A15649 | Elemental Decompress

You are given an array $a$ of $n$ integers.

Find two permutations $^\dagger$ $p$ and $q$ of length $n$ such that $\max(p_i,q_i)=a_i$ for all $1 \leq i \leq n$ or report that such $p$ and $q$ do not exist.

$^\dagger$ A permutation of length $n$ is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ( $2$ appears twice in the array), and $[1,3,4]$ is also not a permutation ( $n=3$ but there is $4$ in the array).

The first line contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ).

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ( $1 \leq a_i \leq n$ ) — the array $a$ .

It is guaranteed that the total sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .

For each test case, if there do not exist $p$ and $q$ that satisfy the conditions, output "NO" (without quotes).

Otherwise, output "YES" (without quotes) and then output $2$ lines. The first line should contain $n$ integers $p_1,p_2,\ldots,p_n$ and the second line should contain $n$ integers $q_1,q_2,\ldots,q_n$ .

If there are multiple solutions, you may output any of them.

You can output "YES" and "NO" in any case (for example, strings "yEs", "yes" and "Yes" will be recognized as a positive response).