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
Omkar has received a message from Anton saying "Your story for problem A is confusing. Just make a formal statement." Because of this, Omkar gives you an array $$$a = [a_1, a_2, \ldots, a_n]$$$ of $$$n$$$ distinct integers. An array $$$b = [b_1, b_2, \ldots, b_k]$$$ is called nice if for any two distinct elements $$$b_i, b_j$$$ of $$$b$$$, $$$|b_i-b_j|$$$ appears in $$$b$$$ at least once. In addition, all elements in $$$b$$$ must be distinct. Can you add several (maybe, $$$0$$$) integers to $$$a$$$ to create a nice array $$$b$$$ of size at most $$$300$$$? If $$$a$$$ is already nice, you don't have to add any elements.

For example, array $$$[3, 6, 9]$$$ is nice, as $$$|6-3|=|9-6| = 3$$$, which appears in the array, and $$$|9-3| = 6$$$, which appears in the array, while array $$$[4, 2, 0, 6, 9]$$$ is not nice, as $$$|9-4| = 5$$$ is not present in the array.

For integers $$$x$$$ and $$$y$$$, $$$|x-y| = x-y$$$ if $$$x > y$$$ and $$$|x-y| = y-x$$$ otherwise.

## Input Format
Each test contains multiple test cases. The first line contains $$$t$$$ ($$$1 \leq t \leq 50$$$), the number of test cases. Description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \leq n \leq 100$$$) — the length of the array $$$a$$$.

The second line of each test case contains $$$n$$$ distinct integers $$$a_1, a_2, \cdots, a_n$$$ ($$$-100 \leq a_i \leq 100$$$) — the elements of the array $$$a$$$.

## Output Format
For each test case, output one line containing YES if Omkar can create a nice array $$$b$$$ by adding elements to $$$a$$$ and NO otherwise. The case of each letter does not matter, so yEs and nO will also be accepted.

If the first line is YES, output a second line containing a single integer $$$k$$$ ($$$n \leq k \leq 300$$$).

Then output one line containing $$$k$$$ distinct integers $$$b_1, b_2, \cdots, b_k$$$ ($$$-10^9 \leq b_i \leq 10^9$$$), the elements of the nice array $$$b$$$. $$$b_1, b_2, \cdots, b_k$$$ can be in any order. For each $$$a_i$$$ in $$$a$$$, $$$a_i$$$ must appear at least once in $$$b$$$.

It can be proved that if Omkar can create such an array $$$b$$$, then he can also do so in a way that satisfies the above constraints.

If multiple solutions exist, you can print any.

## Examples
```input
4
3
3 0 9
2
3 4
5
-7 3 13 -2 8
4
4 8 12 6
```
```output
yes
4
6 0 3 9
yEs
5
5 3 1 2 4
NO
Yes
6
8 12 6 2 4 10
```

## Note
For the first case, you can add integers to $$$a$$$ to receive the array $$$b = [6, 0, 3, 9]$$$. Note that $$$|6-3| = |9-6| = |3-0| = 3$$$ and $$$3$$$ is in $$$b$$$, $$$|6-0| = |9-3| = 6$$$ and $$$6$$$ is in $$$b$$$, and $$$|9-0| = 9$$$ is in $$$b$$$, so $$$b$$$ is nice.

For the second case, you can add integers to $$$a$$$ to receive the array $$$b = [5, 3, 1, 2, 4]$$$. We have that $$$|2-1| = |3-2| = |4-3| = |5-4| = 1$$$ is in $$$b$$$, $$$|3-1| = |4-2| = |5-3| = 2$$$ is in $$$b$$$, $$$|4-1| = |5-2| = 3$$$ is in $$$b$$$, and $$$|5-1| = 4$$$ is in $$$b$$$, so $$$b$$$ is nice.

For the fourth case, you can add integers to $$$a$$$ to receive the array $$$b = [8, 12, 6, 2, 4, 10]$$$. We have that $$$|4-2| = |6-4| = |8-6| = |10-8| = |12-10| = 2$$$ is in $$$b$$$, $$$|6-2| = |8-4| = |10-6| = |12-8| = 4$$$ is in $$$b$$$, $$$|8-2| = |10-4| = |12-6| = 6$$$ is in $$$b$$$, $$$|10-2| = |12-4| = 8$$$ is in $$$b$$$, and $$$|12-2| = 10$$$ is in $$$b$$$, so $$$b$$$ is nice.

It can be proven that for all other test cases it is impossible to create a nice array $$$b$$$.

Now solve the problem and return the code.