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 Python3 (judge verdict: Accepted)

def pp(x):
    if x==0:
        x=0
    return "{0:.3f}".format(round(x,3))


n=int(input())
for i in range(n):
    x1,y1,x2,y2,x3,y3=map(float, input().split())

    a=2*(x2-x1)
    b=2*(y2-y1)
    c=( x2**2 + y2**2 ) - ( x1**2 + y1**2 )
    d=2*(x3-x1)
    e=2*(y3-y1)
    f=( x3**2 + y3**2 ) - ( x1**2 + y1**2 )
    x=(c*e-b*f)/(a*e-b*d)
    y=(a*f-c*d)/(a*e-b*d)
    r=( (x-x1)**2 + (y-y1)**2 )**0.5
 
    print(pp(x), pp(y), pp(r))