A15436 | 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.

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 $2 \cdot 10^3$ .

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.