B"Monocarp tries to get home from work. He is currently at the point O = (0, 0) of a two-dimensional plane; his house is at the point P = (P_x, P_y) . Unfortunately, it is late in the evening, so it is very dark. Monocarp is afraid of the darkness. He would like to go home along a path illuminated by something. Thankfully, there are two lanterns, located in the points A = (A_x, A_y) and B = (B_x, B_y) . You can choose any non-negative number w and set the power of both lanterns to w . If a lantern's power is set to w , it illuminates a circle of radius w centered at the lantern location (including the borders of the circle). You have to choose the minimum non-negative value w for the power of the lanterns in such a way that there is a path from the point O to the point P which is completely illuminated. You may assume that the lanterns don't interfere with Monocarp's movement. The first line of the input contains one integer t ( 1 <= t <= 10^4 ) -- the number of test cases. Each test case consists of three lines: Additional constraint on the input: For each test case, print the answer on a separate line -- one real number equal to the minimum value of w such that there is a completely illuminated path from the point O to the point P . Your answer will be considered correct if its absolute or relative error does not exceed 10^{-6} -- formally, if your answer is a , and the jury's answer is b , your answer will be accepted if dfrac{|a - b|}{ max(1, b)} <= 10^{-6} . "...