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.

import java.util.*;
import java.io.*;
import java.math.*;


import static java.lang.Math.*;

 public class Solution implements Runnable {
     
    public void solve() throws Exception {
         int n=sc.nextInt();
         int arr[]=new int[2*n+1];
         int xx[]=new int[n];
         for(int i=0;i<n;i++)
         {
        	xx[i]=sc.nextInt();
        	
        	arr[xx[i]]=1;
         }
         int result[]=new int[n];
         int count=0;
         HashMap<Integer,Integer> map=new HashMap<>();
         
         int c=0;
         
         while(c!=n)
         {
        	 if(c>=0)
        	 {
        		 	if(c>0 && xx[c]!=xx[c-1])
        		 	{
        		 		if(!map.containsKey(xx[c-1]))
        		 		{
        		 			map.put(xx[c-1],1);
        		 			result[c]=xx[c-1];
        		 			c++;
        		 			if(xx[c-1]==count)
        		 				count++;
        		 		}
        		 	}
        	 
        	 else 
        		 {if(arr[count]!=1 || (count<xx[c]))
        	 {
        		 result[c]=count;
        		 c++;
        		 map.put(count, 1);
        		 
        	 }
        		 count++;
        		 }
        	 
         }
         }
          for(int i=0;i<n;i++)
          {
        	  System.out.print(result[i]+" ");
          }
             
                
            
         }
            
         
    
             
         
        
        
       
        
        
    
    // public boolean binarysearch(int limit )
    
    static Throwable uncaught;

    BufferedReader in;
    FastScanner sc;
    PrintWriter out;

    @Override
    public void run() {
        try {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
            sc = new FastScanner(in);
            solve();
        } catch (Throwable uncaught) {
            Solution.uncaught = uncaught;
        } finally {
            out.close();
        }
    }

    public static void main(String[] args) throws Throwable {
        Thread thread = new Thread(null, new Solution(), "", (1 << 26));
        thread.start();
        thread.join();
        if (Solution.uncaught != null) {
            throw Solution.uncaught;
        }
    }

}

class FastScanner {

    BufferedReader in;
    StringTokenizer st;

    public FastScanner(BufferedReader in) {
        this.in = in;
    }

    public String nextToken() throws Exception {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }

    public int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }

}
                  
                  
                  
            
