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.time.temporal.Temporal;
import java.util.*;

public class A{
    public static void main(String args[])
    {
        Scanner sc=new Scanner(System.in);
        long mod=1000000007l;
        int n=sc.nextInt();
        int arr[]=new int[n];
        for(int j=0;j<n;j++)
        {
            arr[j]=sc.nextInt();
        }

        int ans[]=new int[n+1];


//        TreeMap<Integer,Integer> l=new TreeMap<>();
//        TreeMap<Integer,Integer> map=new TreeMap<>();
        TreeMap<Integer,Integer> f=new TreeMap<>();


//        for(int j=0;j<n;j++)
//        {
//            //if(arr[j]!=arr[j-1])
//            {
//                l.put(arr[j],1);
//                map.put(arr[j],1);
//            }
//        }

        int ind=0;


//        for(int j=0;j<n;j++)
//        {
//            if(l.containsKey(arr[j])&&arr[j]!=0)
//            {
//                ans[j]=f.firstKey();
//                f.remove(ans[j]);
//                l.remove(arr[j]);
//            }
//            else
//            {
//
//
//                while(map.containsKey(ind+1))
//                {
//                    ind++;
//                }
//
//                if(arr[j]<=j)
//                {
//                    ind=j+1;
//                }
//                ans[j]=ind;
//                f.remove(ind);
//                ind++;
//            }
//        }

        for(int j=0;j<n+1;j++)
        {
            ans[j]=j;
            f.put(ans[j],j);
        }

        for(int j=0;j<n;j++)
        {
            if(f.get(arr[j])<=j)
            {
                int temp=ans[j+1];
                int loc=f.get(arr[j]);
                ans[loc]=temp;
                ans[j+1]=arr[j];
                f.put(arr[j],j+1);
                f.put(temp,loc);
            }
        }

        for(int j=0;j<n;j++)
        {
            System.out.print(ans[j]+" ");
        }

    }
}
