CF1768C Elemental Decompress

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).

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.