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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.PriorityQueue;
import java.util.Set;
import java.util.StringTokenizer;



public class q3 {

	public static void main(String[] args) {
		FastReader s = new FastReader();
		
		
		
			int n = s.nextInt();
			int[] inp = new int[n];
			Set<Integer> set = new HashSet<>();
			int flag = 0;
			for(int i=0;i<n;++i)
			{
				inp[i] = s.nextInt();
				set.add(inp[i]);
				
				if(inp[i] > i+1)
					flag = 1;
			}
			
			if(flag == 1)
				System.out.println(-1);
			else{
				PriorityQueue<Integer> q  = new PriorityQueue<>();
				ArrayList<Integer> ans = new ArrayList<>();
				for(int i=0;i<n;++i)
					if(!set.contains(i))
						q.add(i);
				if(q.isEmpty())
					q.add(n+1);
				for(int i=0;i<n;++i)
				{
					int count = q.poll();
					ans.add(count);
					if(i!=n-1 && inp[i] != inp[i+1])
						q.add(inp[i]);
					if(i != n-1 && q.isEmpty() && inp[i] == inp[i+1])
						q.add(count);
				}
				
				
				for(int i=0;i<n;++i)
					System.out.print(ans.get(i)+ " ");
				System.out.println();
			}
			
		


	}


	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;
        }
    }

}
