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 com.company;
import java.util.*;
import java.lang.*;
import java.io.*;
//****Use Integer Wrapper Class for Arrays.sort()****
public class DJ3 {
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
    public static void main(String[] Args){
        FastReader scan=new FastReader();
        int t=1;
//        t=scan.nextInt();
        while(t-->0){
            int n=scan.nextInt();
            int[] arr=new int[n];
            for(int i=0;i<n;i++){
                arr[i]=scan.nextInt();
            }
            int[] ans=new int[n];
            Arrays.fill(ans,-1);
            boolean[] can=new boolean[n+1];
            Arrays.fill(can,true);
            int min=0;
            can[0]=false;
            for(int i=0;i<n;i++){
                if(arr[i]!=min){
                    ans[i]=min;
                    min=arr[i];
                    can[min]=false;
                }
            }
            int s=0;
            for(;s<=n;s++){
                if(can[s]){
                    break;
                }
            }
            for(int i=0;i<n;i++){
                if(ans[i]==-1){
                    ans[i]=s;
                    s++;
                    while(s<=n){
                        if(can[s]){
                            break;
                        }
                        s++;
                    }
                }
            }
            for(int i=0;i<n;i++){
                out.print(ans[i]+" ");
            }
        }
        out.flush();
        out.close();
    }
    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;
        }
    }

}
