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.*;
import java.lang.*;
import java.io.*;
public class Dominated_Subarray {

  public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

  static class FastReader {

    BufferedReader br;
    StringTokenizer st;

    public FastReader() {
      br = new BufferedReader(new
          InputStreamReader(System.in));
    }

    String next() {
      while (st == null || !st.hasMoreElements()) {
        try {
          st = new StringTokenizer(br.readLine());
        } catch (IOException e) {
          e.printStackTrace();
        }
      }
      return st.nextToken();
    }

    int nextInt() {
      return Integer.parseInt(next());
    }

    long nextLong() {
      return Long.parseLong(next());
    }

    double nextDouble() {
      return Double.parseDouble(next());
    }

    String[] nextSArray() {
      String sr[] = null;
      try {
        sr = br.readLine().trim().split(" ");
      } catch (IOException e) {
        e.printStackTrace();
      }
      return sr;
    }

    String nextLine() {
      String str = "";
      try {
        str = br.readLine();
      } catch (IOException e) {
        e.printStackTrace();
      }

      return str;
    }
  }

  //  static int MOD=1000000000+7;
//  public static void sortbyCol(int arr[][],int col)
//  {
//    Arrays.sort(arr,new Comparator<int[]>(){
//      @Override
//      public int compare(int[] o1, int[] o2) {
//        // To sort in descending order revert
//        // the '>' Operator
//        if(o1[col]>o2[col])
//          return 1;
//        else
//          return -1;
//      }
//    });
//  }


  public static void main(String[] args) throws java.lang.Exception {
    FastReader sc = new FastReader();
    int t = sc.nextInt();
    for (int t1 = 0; t1 < t; ++t1) {
      int n=sc.nextInt();
      ArrayList<Integer>al=new ArrayList<>();
      boolean printed=false;
      String s[]=sc.nextLine().trim().split(" ");
    //  System.out.println(s[0]+s[1]+s[2]+s[3]);
      boolean arr[]=new boolean[n];
      int previousele=0,k=0;
      for(int i=0;i<n;++i)
      {
        arr[i]=true;
      }
      for (int i=0; i<n ;++i)
      {
        int currentele=Integer.parseInt(s[i]);
        //System.out.println(previousele+" "+currentele);
          if(i==0)
          {  al.add(currentele);arr[currentele-1]=false;;
          previousele=currentele;
          continue;}

          if(previousele==currentele)
          {
            int ele=currentele;
            boolean found=false;

            for(int j=k;j<currentele-1;++j)
            {
              if(arr[j]==true)
              {
                arr[j]=false;
                k=j;
                al.add(j+1);
                found=true;
                break;
              }

            }

//            for(Integer k:hm.keySet())
//            {
//           if(k<currentele)
//           {
//             al.add(k);
//             hm.remove(k);
//             found=true;
//             break;
//           }

            if(!found)
            {
              out.println(-1);
              printed=true;
              break;
            }
//            al.add(ele);
//            hm.put(ele,false);
          }
          else
          {
            al.add(currentele);
            arr[currentele-1]=false;
           // hm.remove(currentele);
          }
        previousele=currentele;
      }
      if(!printed)
      out.println(al.toString().replaceAll("[\\[|\\]|,]",""));
    }
    out.close();
  }


  }


// out.println(al.toString().replaceAll("[\\[|\\]|,]",""));