G. Cycle Palindrome
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

We say that a sequence of $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ is a palindrome if for all $$$1 \leq i \leq n$$$, $$$a_i = a_{n-i+1}$$$. You are given a sequence of $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ and you have to find, if it exists, a cycle permutation $$$\sigma$$$ so that the sequence $$$a_{\sigma(1)}, a_{\sigma(2)}, \ldots, a_{\sigma(n)}$$$ is a palindrome.

A permutation of $$$1, 2, \ldots, n$$$ is a bijective function from $$$\{1, 2, \ldots, n\}$$$ to $$$\{1, 2, \ldots, n\}$$$. We say that a permutation $$$\sigma$$$ is a cycle permutation if $$$1, \sigma(1), \sigma^2(1), \ldots, \sigma^{n-1}(1)$$$ are pairwise different numbers. Here $$$\sigma^m(1)$$$ denotes $$$\underbrace{\sigma(\sigma(\ldots \sigma}_{m \text{ times}}(1) \ldots))$$$.

Input

The input consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 3 \cdot 10^4$$$) — the number of test cases. Description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$2 \leq n \leq 2 \cdot 10^5$$$) — the size of the sequence.

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

The sum of $$$n$$$ for all test cases is at most $$$2 \cdot 10^5$$$.

Output

For each test case, output one line with YES if a cycle permutation exists, otherwise output one line with NO.

If the answer is YES, output one additional line with $$$n$$$ integers $$$\sigma(1), \sigma(2), \ldots, \sigma(n)$$$, the permutation. If there is more than one permutation, you may print any.

Example
Input
3
4
1 2 2 1
3
1 2 1
7
1 3 3 3 1 2 2
Output
YES
3 1 4 2 
NO
YES
5 3 7 2 6 4 1