B. Intercepted Inputs
brute force; implementation
To help you prepare for your upcoming Codeforces contest, Citlali set a grid problem and is trying to give you a \(n\) by \(m\) grid through your input stream. Specifically, your input stream should contain the following: The first line contains two integers \(n\) and \(m\) — the dimensions of the grid. The following \(n\) lines contain \(m\) integers each — the values of the grid. However, someone has intercepted your input stream, shuffled all given integers, and put them all on one line! Now, there are \(k\) integers all on one line, and you don't know where each integer originally belongs. Instead of asking Citlali to resend the input, you decide to determine the values of \(n\) and \(m\) yourself.Output any possible value of \(n\) and \(m\) that Citlali could have provided.
The first line contains an integer \(t\) (\(1 \leq t \leq 10^4\)) — the number of test cases.The first line of each test case contains an integer \(k\) (\(3 \leq k \leq 2 \cdot 10^5\)) — the total number of inputs in your input stream.The following line of each test case contains \(k\) integers \(a_1, a_2, \ldots, a_k\) (\(1 \leq a_i \leq k\)) — the shuffled inputs of your input stream. It is guaranteed that \(n\) and \(m\) are contained within the \(k\) integers.It is guaranteed that the sum of \(k\) over all test cases does not exceed \(2 \cdot 10^5\).
For each test case, output two integers, one possible value of \(n\) and \(m\). If multiple possible answers exist, output any.
In the first test case, the initial input could have been the following:1 12In the second test case, the initial input could have been the following:3 34 5 67 8 99 10 11