codeforces#P1768C. Elemental Decompress
Elemental Decompress
Description
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).
Input
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 $2 \cdot 10^5$.
Output
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).
3
1
1
5
5 3 4 2 5
2
1 1
YES
1
1
YES
1 3 4 2 5
5 2 3 1 4
NO
Note
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.