G. Cycle Palindrometime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputWe 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)).InputThe 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.OutputFor 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.ExampleInput
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 

3
4
1 2 2 1
3
1 2 1
7
1 3 3 3 1 2 2

YES 3 1 4 2  NO YES 5 3 7 2 6 4 1  
['constructive algorithms', 'graphs', 'math', '*3200']