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 mexx
{
    public static void main(String args[])
    {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int arr[]=new int[n],arr2[]=new int[n];
        for(int i=0;i<n;i++)
            arr[i]=sc.nextInt();
        if(arr[n-1]-1<0)
        {
            System.out.println("-1");
            return;
        }
        else
        {
            arr2[0]=arr[n-1]-1;
            for(int i=1;i<n;i++)
            {
                arr2[i]=arr2[i-1]-1;
                if(arr2[i]==0)
                    break;
            }
        }
        for(int i=0;i<n;i++)
            System.out.print(arr2[i]+" ");
    }
}
            