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 MEX {
    public static void main(String[] args) throws Exception{
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(in.readLine());
        int[] arr = new int[n];
        StringTokenizer st = new StringTokenizer(in.readLine());
        int max = -1;
        Set<Integer> set = new TreeSet<>();
        for(int i = 0; i < n; i++){
            arr[i] = Integer.parseInt(st.nextToken());
            set.add(arr[i]);
            max = Math.max(arr[i], max);
        }
        in.close();

        int currSection = 0;
        int num = 0;
        List<Integer> sections = new ArrayList<>(set);
        sections.add(n);
        int[] ans = new int[n];
        for(int i = 0; i < n; i++){
            if(i != 0) {
                if (arr[i] != arr[i - 1]) {
                    ans[i] = sections.get(currSection);
                    currSection++;
                    continue;
                }
            }
            while(set.contains(num)){
                num++;
            }
            ans[i] = num;
            num++;
        }
        for(int i: ans){
            System.out.print(i + " ");
        }
    }
}
