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:
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Ideone
{
	public static void main(String[] args) throws java.lang.Exception{
        Scanner input = new Scanner(System.in);
        int t = input.nextInt();
        for(int i=0;i<t;i++){
            input.nextLine();
            int n = input.nextInt();
            int[] q = new int[n+1];
            input.nextLine();
            for(int j=1;j<=n;j++){
                q[j] = input.nextInt();
            }
            q[0] = Integer.MIN_VALUE;
            HashSet<Integer> nums = new HashSet<Integer>();
            for(int j=1;j<=n;j++){                                        
                nums.add(j);                                          
            }
            ArrayList<Integer> x = new ArrayList<Integer>(nums);
            int[] p = new int[n+1];
            for(int j=n;j>0;j--){
                if(q[j]!=q[j-1]){
                    p[j] = q[j];
                    nums.remove(p[j]);
                }else {
                    p[j] = -1;
                    x.add(j);
                }
            } 
            boolean res = true;
            Iterator<Integer> it = nums.iterator();
            for(int j=x.size()-1;j>=0;j--){
                int k;
                if(it.hasNext()){
                    k = (int) it.next();
                    if(k>q[x.get(j)]){
                        res = false;
                    }else {
                        p[x.get(j)] = k;
                    }
                }
                if(res==false){
                    break;
                }
            }
            if(res==false) {
                System.out.println("-1");
            }else {
                for(int j=1;j<=n;j++){
                    System.out.print(p[j]+" ");
                }
                System.out.println();
            }
        }   
    }
}