CF1656G Cycle Palindrome

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)) $ .

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 $ .

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.