CF2037B Intercepted Inputs

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 1 2 In the second test case, the initial input could have been the following: 3 3 4 5 6 7 8 9 9 10 11