Problem Description

Koishi picked up a positive integer sequence $a = [a_1, a_2, \cdots, a_n]$ of length $n$ on the road, where $1\le a_i\le n$. Now Koishi computed the prefix maximum sequence $b = [b_1, b_2, \cdots, b_n]$ of $a$, where $b_i$ denotes the maximum among the first $i$ elements of $a$, i.e.

$$b_i = \max\{a_1, a_2, \cdots, a_i\} = \max_{1\le j\le i}\{a_j\}$$

After obtaining the two sequences, Koishi mixed them together: define a sequence $c$ of length $2n$ as $c = [a_1, a_2, \cdots, a_n, b_1, b_2, \cdots, b_n]$, and then sorted $c$ in non-decreasing order.

Because Koishi is an unconscious girl, she lost the values of $a$ and $b$, leaving only the sequence $c$.

Because Koishi is an unconscious girl, she gave you the sequence $c$—the cutest college student of the 21st century—hoping that you can find any valid sequence $a$. There may be multiple valid sequences $a$; in that case, you only need to output any one of them. There may also be no valid sequence $a$ at all; in that case, you need to report that there is no solution.

Input Format

The first line contains an integer $T$, denoting the number of test cases. Then follow $T$ test cases, each described as follows:

• The first line contains an integer $n$, the length of sequence $a$.
• The second line contains a sequence $c$ of length $2 \times n$, where adjacent integers are separated by a single space. It is guaranteed that $c$ is non-decreasing, and $1\le c_i\le n$.

It is guaranteed that $1\le \sum n\le 3\times 10^5$.

Output Format

For each test case:

• If there is a solution, output a string Yes on the first line, and output $n$ integers $[a_1, a_2, \cdots, a_n]$ on the second line, separated by single spaces, representing one valid sequence $a$ you found.
• If there is no solution, output a single line with the string No.

Yes and No are case-insensitive. For example, Yes, YES, and yEs are all considered affirmative, while No, NO, and nO are all considered negative.

5
3
1 1 2 2 3 3
3
1 1 1 1 2 3
6
1 1 1 1 1 4 4 4 5 5 5 5
5
1 1 1 2 3 4 5 5 5 5
9
2 3 3 4 4 5 8 9 9 9 9 9 9 9 9 9 9 9

Yes
1 2 3
No
Yes
1 1 4 5 1 4
No
Yes
9 9 8 2 4 4 3 5 3

Hint

Translated by ChatGPT 5