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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class a{ 
     static int[] count;
     static int[] count1;
     static int[] arr;
     static char[] ch,ch1;
     static long[] darr;
     static long[][] mat;
     static long x;
     static long maxl;
     static double dec;
     static String s;
     // static long minl;
     static int mx = (int)1e6;
     static long mod = 998244353l;
     // static int minl = -1;
     // static long n;
     static int n,n1,n2;
     static long a;
     static long b;
     static long c;
     static long d;
     static long y;
     static long m;
     static long k;
     static int q;
     static String[] str,str1;
     static Set<Long> set,set1;
     static List<Long> list;
     static Map<Long,Integer> map;
     static StringBuilder sb;

     public static void solve(){

        sb = new StringBuilder();
        count = new int[n+1];

        int[] a = new int[n];
        a[0] = arr[0];
        count[a[0]] = 1;
        sb.append(a[0]+" ");
        int limit = 1;
        if(a[0] == 1)
            limit += 1;

        for(int i = 1 ; i < n ; i++){
            if(arr[i] == arr[i-1]){
                int j = limit;
                while((j < arr[i]) && (count[j] != 0)){
                    j += 1;
                }
                
                if(j >= arr[i]){
                    System.out.println("-1");
                    return;
                }
                limit = j;
                a[i] = j;
                count[j] = 1;
            }
            else{
                a[i] = arr[i];
                count[arr[i]] = 1;
            }
            sb.append(a[i] + " ");
        }
        System.out.println(sb);

     }

     public static void main(String[] args) {

            FastScanner sc = new FastScanner();
            // Scanner sc = new Scanner(System.in);
            int t = sc.nextInt();
            // int t = 1;
            while(t > 0){
                 // set = new HashSet<>();
                 // map = new HashMap<>();
                
                // x = sc.nextLong();
                // y = sc.nextLong();
                
                
                
                n = sc.nextInt();
                // n1 = sc.nextInt();
                // n1 = sc.nextInt();

                // a = sc.nextLong();
                // b = sc.nextLong();
                // c = sc.nextLong();
                // d = sc.nextLong();
                // k = sc.nextLong();
                // // n = sc.nextLong();
                // // x = sc.nextLong();
                // ch = sc.next().toCharArray();
                // ch1 = sc.next().toCharArray();
                // s = sc.next();

                 // long x = sc.nextLong();

                
                // k = sc.nextLong();
                // dec = sc.nextDouble();
                // n = sc.nextInt();
                // m = sc.nextLong();
                 
                arr = new int[n];
                for(int i = 0; i < n ; i++){
                    arr[i] = sc.nextInt();
                }
                // // set = new HashSet<>();
                // for(int i = 0 ; i < n ; i++)
                //     set.add(sc.next().charAt(0));
                
                // n1 = sc.nextInt();
                //  darr = new long[n1];
                //  for(int i = 0; i < n1 ; i++){
                //      darr[i] = sc.nextLong();
                //  }

                // mat = new long[n][n1];

                // for(int i = 0 ; i < n ; i++){
                //     for(int j = 0 ; j < n1 ; j++){
                //         mat[i][j] = sc.nextLong();
                //     }
                // }


                // System.out.println(solve()?"YES":"NO");
                 solve();
                 // System.out.println(solve());
                 // sb = new StringBuilder();
                 // sb.append(str);

                 t -= 1;
            }

     }

    public static int log(long n){
         if(n == 0)
             return 0;

         if(n == 1)
             return 0;
         if(n == 2)
             return 1;
         double num = Math.log(n);
         double den = Math.log(2);
         if(den == 0)
             return 0;
         return (int)(num/den);
     }

     public static long gcd(long a,long b){

        if(b%a == 0)
            return a;

        return gcd(b%a,a);

     }

     // public static void swap(int i,int j){
     //     long temp = arr[j];
     //     arr[j] = arr[i];
     //     arr[i] = temp;
     // } 

    static final Random random=new Random();
    
    static void ruffleSort(long[] a) {
        int n=a.length;//shuffle, then sort 
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n);
            long temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }

    static class Node{
        int first;
        int second;
        Node(int f,int s){
            this.first = f;
            this.second = s;
        }
    }

     static class FastScanner {

                BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
                StringTokenizer st=new StringTokenizer("");
                String next() {
                        while (!st.hasMoreTokens())
                                try {
                                        st=new StringTokenizer(br.readLine());
                                } catch (IOException e) {
                                        e.printStackTrace();
                                }
                        return st.nextToken();
                }
                
                int nextInt() {
                        return Integer.parseInt(next());
                }
                int[] readArray(int n) {
                        int[] a=new int[n];
                        for (int i=0; i<n; i++) a[i]=nextInt();
                        return a;
                }
                long nextLong() {
                        return Long.parseLong(next());
                }
        }

}