Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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)

gets.to_i.times{
	list = []
	a,b,c,d,e,f = gets.split.map(&:to_f)
	aa,bb = a,b
	list << 2*(a-c) << 2*(b-d) << a**2+b**2-c**2-d**2 << 2*(a-e) << 2*(b-f) << a**2+b**2-e**2-f**2
	a,b,c,d,e,f = list
	mul = -a/d
	y = (c+f*mul)/(b+e*mul)
	x = (c-b*y)/a
	puts "#{sprintf("%.3f %.3f %.3f",x+0.0,y+0.0,((x-aa)**2+(y-bb)**2)**0.5+0.0)}"
}