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

import static java.lang.Math.*;
import static java.util.Arrays.*;

public class Main {
    public static void main(String[] args) throws IOException {
        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int T = in.nextInt();
        while (T-- > 0){
            int n = in.nextInt();
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = in.nextInt();
            }
            TreeSet<Integer>v = new TreeSet<>();
            for (int i = 0; i < n; i++) {
                v.add(i+1);
            }
            int ans[] = new int[n];
            ans[0] = a[0];
            v.remove(a[0]);
            for (int i = 1; i < n; i++) {
                if(a[i] == a[i-1]){
                    ans[i] = v.pollFirst();
                }
                else{
                    v.remove(a[i]);
                    ans[i] = a[i];
                }
            }
            boolean cn = true;
            int max = 0;
            for (int i = 0; i < n; i++) {
                max = max(max,ans[i]);
                cn&=max == a[i];
            }
            if(!cn)out.print(-1);
            else{
                for (int i = 0; i < n; i++) {
                    out.print(ans[i] + " ");
                }
            }
           out.println();
        }
        out.close();
    }
}
class event implements Comparable<event>{
    int x, T;

    public event(int x, int t) {
        this.x = x;
        T = t;
    }

    @Override
    public int compareTo(event event) {
        return x != event.x ? Integer.compare(x,event.x) : Integer.compare(T,event.T);
    }
}