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 = gets.to_i
 
n.times do
    x1, y1, x2, y2, x3, y3 = gets.split.map(&:to_f)
 
    px = 0.5 * ((x1 ** 2 + y1 ** 2) * (y2 - y3) + (x2 ** 2 + y2 ** 2) * (y3 - y1) + (x3 ** 2 + y3 ** 2) * (y1 - y2)) / (x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)) 
    py = 0.5 * ((x1 ** 2 + y1 ** 2) * (x2 - x3) + (x2 ** 2 + y2 ** 2) * (x3 - x1) + (x3 ** 2 + y3 ** 2) * (x1 - x2)) / (y1 * (x2 - x3) + y2 * (x3 - x1) + y3 * (x1 - x2))
 
    r = ((x1 - px) ** 2 + (y1 - px) ** 2) ** 0.5
 
    puts "%.3f %.3f %.3f" % [px, py, r]
end