Brocard Point

Time limit2sMemory limit512 MB

Summary

Given the coordinates of a triangle's vertices in anticlockwise order, compute the coordinates of its Brocard point and print them to five decimal places.

Level: Medium7 of 10
Topics: Geometry, Math, Implementation, Brute force
Solved: No attempts yet

Problem

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.

Input

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.

Output

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.

Examples2

Example 1

Input

3
0 -1.3 3.4 0.5 1.1 2.3
0 0 3 0 0 4
3.1 0.2 4.3 0.4 0 0.8

Expected output

1.40456 0.82890
1.56047 0.74902
3.87699 0.40167

Example 2

Input

2
-2 -1.373127 5 -1.873127 1 3.626873
0 0 6 0 3 2

Expected output

0.90164 0.00000
2.18824 0.84706