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)

gets.to_i.times{
	x1,y1,x2,y2,x3,y3 = gets.split.map(&:to_f)
	a,b,c,d,e,f = 2*(x1-x2), 2*(y1-y2), x1**2+y1**2-x2**2-y2**2, 2*(x1-x3), 2*(y1-y3), x1**2+y1**2-x3**2-y3**2
	x = (b*f-c*e)/(b*d-a*e)
	y = (c*d-a*f)/(b*d-a*e)
	puts "#{sprintf("%.3f %.3f %.3f",x,y,((x-x1)**2+(y-y1)**2)**0.5)}"
}