F. Rudolf and Imbalancetime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputRudolf has prepared a set of n problems with complexities a_1 < a_2 < a_3 < \dots < 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 \le i \le m, 1 \le j \le 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?InputThe first line of the input contains a single integer t (1 \le t \le 10^4) — the number of testcases.The first line of each test case contains three integers n, m, and k (2 \le n \le 10^5, 1 \le m, k \le 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, \dots a_n (1 \le a_i \le 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, \dots d_m (1 \le d_i \le 10^9) — the complexities of the models.The fourth line of each test case contains k integers f_1, f_2, f_3, \dots f_k (1 \le f_i \le 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 testcases does not exceed 2 \cdot 10^5.It is guaranteed that the sum of k over all testcases does not exceed 2 \cdot 10^5.OutputFor each testcase, output a single number — the minimum imbalance that Rudolf can achieve.ExampleInput
75 5 55 10 15 20 2611 14 16 13 816 4 5 3 17 6 51 4 7 10 18 21 222 3 5 7 4 26 8 9 3 27 6 51 4 7 10 18 21 222 3 5 7 4 26 8 13 3 25 6 32 10 13 20 2511 6 10 16 14 56 17 154 2 211 12 14 1519 1410 68 4 23 10 16 18 21 22 29 309 13 16 154 22 4 74 214 15 14 520 1 15 1 12 5 11Output
5
4
5
8
2
7
11

75 5 55 10 15 20 2611 14 16 13 816 4 5 3 17 6 51 4 7 10 18 21 222 3 5 7 4 26 8 9 3 27 6 51 4 7 10 18 21 222 3 5 7 4 26 8 13 3 25 6 32 10 13 20 2511 6 10 16 14 56 17 154 2 211 12 14 1519 1410 68 4 23 10 16 18 21 22 29 309 13 16 154 22 4 74 214 15 14 520 1 15 1 12 5 11
5 4 5 8 2 7 11 
['binary search', 'greedy', 'sortings', 'two pointers', '*1800']