Brocard Point

Time Limit: 1 Second    Memory Limit: 65536 KB

Label the vertices of a triangle in anticlockwise order by A, B and C. We know there is exactly one point P inside the triangle ABC such that PAB = PBC = PCA. This point is known as Brocard point.

You are to write a program that gets the coordinates of A, B and C and computes the coordinates of the Brocard point of the triangle ABC.

Input

The first line of the input includes the number of test cases, 1≤t≤10000. Each test case comes in one line containing six space separated real numbers x_A, y_A, x_B, y_B,x_C, y_C.

Output

For each test case, output in one line x-coordinate and y-coordinate of Brocard point rounded to five decimal places.

Sample 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

Sample Output

1.40456 0.82890 
1.56047 0.74902 
3.87699 0.40167 

Submit

Source: 13th Iran Nationwide Internet Contest - Final