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.
/******************************************************************************

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                Code, Compile, Run and Debug java program online.
Write your code in this editor and press "Run" button to execute it.

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import java.util.*;
import java.io.*;
public class Main
{
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        PrintWriter out = new PrintWriter(System.out);
        int n = Integer.parseInt(st.nextToken());
        int[] a = new int[n];
        st = new StringTokenizer(br.readLine());
        HashSet<Integer> used = new HashSet<Integer>();
        boolean works = true;
        for(int i = 0 ; i < n; i++){
            a[i] = Integer.parseInt(st.nextToken());
            used.add(a[i]);
            if(a[i] > i+1)
                works = false;
        }
        if(!works)
            out.println(-1);
        else{
            int[] ans = new int[n];
            int next = 0;
            int index = 0;
            while(index < n){
                if(index > 0 && a[index] != a[index-1]){
                    ans[index] = a[index-1];
                    index++;
                }
                else if(used.contains(next))
                    next++;
                else{
                    ans[index] = next;
                    index++;
                    next++;
                }
            }
            StringJoiner sj = new StringJoiner(" ");
            for(int i = 0; i < n; i++){
                sj.add(Integer.toString(ans[i]));
            }
            out.println(sj);
        }
        out.close();
	}
}
