B. Box
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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).

Input

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 $$$10^5$$$.

Output

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.
Example
Input
4
5
1 3 4 5 5
4
1 1 3 4
2
2 2
1
1
Output
1 3 4 5 2 
-1
2 1 
1
Note

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.