CF1227B Box

Permutation $ p $ is a sequence of integers $ p=[p_1, p_2, \dots, p_n] $ , consisting of $ n $ distinct (unique) positive integers between $ 1 $ and $ n $ , inclusive. For example, the following sequences are permutations: $ [3, 4, 1, 2] $ , $ [1] $ , $ [1, 2] $ . The following sequences are not permutations: $ [0] $ , $ [1, 2, 1] $ , $ [2, 3] $ , $ [0, 1, 2] $ . The important key is in the locked box that you need to open. To open the box you need to enter secret code. Secret code is a permutation $ p $ of length $ n $ . You don't know this permutation, you only know the array $ q $ of prefix maximums of this permutation. Formally: - $ q_1=p_1 $ , - $ q_2=\max(p_1, p_2) $ , - $ q_3=\max(p_1, p_2,p_3) $ , - ... - $ q_n=\max(p_1, p_2,\dots,p_n) $ . You want to construct any possible suitable permutation (i.e. any such permutation, that calculated $ q $ for this permutation is equal to the given array).

The first line contains integer number $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases in the input. Then $ t $ test cases follow. The first line of a test case contains one integer $ n $ $ (1 \le n \le 10^{5}) $ — the number of elements in the secret code permutation $ p $ . The second line of a test case contains $ n $ integers $ q_1, q_2, \dots, q_n $ $ (1 \le q_i \le n) $ — elements of the array $ q $ for secret permutation. It is guaranteed that $ q_i \le q_{i+1} $ for all $ i $ ( $ 1 \le i < n $ ). The sum of all values $ n $ over all the test cases in the input doesn't exceed $ 10^5 $ .

For each test case, print: - If it's impossible to find such a permutation $ p $ , print "-1" (without quotes). - Otherwise, print $ n $ distinct integers $ p_1, p_2, \dots, p_n $ ( $ 1 \le p_i \le n $ ). If there are multiple possible answers, you can print any of them.

In the first test case of the example answer $ [1,3,4,5,2] $ is the only possible answer: - $ q_{1} = p_{1} = 1 $ ; - $ q_{2} = \max(p_{1}, p_{2}) = 3 $ ; - $ q_{3} = \max(p_{1}, p_{2}, p_{3}) = 4 $ ; - $ q_{4} = \max(p_{1}, p_{2}, p_{3}, p_{4}) = 5 $ ; - $ q_{5} = \max(p_{1}, p_{2}, p_{3}, p_{4}, p_{5}) = 5 $ . It can be proved that there are no answers for the second test case of the example.