Given an array a of length n, find another array, b, of length n such that:

  * for each i (1 ≤ i ≤ n) MEX(\\{b_1, b_2, …, b_i\})=a_i. 



The MEX of a set of integers is the smallest non-negative integer that doesn't belong to this set.

If such array doesn't exist, determine this.

Input

The first line contains an integer n (1 ≤ n ≤ 10^5) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ i) — the elements of the array a. It's guaranteed that a_i ≤ a_{i+1} for 1≤ i < n.

Output

If there's no such array, print a single line containing -1.

Otherwise, print a single line containing n integers b_1, b_2, …, b_n (0 ≤ b_i ≤ 10^6)

If there are multiple answers, print any.

Examples

Input


3
1 2 3


Output


0 1 2 

Input


4
0 0 0 2


Output


1 3 4 0 

Input


3
1 1 3


Output


0 2 1 

Note

In the second test case, other answers like [1,1,1,0], for example, are valid.
/*Radhe Krishna*/
import javax.management.DynamicMBean;
import javax.print.DocFlavor;
import javax.print.attribute.HashAttributeSet;
import java.awt.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.net.CookieHandler;
import java.nio.file.attribute.FileAttribute;
import java.util.List;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.*;
import java.util.Arrays;
import java.util.concurrent.Callable;



public class Main {
    static int mod=1000000007;
    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 nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    public static void main(String[] args) {
        FastReader sc = new FastReader();
//        PrintWriter out = new PrintWriter(System.out);
       int n=sc.nextInt();
       int[] a=new int[n];
       int[] b=new int[n];
       HashSet<Integer> set=new HashSet<>();
       for(int j=0;j<n;j++){
           a[j]=sc.nextInt();
           set.add(a[j]);
       }
       int flag=1;
       for(int j=0;j<n;j++){
           if(a[j]>(j+1)){
               flag=0;
               break;
           }
           else{
               if(j==0){
                   b[j]=a[j]==0?1:0;
                   continue;
               }
               if(a[j]>a[j-1]){
                   b[j]=a[j-1];
               }
               else{
                   int num=b[j-1]+1;
                   if(num>1000000){
                       flag=0;
                       break;
                   }
                   while(set.contains(num)){
                       num++;
                       if(num>1000000){
                           flag=0;
                           break;
                       }
                   }
                   b[j]=num;
               }

           }
           if(flag==0){
               break;
           }
       }
       if(flag==0){
           System.out.println(-1);
       }
       else{
           for(int j=0;j<n;j++){
               System.out.print(b[j]+" ");
           }
           System.out.println(" ");
       }
    }
}