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

 public class DemoC{
    static  ArrayList<Integer>[] graph;
       static int[] vis;
	public static void main(String[] args) {
	Scanner sc=new Scanner(System.in);
          
             int n=sc.nextInt();
            
             int[] ar=new int[n+1];
             int[] b=new int[n+1];
             Arrays.fill(b,-1);
             int[] vis=new int[n+2];
             for(int i=1;i<=n;i++){
                 ar[i]=sc.nextInt();
             }
               vis[ar[1]]=1;
             for(int i=2;i<=n;i++){
                 vis[ar[i]]=1;
                 if(ar[i]!=ar[i-1]){
                     b[i]=ar[i-1];
                   
                     
                 }
             }
             int m=0;
             for(int i=1;i<=n;i++){
               
               if(b[i]==-1){
                   if(vis[m]==0){
                       b[i]=m;
                       vis[m]=1;
                   }
                     else{  
                       while(vis[m]!=0){
                           if(m<n+1){
                       m++;}
                       else{
                           break;
                       }
                       }
                       b[i]=m;
                       vis[m]=1;
                     }
                   }
               }
             
               StringBuffer ans=new StringBuffer();
               for(int i=1;i<=n;i++){
                  ans.append(b[i]);
                  ans.append(" ");
               }
             System.out.println(ans);
           
    
  }
}