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.
/* package codechef; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner input = new Scanner(System.in);
		int n = input.nextInt();
		int arr[] = new int[n];
		TreeSet<Integer>set = new TreeSet<>();
		for(int i =0;i<n;i++){
		    arr[i] = input.nextInt();
		    set.add(arr[i]);
		    
		}
		int prev = 0;
		if(arr[0] != 0){
		    System.out.print((arr[0]-1)+" ");
		}else{
		    for(int i =0;i<n;i++){
		        if(!set.contains(i)){
		            System.out.print(i+" ");
		            prev =i;
		            break;
		        }
		    }
		}
		if(set.size() == n){
		    for(int i =1;i<n;i++){
		        
		        System.out.print(arr[i-1]+" ");
		    }
		    return;
		}else{
		    
		    for(int i =1;i<n;i++){
		        
		        if(arr[i] == arr[i-1])System.out.print(prev+" ");
		        else{System.out.print(arr[i-1]+" ");prev = arr[i-1];}
		    }
		}
	}
}
