x3**2)+(x1-x3)*y2**2+(x3-x2)*y1**2+x1**2*x3+x2**2*(x1-x3))

    x = numx / dnm
    y = numy / dnm

    r = Math.sqrt( (x1 - x) ** 2 + (y1 - y)**2)

    print "%.3f %.3f %.3f\n" % [x, y, r]

    # p numx, numy, dnm

}