Given a point at height zero and a triangle with uniform mass, we use three ropes with length , , and to connect , , and respectively. The mass of the ropes can be ignored. Let the triangle fall naturally and stabilize at the lowest position of the center of gravity. Find the final heights of points , , and .

输入描述:

There are multiple test cases. The first line of the input contains an integer  (about ) indicating the number of test cases. For each test case:

The first and only line contains six integers , , , ,  and  (, , , ) indicating the length of three ropes and the length of ,  and .

You can assume that the solution always exists.

输出描述:

For each test case output one line containing threes real numbers indicating the height of points ,  and .

Your answer will be considered correct if and only if the absolute or relative error does not exceed .

2
1 1 1 1 1 1
2 3 3 1 1 1

-0.816496580927726 -0.816496580927726 -0.816496580927726
-2.000000000000000 -2.866025403784439 -2.866025403784439