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).

In the first test case, $p=q=[1]$ . It is correct since $a_1 = max(p_1,q_1) = 1$ .

In the second test case, $p=[1,3,4,2,5]$ and $q=[5,2,3,1,4]$ . It is correct since:

- $a_1 = \max(p_1, q_1) = \max(1, 5) = 5$ ,
- $a_2 = \max(p_2, q_2) = \max(3, 2) = 3$ ,
- $a_3 = \max(p_3, q_3) = \max(4, 3) = 4$ ,
- $a_4 = \max(p_4, q_4) = \max(2, 1) = 2$ ,
- $a_5 = \max(p_5, q_5) = \max(5, 4) = 5$ .

In the third test case, one can show that no such $p$ and $q$ exist.