You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
In fact, the problems E1 and E2 do not have much in common. You should probably think of them as two separate problems.

A permutation $$$p$$$ of size $$$n$$$ is given. A permutation of size $$$n$$$ is an array of size $$$n$$$ in which each integer from $$$1$$$ to $$$n$$$ occurs exactly once. For example, $$$[1, 4, 3, 2]$$$ and $$$[4, 2, 1, 3]$$$ are correct permutations while $$$[1, 2, 4]$$$ and $$$[1, 2, 2]$$$ are not.

Let us consider an empty deque (double-ended queue). A deque is a data structure that supports adding elements to both the beginning and the end. So, if there are elements $$$[1, 5, 2]$$$ currently in the deque, adding an element $$$4$$$ to the beginning will produce the sequence $$$[\color{red}{4}, 1, 5, 2]$$$, and adding same element to the end will produce $$$[1, 5, 2, \color{red}{4}]$$$.

The elements of the permutation are sequentially added to the initially empty deque, starting with $$$p_1$$$ and finishing with $$$p_n$$$. Before adding each element to the deque, you may choose whether to add it to the beginning or the end.

For example, if we consider a permutation $$$p = [3, 1, 2, 4]$$$, one of the possible sequences of actions looks like this: $$$\quad$$$ 1.add $$$3$$$ to the end of the deque:deque has a sequence $$$[\color{red}{3}]$$$ in it;$$$\quad$$$ 2.add $$$1$$$ to the beginning of the deque:deque has a sequence $$$[\color{red}{1}, 3]$$$ in it;$$$\quad$$$ 3.add $$$2$$$ to the end of the deque:deque has a sequence $$$[1, 3, \color{red}{2}]$$$ in it;$$$\quad$$$ 4.add $$$4$$$ to the end of the deque:deque has a sequence $$$[1, 3, 2, \color{red}{4}]$$$ in it;

Find the lexicographically smallest possible sequence of elements in the deque after the entire permutation has been processed.

A sequence $$$[x_1, x_2, \ldots, x_n]$$$ is lexicographically smaller than the sequence $$$[y_1, y_2, \ldots, y_n]$$$ if there exists such $$$i \leq n$$$ that $$$x_1 = y_1$$$, $$$x_2 = y_2$$$, $$$\ldots$$$, $$$x_{i - 1} = y_{i - 1}$$$ and $$$x_i < y_i$$$. In other words, if the sequences $$$x$$$ and $$$y$$$ have some (possibly empty) matching prefix, and the next element of the sequence $$$x$$$ is strictly smaller than the corresponding element of the sequence $$$y$$$. For example, the sequence $$$[1, 3, 2, 4]$$$ is smaller than the sequence $$$[1, 3, 4, 2]$$$ because after the two matching elements $$$[1, 3]$$$ in the start the first sequence has an element $$$2$$$ which is smaller than the corresponding element $$$4$$$ in the second sequence.

## Input Format
The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 1000$$$) — the number of test cases.

The next $$$2t$$$ lines contain descriptions of the test cases.

The first line of each test case description contains an integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — permutation size. The second line of the description contains $$$n$$$ space-separated integers $$$p_i$$$ ($$$1 \le p_i \le n$$$; all $$$p_i$$$ are all unique) — elements of the permutation.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

## Output Format
Print $$$t$$$ lines, each line containing the answer to the corresponding test case. The answer to a test case should contain $$$n$$$ space-separated integer numbers — the elements of the lexicographically smallest permutation that is possible to find in the deque after executing the described algorithm.

## Examples
```input
5
4
3 1 2 4
3
3 2 1
3
3 1 2
2
1 2
2
2 1
```
```output
1 3 2 4 
1 2 3 
1 3 2 
1 2 
1 2
```

## Note
One of the ways to get a lexicographically smallest permutation $$$[1, 3, 2, 4]$$$ from the permutation $$$[3, 1, 2, 4]$$$ (the first sample test case) is described in the problem statement.

Now solve the problem and return the code.