402900: GYM100942 A Three seamarks

The "Victory" ship sailed away from the shore to participate in an international regatta. Having no positioning device onboard the ship went off the course and got lost in the seas. Luckily, the captain could see three seamarks through his binoculars with their coordinates known. As everyone knows, binoculars make it is possible not only to observe the objects, but also measure their angular sizes, i.e angles between straight lines connecting objects' corner points with an observing eye. For example, if two seamarks are located at points M₁ and M₂, and the ship is at point K, then the angular size of segment M₁M₂ is an angle M₁KM₂.

You need to find the ship's coordinates by given angular sizes of two segments connecting seamarks M₁ and M₂, M₂ and M₃.

The first line contains an integer n — number of possible locations of the seamarks (1 ≤ n ≤ 50 000). Each of the next n lines contains eight integers. The first six integers describe Cartesian coordinates of different points M₁, M₂, M₃ that do not exceed 10 000 by absolute value; the next two integers from the range [1; 179] are angular sizes (in degrees) of segments M₁M₂ and M₂M₃. It is guaranteed that the solution exists for each of the test cases.

For each location of the seamarks output coordinates of any possible ship position separated by space in a separate line. The answer will be considered correct if its absolute or relative error does not exceed 10^- 6.

1
0 0 2 0 2 2 90 90

1.0000000000 1.0000000000