Little $D$ has a sequence $a_1, a_2, a_3, \dots, a_{2n}$ of length $2n$, where each number from $1$ to $n$ appears exactly twice. Furthermore, $a_1, a_2, a_3, \dots, a_n$ forms a permutation of $1 \sim n$.

Little $D$ denotes the two positions of the number $i$ as $x_i$ and $y_i$, satisfying $1 \le x_i \le n < y_i \le 2n$.

Little $D$ also defines a set operation $\oplus$ as follows:

$A \oplus B = \{x \mid [x \in A] + [x \in B] = 1\}$

Let $f(S)$ be the smallest positive integer that does not appear in $S$.

Now, Little $D$ will provide you with $v_i = f(\{a_{x_i}\} \oplus \{a_{x_i+1}\} \oplus \cdots \oplus \{a_{y_i}\})$. He wants you to construct a sequence $a$ that satisfies the conditions based on the sequence $v$.

Input

The first line contains a positive integer $T$, representing the number of test cases.

The next $2T$ lines describe $T$ test cases.

The first line of each test case contains a positive integer $n$, representing the number of distinct values in the sequence.

The second line of each test case contains $n$ positive integers $v_1, v_2, v_3, \dots, v_n$, representing the calculated values.

Output

For each test case, output the answer.

The first line of each test case should be the string Yes or No, indicating whether a solution exists.

If a solution exists, output $2n$ positive integers $a_1, a_2, a_3, \dots, a_{2n}$ on the second line, representing the sequence you constructed. If multiple valid constructions exist, any one of them is acceptable.

Examples

Input 1

2
4
1 2 2 2
3
3 2 1

Output 1

Yes
3 2 4 1 4 2 3 1
No

Constraints

Special Property $A$: $v_i \le 4$.

Special Property $B$: $v_{v_i} = v_i$.

For $100\%$ of the data, $1 \le T \le 10$, $1 \le n \le 2 \times 10^5$, $1 \le \sum n \le 2 \times 10^6$, $1 \le v_i \le n$.

The answer files provided do not contain the construction schemes.