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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public final class CodeForces648C {
    public static void main(String args[]){
        FastReader sc=new FastReader(); 
        PrintWriter out = new PrintWriter(System.out);
        int n =sc.nextInt();
        int a[] = new int[n];
        int f[] = new int[1000001];
        for(int j=0;j<n;j++){
            a[j] = sc.nextInt();
            f[a[j]] = 1;
        }
        
        
        for(int j=0;j<n;j++){
            if(a[j]>j+1){
                System.out.println("-1");
                System.exit(0);
            }
        }
        
        int max = a[n-1];
        int b[] = new int[n+1];
        int c[] = new int[n+1];
        int fLen = f.length;
        int k=0,t=0;
        for(int j=0;j<=n;j++){
            if(f[j]==0){
                b[k++]=j;
            }
            else{
                c[t++]=j;
            }
        }
        
        int z=0,m=0;
        
        StringBuilder ans = new StringBuilder();
        ans.append(b[z++]+" ");
        for(int j=1;j<n;j++){
            if(a[j]!=a[j-1]){
                ans.append(a[j-1]+" ");
            }
            else{
                ans.append(b[z++]+" ");
            }
        }
        System.out.println(ans);
        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) 
                { 
                } 
            } 
            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) 
            { 
                
            } 
            return str; 
        } 
    } 
}
