CF1631A Min Max Swap

You are given two arrays $ a $ and $ b $ of $ n $ positive integers each. You can apply the following operation to them any number of times: - Select an index $ i $ ( $ 1\leq i\leq n $ ) and swap $ a_i $ with $ b_i $ (i. e. $ a_i $ becomes $ b_i $ and vice versa). Find the minimum possible value of $ \max(a_1, a_2, \ldots, a_n) \cdot \max(b_1, b_2, \ldots, b_n) $ you can get after applying such operation any number of times (possibly zero).

The input consists of multiple test cases. The first line contains a single integer $ t $ ( $ 1 \leq t \leq 100 $ ) — the number of test cases. Description of the test cases follows. The first line of each test case contains an integer $ n $ ( $ 1\le n\le 100 $ ) — the length of the arrays. The second line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \le a_i \le 10\,000 $ ) where $ a_i $ is the $ i $ -th element of the array $ a $ . The third line of each test case contains $ n $ integers $ b_1, b_2, \ldots, b_n $ ( $ 1 \le b_i \le 10\,000 $ ) where $ b_i $ is the $ i $ -th element of the array $ b $ .

For each test case, print a single integer, the minimum possible value of $ \max(a_1, a_2, \ldots, a_n) \cdot \max(b_1, b_2, \ldots, b_n) $ you can get after applying such operation any number of times.

In the first test, you can apply the operations at indices $ 2 $ and $ 6 $ , then $ a = [1, 4, 6, 5, 1, 5] $ and $ b = [3, 2, 3, 2, 2, 2] $ , $ \max(1, 4, 6, 5, 1, 5) \cdot \max(3, 2, 3, 2, 2, 2) = 6 \cdot 3 = 18 $ . In the second test, no matter how you apply the operations, $ a = [3, 3, 3] $ and $ b = [3, 3, 3] $ will always hold, so the answer is $ \max(3, 3, 3) \cdot \max(3, 3, 3) = 3 \cdot 3 = 9 $ . In the third test, you can apply the operation at index $ 1 $ , then $ a = [2, 2] $ , $ b = [1, 1] $ , so the answer is $ \max(2, 2) \cdot \max(1, 1) = 2 \cdot 1 = 2 $ .