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.

// Problem: C. Ehab and Prefix MEXs
// Contest: Codeforces - Codeforces Round #649 (Div. 2)
// URL: https://codeforces.com/contest/1364/problem/C
// Memory Limit: 256 MB
// Time Limit: 1000 ms
// Powered by CP Editor (https://github.com/cpeditor/cpeditor)

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

public class Main {
    private static PrintWriter pw = new PrintWriter(System.out);
    private static InputReader sc = new InputReader();
    private static final int intmax = Integer.MAX_VALUE, intmin = Integer.MIN_VALUE;

    static class Pair<T1, T2>{
        T1 first;
        T2 second;
        Pair(T1 first, T2 second){
            this.first = first;
            this.second = second;
        }
    }

    static class InputReader{
        private static BufferedReader r = new BufferedReader(new InputStreamReader(System.in));
        private static StringTokenizer tk;

        private void next()throws IOException{
            if(tk == null || !tk.hasMoreTokens())   
                tk = new StringTokenizer(r.readLine());
        }

        private int nextInt()throws IOException{
            next();
            return Integer.parseInt(tk.nextToken());
        }

        private long nextLong()throws IOException{
            next();
            return Long.parseLong(tk.nextToken());
        }

        private String readString()throws IOException{
            next();
            return tk.nextToken();
        }

        private double nextDouble()throws IOException{
            next();
            return Double.parseDouble(tk.nextToken());
        }

        private int[] intArray(int n)throws IOException{
            next();
            int arr[] = new int[n];

            for(int i=0; i<n; i++)
                arr[i] = nextInt();

            return arr;
        }

        private long[] longArray(int n)throws IOException{
            next();
            long arr[] = new long[n];

            for(int i=0; i<n; i++)
                arr[i] = nextLong();

            return arr;
        }
    }

    public static void main(String args[])throws IOException{
        int t = 1;
        while(t-->0)    solve();
        pw.flush();
        pw.close();
    }

    private static void solve()throws IOException{
		int n = sc.nextInt(), mex[] = sc.intArray(n), arr[] = new int[n];
		boolean na[] = new boolean[n+1];
		
		for(int i=0; i<n; i++)	arr[i] = -1;
		
		for(int i=1; i<n; i++){
			if(mex[i] != mex[i-1]){
				arr[i] = mex[i-1];
				na[mex[i-1]] = true;
			}
		}
		
		na[mex[n-1]] = true;
		
		if(mex[0] == 1){
			arr[0] = 0;
			na[0] = true;
		}
		
		int no = 0;
		for(int i=0; i<n; i++){
			if(arr[i] == -1){
				while(na[no]){
					no++;
				}
				arr[i] = no;
				na[no] = true;
				// pw.println(Arrays.toString(arr)+" "+no);
			}
		}
		
		// pw.println(Arrays.toString(arr));
		
		boolean w[] = new boolean[n+1]; 
		int curr = 0;
		
		for(int i=0; i<n; i++){
			w[arr[i]] = true;
			
			while(curr<=n && w[curr])	curr++;
			
			if(mex[i] != curr){
				pw.println(-1);
				return;
			}
		}
		
		for(int i=0; i<n; i++)
			pw.print(+arr[i]+" ");
		pw.println();
    }
}