B'There are n houses in your city arranged on an axis at points h_1, h_2, ldots, h_n . You want to build a new house for yourself and consider two options where to place it: points p_1 and p_2 . As you like visiting friends, you have calculated in advance the distances from both options to all existing houses. More formally, you have calculated two arrays d_1 , d_2 : d_{i, j} = <= ft|p_i - h_j right| , where |x| defines the absolute value of x . After a long time of inactivity you have forgotten the locations of the houses h and the options p_1 , p_2 . But your diary still keeps two arrays -- d_1 , d_2 , whose authenticity you doubt. Also, the values inside each array could be shuffled, so values at the same positions of d_1 and d_2 may correspond to different houses. Pay attention, that values from one array could not get to another, in other words, all values in the array d_1 correspond the distances from p_1 to the houses, and in the array d_2 -- from p_2 to the houses. Also pay attention, that the locations of the houses h_i and the considered options p_j could match. For example, the next locations are correct: h = {1, 0, 3, 3 } , p = {1, 1 } , that could correspond to already shuffled d_1 = {0, 2, 1, 2 } , d_2 = {2, 2, 1, 0 } . Check whether there are locations of houses h and considered points p_1 , p_2 , for which the founded arrays of distances would be correct. If it is possible, find appropriate locations of houses and considered options. The first line of the input contains a single integer t ( 1 <= t <= 10^3 ) -- the number of test cases. The description of test cases follows. The first line of each test case contains one integer n ( 1 <= n <= 10^3 ) -- the length of arrays d_1 , d_2 . The next two lines contain n integers each: arrays '...