CF2229B Absolute Cinema

You find yourself with two arrays of positive integers $ a $ and $ b $ , both of length $ n $ . You are to perform the following operation any number of times: - select an integer $ i $ ( $ 1 \le i \le n $ ) and swap $ a_i $ and $ b_i $ . Determine the maximum value of $ \max(a) + \sum^{n}_{i = 1}{b_i} $ attainable if you perform the operations optimally.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). The description of the test cases follows. The first line of each testcase contains an integer $ n $ ( $ 1 \le n \le 10^5 $ ) — the length of the arrays $ a $ and $ b $ . The second line of each testcase contains $ n $ integers $ a_1,a_2,\ldots,a_{n} $ ( $ 1 \le a_i \le 10^9 $ ). The third line of each testcase contains $ n $ integers $ b_1,b_2,\ldots,b_{n} $ ( $ 1 \le b_i \le 10^9 $ ). It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 10^5 $ .

For each testcase, output the maximum value of $ \max(a) + \sum^{n}_{i = 1}{b_i} $ attainable.

Test Case 3: No swaps are required, so the answer is $ \max([1, 2, 3]) + 4 + 5 + 6 = 3 + 15 = 18 $ , it can be proven that this is optimal. Test Case 4: You can achieve the maximum by swapping indices $ 1 $ , $ 3 $ and $ 4 $ . So we get: - $ a = [1, 3, 5, 8] $ - $ b = [2, 4, 6, 7] $ This gives an answer of $ \max([1, 3, 5, 8]) + 2 + 4 + 6 + 7 = 8 + 19 = 27 $ , it can be proven that this is optimal.