Box

Permutation p is a sequence of integers p=[p_1, p_2, ..., 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,...,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 ≤ t ≤ 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 ≤ n ≤ 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, ..., q_n (1 ≤ q_i ≤ n) — elements of the array q for secret permutation. It is guaranteed that q_i ≤ q_{i+1} for all i (1 ≤ 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, ..., p_n (1 ≤ p_i ≤ 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.

inputFormat

Input

The first line contains integer number t (1 ≤ t ≤ 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 ≤ n ≤ 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, ..., q_n (1 ≤ q_i ≤ n) — elements of the array q for secret permutation. It is guaranteed that q_i ≤ q_{i+1} for all i (1 ≤ i < n).

The sum of all values n over all the test cases in the input doesn't exceed 10^5.

outputFormat

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, ..., p_n (1 ≤ p_i ≤ 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.

样例

4
5
1 3 4 5 5
4
1 1 3 4
2
2 2
1
1

1 3 4 5 2 
-1
2 1
1

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