CF1536A.Omkar and Bad Story

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.

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 $a$ .

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.

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 $b$ .