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 $x \gt y$ and $|x-y| = y-x$ otherwise.

奥姆卡尔收到了安东发来的一条消息：“问题 A 的题面故事令人困惑，直接给出形式化的题意即可。”因此，奥姆卡尔给你一个由 $n$ 个互不相同的整数组成的数组 $a = [a_1, a_2, \ldots, a_n]$。称一个数组 $b = [b_1, b_2, \ldots, b_k]$ 是优美的（nice），当且仅当对 $b$ 中任意两个不同元素 $b_i, b_j$，其绝对差值 $|b_i-b_j|$ 至少在 $b$ 中出现一次；此外，$b$ 中所有元素必须互不相同。你能否向 $a$ 中添加若干（可能为 $0$ 个）整数，构造出一个大小不超过 $300$ 的优美数组 $b$？如果 $a$ 本身已是优美的，则无需添加任何元素。

例如，数组 $[3, 6, 9]$ 是优美的，因为 $|6-3|=|9-6| = 3$ 出现在该数组中，且 $|9-3| = 6$ 也出现在该数组中；而数组 $[4, 2, 0, 6, 9]$ 不是优美的，因为 $|9-4| = 5$ 并未出现在该数组中。

对于整数 $x$ 和 $y$，定义 $|x-y| = x-y$（若 $x > y$），否则 $|x-y| = y-x$。

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 $a$.

每个测试包含多个测试用例。第一行包含一个整数 $t$（$1 \leq t \leq 50$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$2 \leq n \leq 100$）—— 表示数组 $a$ 的长度。

每个测试用例的第二行包含 $n$ 个互不相同的整数 $a_1, a_2, \cdots, a_n$（$-100 \leq a_i \leq 100$）—— 表示数组 $a$ 的元素。

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.

对于每个测试用例，如果 Omkar 能够通过向数组 $a$ 中添加元素来构造一个“好”数组 $b$，则输出一行 YES；否则输出 NO。字母大小写不敏感，因此 yEs 和 nO 同样被接受。

若首行为 YES，则需在第二行输出一个整数 $k$（满足 $n \leq k \leq 300$）。

接着输出一行，包含 $k$ 个互不相同的整数 $b_1, b_2, \cdots, b_k$（满足 $-10^9 \leq b_i \leq 10^9$），即“好”数组 $b$ 的元素。$b_1, b_2, \cdots, b_k$ 的顺序可任意。对 $a$ 中的每个 $a_i$，它必须至少在 $b$ 中出现一次。

可以证明：若 Omkar 能构造出这样的数组 $b$，则他一定也能以满足上述约束的方式构造出来。

若存在多个可行解，输出任意一个即可。

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 $b$.

对于第一种情况，你可以向数组 $a$ 中添加整数，得到数组 $b = [6, 0, 3, 9]$。注意 $|6-3| = |9-6| = |3-0| = 3$，且 $3 \in b$；$|6-0| = |9-3| = 6$，且 $6 \in b$；$|9-0| = 9$，且 $9 \in b$，因此 $b$ 是“优美的”。

对于第二种情况，你可以向数组 $a$ 中添加整数，得到数组 $b = [5, 3, 1, 2, 4]$。我们有 $|2-1| = |3-2| = |4-3| = |5-4| = 1$，且 $1 \in b$；$|3-1| = |4-2| = |5-3| = 2$，且 $2 \in b$；$|4-1| = |5-2| = 3$，且 $3 \in b$；$|5-1| = 4$，且 $4 \in b$，因此 $b$ 是“优美的”。

对于第四种情况，你可以向数组 $a$ 中添加整数，得到数组 $b = [8, 12, 6, 2, 4, 10]$。我们有 $|4-2| = |6-4| = |8-6| = |10-8| = |12-10| = 2$，且 $2 \in b$；$|6-2| = |8-4| = |10-6| = |12-8| = 4$，且 $4 \in b$；$|8-2| = |10-4| = |12-6| = 6$，且 $6 \in b$；$|10-2| = |12-4| = 8$，且 $8 \in b$；$|12-2| = 10$，且 $10 \in b$，因此 $b$ 是“优美的”。

可以证明：对于其余所有测试用例，均无法构造出“优美”的数组 $b$。