Problem: 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.

Solution (in PYTHON3):

Solution:
import sys as _sys


def main():
    t = int(input())
    for i_t in range(t):
        n, = _read_ints()
        q = tuple(_read_ints())
        try:
            result = find_p(q)
        except ValueError:
            print(-1)
        else:
            print(*result)


def _read_line():
    result = _sys.stdin.readline()
    assert result[-1] == "\n"
    return result[:-1]


def _read_ints():
    return map(int, _read_line().split())


def find_p(prefix_maximums):
    if not prefix_maximums:
        return []
    n = len(prefix_maximums)
    stairs_indices = [0]
    for i in range(1, n):
        if prefix_maximums[i] < prefix_maximums[i-1]:
            raise ValueError
        if prefix_maximums[i] > prefix_maximums[i-1]:
            stairs_indices.append(i)
    
    result = []
    is_number_used = [None] + [False] * n
    i_curr_number = 1
    
    for i_i_curr_stair, i_curr_stair in enumerate(stairs_indices):
        if i_i_curr_stair + 1 < len(stairs_indices):
            i_next_stair = stairs_indices[i_i_curr_stair + 1]
        else:
            i_next_stair = n
        
        stair_content = prefix_maximums[i_curr_stair]
        if is_number_used[stair_content]:
            raise ValueError
        result.append(stair_content)
        is_number_used[stair_content] = True
        
        for i_cell in range(i_curr_stair + 1, i_next_stair):
            while is_number_used[i_curr_number]:
                i_curr_number += 1
                if i_curr_number >= len(is_number_used):
                    raise ValueError
            cell_content = i_curr_number
            if cell_content > stair_content:
                raise ValueError
            result.append(cell_content)
            is_number_used[cell_content] = True
    
    return result


if __name__ == '__main__':
    main()