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)

n = gets.to_i
n.times do
  line = gets
  s = line.split(" ").map(&:to_f)
  a1 = 2 * (s[2] - s[0])
  a2 = 2 * (s[4] - s[0])
  b1 = 2 * (s[3] - s[1])
  b2 = 2 * (s[5] - s[1])
  c1 = s[0] * s[0] - s[2] * s[2] + s[1] * s[1] - s[3] * s[3]
  c2 = s[0] * s[0] - s[4] * s[4] + s[1] * s[1] - s[5] * s[5]
  x = (b1 * c2 - b2 * c1) / (a1 * b2 - a2 * b1)
  y = (c1 * a2 - c2 * a1) / (a1 * b2 - a2 * b1)
  r = Math.sqrt((x - s[0]) * (x - s[0]) + (y - s[1]) * (y - s[1]))
  printf("%.3f %.3f %.3f\n", x, y, r)
end