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 javax.swing.*;
import java.util.*;
import java.io.*;
import static java.lang.Math.*;

public class C
{
    /*
     * This FastReader code is taken from GeeksForGeeks.com
     * https://www.geeksforgeeks.org/fast-io-in-java-in-competitive-programming/
     *
     * The article was written by Rishabh Mahrsee
     */
    public 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 FastReader in = new FastReader();
    public static PrintWriter out = new PrintWriter(System.out);
    public static final int MOD = (int)1e9 + 7;

    public static void main(String[] args)
    {
        int n = in.nextInt();
        boolean[] used = new boolean[(int)1e6 + 1];
        int[] arr = new int[n];
        int[] answer = new int[n];

        for (int i = 0; i < n; i++)
        {
            arr[i] = in.nextInt();
            used[arr[i]] = true;
        }
        int curUnused = 0;
        while (used[curUnused]) curUnused++;

        int i = 0;
        while (i < n)
        {
            while ( i - 1 >= 0 && i < n && arr[i] == arr[i - 1])
            {
                answer[i++] = curUnused++;
                while (used[curUnused]) curUnused++;
            }
            if (i < n)
            {
                answer[i] = i != 0 ? arr[i - 1] : curUnused++;
                while (used[curUnused]) curUnused++;
                i++;
            }
        }

        for (int x : answer) out.print(x + " ");
        out.println();
        out.close();
    }


}
