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.util.*;
public class Main
{
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long t = sc.nextLong();
		while(t>0){
		    int n = sc.nextInt();
		    int a[] = new int[n];
		    int ori[] = new int[n];
		    int missing[] = new int[n];
		    for(int i=0;i<n;i++){
		        a[i] = sc.nextInt();
		        ori[i] = a[i];
		        missing[i] = 1+i;
		    }
		    Arrays.sort(a);
		    int cnt = 0;
		    for(int i=0;i<n;i++){
		        missing[a[i]-1] = 0;
		    }
		    for(int i=0;i<n;i++){
		        if(missing[i]>0){
		            cnt++;
		        }
		    }
		    int len = cnt;
		    int avai[] = new int[cnt];
		    for(int i=0;i<n;i++){
		        if(missing[i]>0){
		            avai[cnt-1] = missing[i];
		            cnt--;
		        }
		    }
		    int j = 0;
		    Arrays.sort(avai);
		    boolean flag = true;
		    
		    if(n>1){
		        if(ori[1]==1){
		            flag = false;
		        }
		    }
		    
		        int max = ori[0];
		        for(int i=1;i<n;i++){
		            if(ori[i]==max){
		                if(ori[i]>avai[j]){
		                    ori[i] = avai[j];
		                    j++;
		                }
		                else{
		                    flag = false;
		                    break;
		                }
	    	        }
	    	        else{
	    	            max = ori[i];
	    	        }
    		    }    
    		    if(flag){
    		        for(int i=0;i<n;i++){
    		            System.out.print(ori[i]+" ");
    		        }
    		        System.out.print("\n");
    		    }
    		    else{
    		        System.out.println(-1);
    		    }
		    
            t--;
		}
	}
}