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.
// Working program with FastReader 
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.Scanner; 
import java.util.StringTokenizer; 
import java.util.*;
import java.io.*;
public class C_Ehab_and_Prefix_MEXs{
    public static void main(String[] args) {
       FastReader sc=new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        int n =sc.nextInt();
        int[] array = new int[n];
        for(int i =0;i<n;i++)array[i] = sc.nextInt();
        boolean ispossible = true;
        for(int i =0;i<n;i++){
            if(array[i]>(i+1))ispossible=false;
            if(i>0 && array[i]<array[i-1])ispossible=false;
        }
        HashSet<Integer> store = new HashSet<>();
        if(ispossible){
            int[] b= new int[n];
            for(int i=0;i<n;i++){
                // store.add(array[i]);
                if(i>0 && array[i]!=array[i-1]){
                    b[i] = array[i-1];
                    store.add(b[i]);
                }
                else{
                    b[i] = -1;
                }
            }
            int max = 0;
            store.add(array[0]);
            store.add(array[n-1]);
            // if(array[0]==0)max++;
            for(int i =0;i<n;i++){
                if(b[i]==-1){
                    while(store.contains(max))max++;
                    b[i] = max;
                    store.add(max);
                }
            }
            for(int i =0;i<n;i++){
                out.print(b[i]+" ");
            }
            out.println();
        }
        else{
            out.println(-1);
        }
        out.close();
    }

    
    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; 
        } 
}
}
