CF1735E.House Planning

There are $n$ houses in your city arranged on an axis at points $h_1, h_2, \ldots, h_n$. You want to build a new house for yourself and consider two options where to place it: points $p_1$ and $p_2$.

As you like visiting friends, you have calculated in advance the distances from both options to all existing houses. More formally, you have calculated two arrays $d_1$, $d_2$: $d_{i, j} = \left|p_i - h_j\right|$, where $|x|$ defines the absolute value of $x$.

After a long time of inactivity you have forgotten the locations of the houses $h$ and the options $p_1$, $p_2$. But your diary still keeps two arrays — $d_1$, $d_2$, whose authenticity you doubt. Also, the values inside each array could be shuffled, so values at the same positions of $d_1$ and $d_2$ may correspond to different houses. Pay attention, that values from one array could not get to another, in other words, all values in the array $d_1$ correspond the distances from $p_1$ to the houses, and in the array $d_2$ — from $p_2$ to the houses.

Also pay attention, that the locations of the houses $h_i$ and the considered options $p_j$ could match. For example, the next locations are correct: $h = {1, 0, 3, 3}$, $p = {1, 1}$, that could correspond to already shuffled $d_1 = {0, 2, 1, 2}$, $d_2 = {2, 2, 1, 0}$.

Check whether there are locations of houses $h$ and considered points $p_1$, $p_2$, for which the founded arrays of distances would be correct. If it is possible, find appropriate locations of houses and considered options.

你的城市中有 $n$ 座房屋，沿数轴排列在位置 $h_1, h_2, \ldots, h_n$ 上。你想为自己新建一座房屋，并考虑两种选址方案：位置 $p_1$ 和 $p_2$。

由于你喜欢拜访朋友，你已预先计算出这两种选址方案到所有现有房屋的距离。更准确地说，你计算出了两个数组 $d_1$ 和 $d_2$：其中 $d_{i, j} = \left|p_i - h_j\right|$，$|x|$ 表示 $x$ 的绝对值。

经过长时间的搁置，你已忘记了房屋位置 $h$ 以及候选位置 $p_1$、$p_2$ 的具体取值。但你的日记中仍保留着两个数组——$d_1$ 和 $d_2$，而你对其真实性存疑。此外，每个数组内部的元素顺序可能已被打乱，即 $d_1$ 和 $d_2$ 中相同下标位置上的值可能对应于不同的房屋。请注意：一个数组中的数值不可能混入另一个数组，换言之，数组 $d_1$ 中的所有值均表示从 $p_1$ 到各房屋的距离，而数组 $d_2$ 中的所有值均表示从 $p_2$ 到各房屋的距离。

还需注意：房屋位置 $h_i$ 与候选位置 $p_j$ 可以重合。例如，以下情形是合法的：$h = \{1, 0, 3, 3\}$，$p = \{1, 1\}$，其对应已打乱的 $d_1 = \{0, 2, 1, 2\}$、$d_2 = \{2, 2, 1, 0\}$。

请判断是否存在一组房屋位置 $h$ 和候选位置 $p_1$、$p_2$，使得所给定的距离数组 $d_1$、$d_2$ 成立。若存在，请找出一组满足条件的房屋位置和候选位置。

The first line of the input contains a single integer $t$ ($1 \le t \le 10^3$) — the number of test cases. The description of test cases follows.

The first line of each test case contains one integer $n$ ($1 \le n \le 10^3$) — the length of arrays $d_1$, $d_2$.

The next two lines contain $n$ integers each: arrays $d_1$ and $d_2$ ($0 \le d_{i, j} \le 10^9$) respectively.

It is guaranteed that the sum of $n$ over all test cases doesn't exceed $2 \cdot 10^3$.

输入的第一行包含一个整数 $t$（$1 \le t \le 10^3$），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 $n$（$1 \le n \le 10^3$），表示数组 $d_1$ 和 $d_2$ 的长度。

接下来的两行每行包含 $n$ 个整数：分别为数组 $d_1$ 和 $d_2$（$0 \le d_{i, j} \le 10^9$）。

保证所有测试用例中 $n$ 的总和不超过 $2 \cdot 10^3$。

For each test case, output a single line "NO" if there is no answer.

Otherwise output three lines. The first line must contain "YES". In the second line, print $n$ integers $h_1, h_2, \ldots, h_n$. In the third line print two integers $p_1$, $p_2$.

It must be satisfied that $0 \le h_i, p_1, p_2 \le 2 \cdot 10^9$. We can show that if there is an answer, then there is one satisfying these constraints.

If there are several answers, output any of them.

对于每个测试用例，若无解，则输出一行 "NO"。

否则输出三行。第一行必须为 "YES"。第二行输出 $n$ 个整数 $h_1, h_2, \ldots, h_n$。第三行输出两个整数 $p_1$、$p_2$。

需满足 $0 \le h_i, p_1, p_2 \le 2 \cdot 10^9$。可以证明：若存在解，则必存在满足上述约束条件的解。

若存在多个解，输出任意一个即可。

In the image below you can see the sample solutions. Planned houses are shown in bright colours: pink and purple. Existing houses are dim.

In test case $1$, the first planned house is located at point $0$, the second at point $10$. The existing house is located at point $5$ and is at a distance of $5$ from both planned houses.

It can be shown that there is no answer for test case $2$.

In test case $3$, the planned houses are located at points $33$ and $69$.

Note that in test case $4$, both plans are located at point $1$, where one of the existing houses is located at the same time. It is a correct placement.

在下方图片中，您可以查看样例解。规划中的房屋以亮色显示：粉色和紫色；已存在的房屋则以暗色显示。

在测试用例 $1$ 中，第一栋规划房屋位于坐标 $0$ 处，第二栋位于坐标 $10$ 处。已存在的房屋位于坐标 $5$ 处，到两栋规划房屋的距离均为 $5$。

可以证明：测试用例 $2$ 无解。

在测试用例 $3$ 中，规划房屋位于坐标 $33$ 和 $69$ 处。

注意，在测试用例 $4$ 中，两栋规划房屋均位于坐标 $1$ 处，而恰好有一栋已存在的房屋也位于该位置。这是一种合法的布置方式。