B'Rudolf has prepared a set of n problems with complexities a_1 < a_2 < a_3 < ... < a_n . He is not entirely satisfied with the balance, so he wants to add at most one problem to fix it. For this, Rudolf came up with m models of problems and k functions. The complexity of the i -th model is d_i , and the complexity of the j -th function is f_j . To create a problem, he selects values i and j ( 1 <= i <= m , 1 <= j <= k ) and by combining the i -th model with the j -th function, he obtains a new problem with complexity d_i + f_j (a new element is inserted into the array a ). To determine the imbalance of the set, Rudolf sorts the complexities of the problems in ascending order and finds the largest value of a_i - a_{i - 1} ( i > 1 ). What is the minimum value of imbalance that Rudolf can achieve by adding at most one problem, created according to the described rules? The first line of the input contains a single integer t ( 1 <= t <= 10^4 ) -- the number of testcases. The first line of each test case contains three integers n , m , and k ( 2 <= n <= 10^5 , 1 <= m, k <= 2 cdot 10^5 ) -- the number of prepared problems, the number of models, and the number of functions, respectively. The second line of each test case contains n integers a_1, a_2, a_3, ... a_n ( 1 <= a_i <= 2 cdot 10^9 , a_i < a_{i+1} ) -- the complexities of the prepared problems. The third line of each test case contains m integers d_1, d_2, d_3, ... d_m ( 1 <= d_i <= 10^9 ) -- the complexities of the models. The fourth line of each test case contains k integers f_1, f_2, f_3, ... f_k ( 1 <= f_i <= 10^9 ) -- the complexities of the functions. It is guaranteed that the sum of n over all testcases does not exceed 10^5 . It is guaranteed that the sum of m over all '...