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)

gets
ARGF.each_line do |line|
  x1, y1, x2, y2, x3, y3 = line.split.map(&:to_i)
  
  px = -((y2-y1)*y3**2+(-y2**2+y1**2-x2**2+x1**2)*y3+y1*y2**2+(-y1**2+x3**2-x1**2)*y2+(x2**2-x3**2)*y1)/((2*x2-2*x1)*y3+(2*x1-2*x3)*y2+(2*x3-2*x2)*y1)
  py = ((x2-x1)*y3**2+(x1-x3)*y2**2+(x3-x2)*y1**2+(x2-x1)*x3**2+(x1**2-x2**2)*x3+x1*x2**2-x1**2*x2)/((2*x2-2*x1)*y3+(2*x1-2*x3)*y2+(2*x3-2*x2)*y1)
  r = Math.sqrt((px - x1)**2 + (py - y1)**2)
  puts [sprintf("%#.04g", (px * 1000).round / 1000.0) , sprintf("%#.04g", (py * 1000).round / 1000.0), sprintf("%#.04g", (r * 1000).round / 1000.0)].join("\s")
end