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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author abacaba
 */
public class c {
    public static void main(String[] args) {
        FS in = new FS(System.in);
        PrintWriter out = new PrintWriter(System.out);
        
//        int t = in.nextInt(); int c = 0; while(c++<t) {
//            out.print("Case #" + c + ": ");
            new c().solve(in, out);
//        }
        
        out.close();
    }
    
    static int MAX = 10_000_000;
    
    void solve(FS in, PrintWriter out) {
        int n = in.nextInt();
        boolean[] has = new boolean[1_000_000];
        int next = 0;
        int[] arr = new int[n];
        for(int i = 0; i < n; i++) {
            has[arr[i] = in.nextInt()] = true;
        }
        for(int i = 0; i < n; i++) {
            if(i != 0 && arr[i] != arr[i-1]) out.print(arr[i-1] + " ");
            else {
                while(has[next]) next++;
                out.print(next++ + " ");
            }
        }
        out.println();
    }
    
    static class FS {
        BufferedReader in; StringTokenizer tk;
        public FS(InputStream st) {
            in = new BufferedReader(new InputStreamReader(st));
            tk = new StringTokenizer("");
        }
        
        public String next() {
            if(tk.hasMoreTokens()) return tk.nextToken();
            try { tk = new StringTokenizer(in.readLine()); } catch(Exception e) {}
            return next();
        }
        
        public int nextInt() { return Integer.parseInt(next()); }
    }
}
