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 problems;

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

public class Main {
    public static void main(String[] args) throws IOException {
        //BufferedReader in = new BufferedReader(new FileReader("haybales.in"));
        //PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("haybales.out")));
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));

        int t = Integer.parseInt(in.readLine());
        for (int c = 0; c < t; c++) {
            boolean poss = true;
            int n = Integer.parseInt(in.readLine());
            HashSet<Integer> set = new HashSet<>();
            StringTokenizer st = new StringTokenizer(in.readLine());
            int[] ans = new int[n];
            ans[0] = Integer.parseInt(st.nextToken());
            set.add(ans[0]);
            int x = 1;
            for (int i = 1; i < n; i++) {
                int a = Integer.parseInt(st.nextToken());
                if (!set.contains(a)) {
                    ans[i] = a;
                    set.add(ans[i]);
                } else {
                    for (; x < a; x++) {
                        if (!set.contains(x)) break;
                    }
                    if (set.contains(x)) poss = false;
                    else {
                        ans[i] = x;
                        set.add(ans[i]);
                    }
                }
            }

            if (poss) {
                for (int i = 0; i < n; i++) {
                    System.out.print(ans[i] + " ");
                }
                System.out.println();
            } else {
                System.out.println(-1);
            }
        }

        //System.out.println();
        //out.println();
        //out.close();
    }
}