A. Min Max Swap
greedy
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 \(\max(2, 2) \cdot \max(1, 1) = 2 \cdot 1 = 2\).