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: 512.0 MB

# Problem
Ntarsis has an array $$$a$$$ of length $$$n$$$.

The power of a subarray $$$a_l \dots a_r$$$ ($$$1 \leq l \leq r \leq n$$$) is defined as:

- The largest value $$$x$$$ such that $$$a_l \dots a_r$$$ contains $$$x$$$ and neither $$$a_1 \dots a_{l-1}$$$ nor $$$a_{r+1} \dots a_n$$$ contains $$$x$$$.
- If no such $$$x$$$ exists, the power is $$$0$$$.

Call an array $$$b$$$ a rival to $$$a$$$ if the following holds:

- The length of both $$$a$$$ and $$$b$$$ are equal to some $$$n$$$.
- Over all $$$l, r$$$ where $$$1 \leq l \leq r \leq n$$$, the power of $$$a_l \dots a_r$$$ equals the power of $$$b_l \dots b_r$$$.
- The elements of $$$b$$$ are positive.

Ntarsis wants you to find a rival $$$b$$$ to $$$a$$$ such that the sum of $$$b_i$$$ over $$$1 \leq i \leq n$$$ is maximized. Help him with this task!

## Input Format
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^5$$$). The description of the test cases follows.

The first line of each test case has a single integer $$$n$$$ ($$$1 \leq n \leq 10^5$$$).

The next line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \leq a_i \leq 10^9$$$).

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

## Output Format
For each test case, output $$$n$$$ integers $$$b_1, b_2, \ldots, b_n$$$ — a valid rival to $$$a$$$ such that $$$b_1 + b_2 + \cdots + b_n$$$ is maximal.

If there exist multiple rivals with the maximum sum, output any of them.

## Examples
```input
7
5
1 4 1 3 3
5
1 4 1 8 8
5
2 1 1 1 2
8
3 2 3 5 2 2 5 3
8
1 1 1 1 4 3 3 3
10
1 9 5 9 8 1 5 8 9 1
16
1 1 1 1 5 5 5 5 9 9 9 9 7 7 7 7
```
```output
2 4 2 3 3
3 4 3 8 8
2 1 2 1 2
4 2 4 5 5 2 5 4
1 2 2 1 4 3 2 3
7 9 5 9 8 9 5 8 9 7
1 8 8 1 5 8 8 5 9 9 9 9 7 8 8 7
```

## Note
For the first test case, one rival with the maximal sum is $$$[2, 4, 2, 3, 3]$$$.

$$$[2, 4, 2, 3, 3]$$$ can be shown to be a rival to $$$[1, 4, 1, 3, 3]$$$.

All possible subarrays of $$$a$$$ and $$$b$$$ and their corresponding powers are listed below:

- The power of $$$a[1:1] = [1] = 0$$$, the power of $$$b[1:1] = [2] = 0$$$.
- The power of $$$a[1:2] = [1, 4] = 4$$$, the power of $$$b[1:2] = [2, 4] = 4$$$.
- The power of $$$a[1:3] = [1, 4, 1] = 4$$$, the power of $$$b[1:3] = [2, 4, 2] = 4$$$.
- The power of $$$a[1:4] = [1, 4, 1, 3] = 4$$$, the power of $$$b[1:4] = [2, 4, 2, 3] = 4$$$.
- The power of $$$a[1:5] = [1, 4, 1, 3, 3] = 4$$$, the power of $$$b[1:5] = [2, 4, 2, 3, 3] = 4$$$.
- The power of $$$a[2:2] = [4] = 4$$$, the power of $$$b[2:2] = [4] = 4$$$.
- The power of $$$a[2:3] = [4, 1] = 4$$$, the power of $$$b[2:3] = [4, 2] = 4$$$.
- The power of $$$a[2:4] = [4, 1, 3] = 4$$$, the power of $$$b[2:4] = [4, 2, 3] = 4$$$.
- The power of $$$a[2:5] = [4, 1, 3, 3] = 4$$$, the power of $$$b[2:5] = [4, 2, 3, 3] = 4$$$.
- The power of $$$a[3:3] = [1] = 0$$$, the power of $$$b[3:3] = [2] = 0$$$.
- The power of $$$a[3:4] = [1, 3] = 0$$$, the power of $$$b[3:4] = [2, 3] = 0$$$.
- The power of $$$a[3:5] = [1, 3, 3] = 3$$$, the power of $$$b[3:5] = [2, 3, 3] = 3$$$.
- The power of $$$a[4:4] = [3] = 0$$$, the power of $$$b[4:4] = [3] = 0$$$.
- The power of $$$a[4:5] = [3, 3] = 3$$$, the power of $$$b[4:5] = [3, 3] = 3$$$.
- The power of $$$a[5:5] = [3] = 0$$$, the power of $$$b[5:5] = [3] = 0$$$.

It can be shown there exists no rival with a greater sum than $$$2 + 4 + 2 + 3 + 3 = 14$$$.

Now solve the problem and return the code.