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 do
  x1, y1, x2, y2, x3, y3 = gets.split.map(&:to_f)

  # http://www.h6.dion.ne.jp/~jpe02_tn/ki-5.html
  a1 = 2*(x2 - x1)
  b1 = 2*(y2 - y1)
  c1 = x1**2 - x2**2 + y1**2 - y2**2
  a2 = 2*(x3 - x1)
  b2 = 2*(y3 - y1)
  c2 = x1**2 - x3**2 + y1**2 - y3**2
  x = (b1*c2 - b2*c1) / (a1*b2 - a2*b1)
  y = (c1*a2 - c2*a1) / (a1*b2 - a2*b1)

  # http://keisan.casio.jp/exec/system/1161228797
  a = Math.sqrt((x2-x1)**2 + (y2-y1)**2)
  b = Math.sqrt((x3-x2)**2 + (y3-y2)**2)
  c = Math.sqrt((x1-x3)**2 + (y1-y3)**2)
  s = (a+b+c) / 2
  r = (a*b*c) / (4*Math.sqrt(s*(s-a)*(s-b)*(s-c)))

  puts "#{'%.3f'%x} #{'%.3f'%y} #{'%.3f'%r}"
end