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)

n = STDIN.gets.chomp.to_i

n.times do 
  x1, y1, x2, y2, x3, y3 = STDIN.gets.chomp.split(" ").map { |item| item.to_f }
  a1 = 2*(x2-x1)
  a2 = 2*(x3-x1)
  b1 = 2*(y2-y1)
  b2 = 2*(y3-y1)
  c1 = x1*x1-x2*x2+y1*y1-y2*y2
  c2 = x1*x1-x3*x3+y1*y1-y3*y3
  xp = (b1*c2-b2*c1)/(a1*b2-a2*b1)
  yp = (c1*a2-c2*a1)/(a1*b2-a2*b1)
  r  = Math.sqrt((xp-x1)*(xp-x1)+(yp-y1)*(yp-y1))
  puts "#{xp.round(3)} #{yp.round(3)} #{r.round(3)}"
end