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문제

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.

입력

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 xA, yA, xB, yB, xC, yC.

출력

For each test case, output in one line x-coordinate and y0coordinate of Brocard point rounded to five decimal places. 

예제 입력

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

예제 출력

1.40456 0.82890
1.56047 0.74902
3.87699 0.40167

힌트