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 codechef; // 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 Main
{
    
	public static void main (String[] args) throws java.lang.Exception
	{
	
	BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
	int t=Integer.parseInt(bf.readLine());
	while(t-->0)
	{
	    int n=Integer.parseInt(bf.readLine());
	    int a[]=new int[n];
	    boolean min[]=new boolean[n];
	    String s[]=bf.readLine().split(" ");
	    int tis=0;
	    boolean sangam=false;
	    ArrayList<Integer> al=new ArrayList<>();
	    for(int i=0;i<n;i++)
	    {
	        int z=Integer.parseInt(s[i]);
	        if(min[z-1]==false)
	        {
	          a[i]=z;
	     //     al.add(z);
	          min[z-1]=true;
	       //   if(z==tis)
	       //   {
	       //       tis++;
	       //   }
//	          System.out.println(Arrays.toString(a));
	          
	        }
	        else
	        {
	           // if(tis<z)
	           // {
	           //     a[i]=tis;
	           //     al.add(tis);
	           //     tis++;
	           //     while(al.contains(tis))
	           //     {
	           //     tis++;
	           //     }
	           // }
	           
	            int k=check(min,tis);
	            tis=k;
	            if(k!=-1 && k<z-1)
	            {
	                a[i]=k+1;
	                min[k]=true;
	            }
	            else
	            {
	                sangam=true;
	                break;
	            }
	            
	        }
	    }
	    if(sangam)
	    {
	        System.out.println(-1);
	    }
	    else
	    {
	        for(int i=0;i<n;i++)
	        {
	            System.out.print(a[i]+" ");
	        }
	        System.out.println();
	    }
	//    System.out.println(tis);
	    
	}
	
	}
public static int check(boolean []a,int index)
{
    for(int i=index;i<a.length;i++)
    {
        if(a[i]==false)
        {
          //  index=i;
            return i;
        }
    }
    return -1;
}
	
}