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.io.*;
import java.math.*;
 
public class A {
 
    public static void main(String[] args) throws Exception {
        // FileInputStream inputStream = new FileInputStream("input.txt");
        // FileOutputStream outputStream = new FileOutputStream("output.txt");
 
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
         
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
 
        Solver solver = new Solver();     
        int t = in.nextInt();
        // int t = 1;
        for (int i = 0 ; i < t ; i++) {
            solver.solve(1, in, out);
        }
                 
        out.close();
    }
 
    static class Solver {

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int[] q = new int[n];
            for (int i = 0 ; i < n ; i++) {
                q[i] = in.nextInt();
            }
            boolean[] used = new boolean[n + 1];
            int current = 1;
            int[] p = new int[n];
            p[0] = q[0];
            used[p[0]] = true;
            for (int i = 1 ; i < n ; i++) {
                if (q[i] > q[i - 1]) {
                    p[i] = q[i];
                    used[p[i]] = true;
                } else {
                    boolean found = false;
                    while (current < q[i]) {
                        if (used[current]) current++; else {
                            found = true;
                            break;
                        }
                    }
                    if (found) {
                        p[i] = current;
                        used[current] = true;
                    } else {
                        out.println(-1);
                        return;
                    }
                }
            }
            for (int i = 0 ; i < n ; i++) out.print(p[i] + " "); out.println();
        }

    }

    
             
 
    static class InputReader {
 
        public BufferedReader reader;
        public StringTokenizer tokenizer;
 
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
 
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
 
        public int nextInt() {
            return Integer.parseInt(next());
        }
 
        public long nextLong() {
            return Long.parseLong(next());
        }
 
        public double nextDouble() {
            return Double.parseDouble(next());
        }
 
        public float nextFloat() {
            return Float.parseFloat(next());
        }
    }
}