B" n people live on the coordinate line, the i -th one lives at the point x_i ( 1 <= i <= n ). They want to choose a position x_0 to meet. The i -th person will spend |x_i - x_0| minutes to get to the meeting place. Also, the i -th person needs t_i minutes to get dressed, so in total he or she needs t_i + |x_i - x_0| minutes. Here |y| denotes the absolute value of y . These people ask you to find a position x_0 that minimizes the time in which all n people can gather at the meeting place. The first line contains a single integer t ( 1 <= t <= 10^3 ) -- the number of test cases. Then the test cases follow. Each test case consists of three lines. The first line contains a single integer n ( 1 <= n <= 10^5 ) -- the number of people. The second line contains n integers x_1, x_2, ... , x_n ( 0 <= x_i <= 10^{8} ) -- the positions of the people. The third line contains n integers t_1, t_2, ... , t_n ( 0 <= t_i <= 10^{8} ), where t_i is the time i -th person needs to get dressed. It is guaranteed that the sum of n over all test cases does not exceed 2 cdot 10^5 . For each test case, print a single real number -- the optimum position x_0 . It can be shown that the optimal position x_0 is unique. Your answer will be considered correct if its absolute or relative error does not exceed 10^{ xe2 x88 x926} . Formally, let your answer be a , the jury's answer be b . Your answer will be considered correct if frac{|a xe2 x88 x92b|}{max(1,|b|)} <= 10^{ xe2 x88 x926} . "...