Oscar's Round Must Have a Constructive Problem

Grammy has a sequence $A$ of length $n$.

Please find a permutation $P$ such that $P\_i \neq A\_i$ for all $i$.

There are multiple test cases.

The first line contains a single integer $T$ ($1 \leq T \leq 100\\,000$), denoting the number of test cases.

For each test case:

The first line contains a single integer $n$ ($1 \leq n \leq 100\\,000$).

The second line contains $n$ integers $A\_1,A\_2,\ldots,A\_n$ ($1 \leq A\_i \leq n$).

It is guaranteed that the sum of $n$ does not exceed $500\\,000$.

For each test case:

If the permutation does not exist, output "NO" on a single line.

Otherwise, output "YES" one the first line, then output $n$ integers one the second line, denoting the permutation $P\_1,P\_2,\ldots,P\_n$.