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.*;
import java.util.*;
 

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Unstoppable solver = new Unstoppable();
//	  int t=in.nextInt();
//	  while(t-->0)
        solver.solve(in, out);
        out.close();
    }
 
    static class Unstoppable { 

       public void solve(InputReader in, PrintWriter out) {
       int n=in.nextInt();
       int a[]=new int[n];
       int max=0;
       for(int i=0;i<n;i++){ a[i]=in.nextInt(); max=Math.max(max,a[i]); }
       int ans[]=new int[n];

           for(int i=0;i<n;i++) ans[i]=Math.min(i,(max-1));
           // for(int i=0;i<n;i++) out.print(ans[i]+" "); out.println("");
           for(int i=0;i<n;i++){
           //    if(i>0&&a[i]==a[i-1]){ ans[i]=ans[i-1]; continue; }
               if(ans[i]==a[i]){
                   int k=ans[i];
                   ans[i]=ans[i+1];
                   ans[i+1]=k;
               }
              if(ans[i]==a[i]) ans[i]=1000000;
           }
          
         //    for(int i=0;i<n;i++) out.print(ans[i]+" "); out.println("");
           // for(int i=0;i<n;i++) {  h.add(ans[i]); if(h.contains(a[i])) { out.println("-1"); return; } }
           for(int i=0;i<n;i++) out.print(ans[i]+" "); out.println("");
            
       
       } 
    }
    
 

 
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
 
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
 
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        public long nextLong(){
            return Long.parseLong(next());
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }
 
    }
}
   