Brocard Point

Label the vertices of a triangle in anticlockwise order as A, B and C. Inside triangle ABC there is exactly one point P with $\angle PAB = \angle PBC = \angle PCA$. That point is called the Brocard point.

Given the coordinates of A, B and C, write a program that computes the coordinates of the Brocard point of triangle ABC.

The first line contains the number of test cases $t$ ($1 \le t \le 10000$).

Each of the next $t$ lines contains six space separated real numbers $x_A$, $y_A$, $x_B$, $y_B$, $x_C$, $y_C$. Every coordinate has absolute value at most $1000$ and at most six digits after the decimal point. The three points are not collinear and are given in anticlockwise order.

For each test case, print the $x$ coordinate and the $y$ coordinate of the Brocard point on one line, separated by a space, each rounded to five decimal places. Always print all five digits after the decimal point. If a rounded coordinate is zero, print 0.00000 with no sign.