CF1506E Restoring the Permutation

A permutation is a sequence of $ n $ integers from $ 1 $ to $ n $ , in which all numbers occur exactly once. For example, $ [1] $ , $ [3, 5, 2, 1, 4] $ , $ [1, 3, 2] $ are permutations, and $ [2, 3, 2] $ , $ [4, 3, 1] $ , $ [0] $ are not. Polycarp was presented with a permutation $ p $ of numbers from $ 1 $ to $ n $ . However, when Polycarp came home, he noticed that in his pocket, the permutation $ p $ had turned into an array $ q $ according to the following rule: - $ q_i = \max(p_1, p_2, \ldots, p_i) $ . Now Polycarp wondered what lexicographically minimal and lexicographically maximal permutations could be presented to him. An array $ a $ of length $ n $ is lexicographically smaller than an array $ b $ of length $ n $ if there is an index $ i $ ( $ 1 \le i \le n $ ) such that the first $ i-1 $ elements of arrays $ a $ and $ b $ are the same, and the $ i $ -th element of the array $ a $ is less than the $ i $ -th element of the array $ b $ . For example, the array $ a=[1, 3, 2, 3] $ is lexicographically smaller than the array $ b=[1, 3, 4, 2] $ . For example, if $ n=7 $ and $ p=[3, 2, 4, 1, 7, 5, 6] $ , then $ q=[3, 3, 4, 4, 7, 7, 7] $ and the following permutations could have been as $ p $ initially: - $ [3, 1, 4, 2, 7, 5, 6] $ (lexicographically minimal permutation); - $ [3, 1, 4, 2, 7, 6, 5] $ ; - $ [3, 2, 4, 1, 7, 5, 6] $ ; - $ [3, 2, 4, 1, 7, 6, 5] $ (lexicographically maximum permutation). For a given array $ q $ , find the lexicographically minimal and lexicographically maximal permutations that could have been originally presented to Polycarp.

The first line contains one integer $ t $ ( $ 1 \le t \le 10^4 $ ). Then $ t $ test cases follow. The first line of each test case contains one integer $ n $ ( $ 1 \le n \le 2 \cdot 10^5 $ ). The second line of each test case contains $ n $ integers $ q_1, q_2, \ldots, q_n $ ( $ 1 \le q_i \le n $ ). It is guaranteed that the array $ q $ was obtained by applying the rule from the statement to some permutation $ p $ . It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case, output two lines: - on the first line output $ n $ integers — lexicographically minimal permutation that could have been originally presented to Polycarp; - on the second line print $ n $ integers — lexicographically maximal permutation that could have been originally presented to Polycarp;