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 Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		while(t-- != 0){
		    int n = sc.nextInt();
		    int a[] = new int [n];
		    HashSet<Integer> hs = new HashSet<>();
		    for(int i = 0 ; i < n ; i++){
		        a[i] = sc.nextInt();
		    }
		    for(int i = 0 ; i < n ; i++){
		        hs.add(i+1);
		    }
		    int m[] = new int [n];
		    HashSet<Integer> hm = new HashSet<>();
		    boolean ss = false;
		    for(int i = 0 ; i < n ; i++){
		        if(a[i] == i){
		            ss = true;
		            break;
		        }else{
		            if(hm.contains(a[i])){
		                continue;
		            }else{
		                m[i] = a[i];
		                hm.add(a[i]);
		                hs.remove(a[i]);
		            }
		        }
		    }
		    ArrayList<Integer> al = new ArrayList<>();
		    Iterator<Integer> it = hs.iterator();
		    while(it.hasNext()){
		        al.add(it.next());
		    }
		    Collections.sort(al);
		    int ind = 0;
		    for(int i = 0 ; i < n ; i++){
		        if(m[i] == 0){
		            if(ind == al.size()){
		                ss = true;
		                break;
		            }
		            m[i] = al.get(ind);
		            ind++;
		        }
		    }
		    if(ss){
		        System.out.println(-1);
		    }else{
    		    for(int i = 0 ; i < n ; i++){
    		        System.out.print(m[i] + " ");
    		    }
    		    System.out.println();
		    }
		}
	}
}