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.
/* package codechef; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{   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();
     	int t= 1;
     	while(t-->0)
     	{
     	    int n= sc.nextInt();
     	    //int x= sc.nextInt();
     	   // int m= sc.nextInt();
     	    int a[]= new int[n];
     	    int min=0;
     	    HashMap<Integer,Integer> h =new HashMap<>();
     	   for(int i=0;i<n;i++)
     	   {
     	       a[i]=sc.nextInt();
     	       if(h.containsKey(a[i]))
     	       h.put(a[i],h.get(a[i])+1);
     	       else
     	       h.put(a[i],1);
     	   }
     	   PriorityQueue<Integer> p= new PriorityQueue<>();
     	   for(int i=0;i<2*n;i++)
     	   {
     	       if(!h.containsKey(i))
     	       p.add(i);
     	   }
     	   HashMap<Integer,Integer> h1= new HashMap<>();
     	   int flag=0;
     	   int b[]=new int[n];
     	   for(int i=0;i<n;i++)
     	   {
     	       int x= p.poll();
     	       b[i]=x;
     	       h1.put(x,1);
     	       while(h1.containsKey(min))
     	       min++;
     	       if(min!=a[i])
     	       {
     	           flag=1;
     	           break;
     	       }
     	       if(h.get(a[i])>1)
     	       h.put(a[i],h.get(a[i])-1);
     	       else
     	       {h.remove(a[i]);
     	       p.add(a[i]);}
     	   }
     	   if(flag==1)
     	   System.out.println("-1");
     	   else
     	   {
     	       for(int i=0;i<n;i++)
     	       System.out.print(b[i]+" ");
     	   }
     	}
     	
	}
	static class Pair
	{
	    int x;
	    int y;
	    public Pair(int a, int b)
	    {
	        x=a;
	        y=b;
	    }
	}
}
