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 JAVA):

Solution:
import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;

public class Day9 {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter writer = new PrintWriter(System.out);
        int t = Integer.parseInt(reader.readLine());
        for(int q = 0; q < t; ++q){
            int n = Integer.parseInt(reader.readLine());
            StringTokenizer st = new StringTokenizer(reader.readLine());
            int[] array = new int[n];
            int l = 0;
            boolean[] used = new boolean[n];
            for(int i = 0; i < n; ++i){
                array[i] = Integer.parseInt(st.nextToken());
            }
            used[array[0] - 1] = true;
            int max = array[0];
            boolean can = true;
            for(int i = 1; i < n; ++i){
                if(!used[array[i] - 1]){
                    used[array[i] - 1] = true;
                    max = array[i];
                }
                else{
                     while( l < n &&  used[l]){
                         ++l;
                     }
                     if(l >= n || l + 1 > max){
                         can = false;
                         break;
                     }
                     array[i] = l + 1;
                     used[l] = true;
                     ++l;
                }
            }
            if(!can){
                writer.println(-1);
                continue;
            }
            StringBuilder ans = new StringBuilder();
            for(int i = 0; i < n; ++i){
                ans.append(array[i]);
                ans.append(" ");
            }
            writer.println(ans);
        }
        writer.close();
    }
}