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 solution {
	public static void main(String[] args)  {
		 Scanner sc=new Scanner(System.in);
	     int t=sc.nextInt();
	     for(int i=0;i<t;i++) {
	    	 int n=sc.nextInt();
	    	 HashSet<Integer> h=new HashSet<Integer>();
	    	 ArrayList<Integer> a=new ArrayList<Integer>();
	    	 ArrayList<Integer> v=new ArrayList<Integer>();
	    	 for(int j=0;j<n;j++) {
	    		 a.add(sc.nextInt());
	    		 h.add(a.get(j));
	    	 }
	    	 for(int j=0;j<n;j++) {
	    		 if(!h.contains(j+1)) {
	    			 v.add(j+1);
	    		 }
	    	 }
	    	 int m=0;
	    	 int[] ans=new int[n];
	    	 ans[0]=a.get(0);
	    	 m=0;
	    	 boolean f=true;
	    	 for(int j=1;j<n;j++) {
	    		 if(a.get(j)>a.get(j-1)) {
	    			 ans[j]=a.get(j);
	    		 }
	    		 else{
	    			 if(v.get(m)<a.get(j)) {
	    				 ans[j]=v.get(m);
	    				 m++;
	    			 }
	    			 else {
	    				 f=false;
	    				 break;
	    			 }
	    		 }
	    	 }
	    	 if(f) {
	    		 for(int j=0;j<n;j++) {
		    		 System.out.print(ans[j]+" ");
		    	 } 
	    		 System.out.println();
	    	 }
	    	 else {
	    		 System.out.println(-1);
	    	 }
	     }
	}
}