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: Wrong Answer)

num = gets()

num.to_i.times{

	dataset = gets()
	strAry = dataset.split(" ")

	#puts(strAry)
	
	x1 = strAry[0].to_f 
	y1 = strAry[1].to_f
	x2 = strAry[2].to_f
	y2 = strAry[3].to_f
	x3 = strAry[4].to_f
	y3 = strAry[5].to_f

	#http://oshiete.goo.ne.jp/qa/7112206.html
	p = ((y1-y3)*(y1**2-y2**2+x1**2-x2**2)-(y1-y2)*(y1**2-y3**2+x1**2-x3**2))/(2*(y1-y3)*(x1-x2)-2*(y1-y2)*(x1-x3))
	q = ((x1-x3)*(x1**2-x2**2+y1**2-y2**2)-(x1-x2)*(x1**2-x3**2+y1**2-y3**2))/(2*(x1-x3)*(y1-y2)-2*(x1-x2)*(y1-y3))

	#http://ja.wikipedia.org/wiki/%E5%A4%96%E6%8E%A5%E5%86%86	
	a =((x2-x1)**2+(y2-y1)**2)**(1/2.0)
	b =((x3-x3)**2+(y3-y2)**2)**(1/2.0)
	c =((x1-x3)**2+(y1-y3)**2)**(1/2.0)

	#r = a*b*c/((a+b+c)*(-a+b+c)*(a-b+c)*(a+b-c))**(1/2.0)
	
	#puts("#{p.round(3)} #{q.round(3)} #{r.round(3)}")
	#puts sprintf("%.3f %.3f %.3f",p,q,r)
}