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
while vals = gets
  x1, y1, x2, y2, x3, y3 = vals.split.map(&:to_f)
  a = ( x2 - x1 ) ** 2.0 + ( y2 - y1 ) ** 2.0
  b = ( x3 - x2 ) ** 2.0 + ( y3 - y2 ) ** 2.0
  c = ( x1 - x3 ) ** 2.0 + ( y1 - y3 ) ** 2.0
  s = a * ( b + c - a ) + b * ( c + a - b ) + c * ( a + b - c )
  rx = ( a * ( b + c - a ) * x1 + b * ( c + a - b ) * x2 + c * ( a + b - c ) * x3 ) / s
  ry = ( a * ( b + c - a ) * y2 + b * ( c + a - b ) * y3 + c * ( a + b - c ) * y1 ) / s
  radius = ( ( rx - x1 ) ** 2.0 + ( ry - y1 ) ** 2.0 ) ** 0.5
  printf( "%5.3f %5.3f %5.3f\n", rx, ry, radius )
end