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.

Input

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 $2 \cdot 10^5$.

Output

For each test case, output two integers, one possible value of $n$ and $m$. If multiple possible answers exist, output any.

Note

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

Samples

5
3
1 1 2
11
3 3 4 5 6 7 8 9 9 10 11
8
8 4 8 3 8 2 8 1
6
2 1 4 5 3 3
8
1 2 6 3 8 5 5 3

1 1
3 3
2 3
4 1
1 6