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 ehabandprefix {
    public static void main(String[]args)throws Exception{
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        ArrayList<Integer>list = new ArrayList<>();
        HashSet<Integer>set = new HashSet<>();
        ArrayList<Integer>blist = new ArrayList<>();
        int n = sc.nextInt();
        int inc = 0;
        for(int i = 0; i < n; i++){
            int a = sc.nextInt();
            list.add(a);
            set.add(a);
        }
        if(list.get(inc) == 0){
            blist.add(1);
            set.add(1);
        }
        else{
            blist.add(0);
            set.add(0);
            inc++;
        }
        for(int i = 1; i < n; i++){
            if(list.get(i) == list.get(i-1)){
                while(set.contains(inc)){
                    inc++;
                }
                blist.add(inc);
                set.add(inc);
            }
            else{
                blist.add(list.get(i-1));
            }
        }
        for(int i = 0; i < n; i++){
            out.print(blist.get(i) + " ");
        }
        out.close();
    }
}
