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.*;

public class Main {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int N=1;
        for(int i=0;i<N;i++){
            help(s);
        }
    }
    public static void help(Scanner s){
        int n=s.nextInt();
        int[] a=new int[n];
        int[] used=new int[n+1];
        for(int i=0;i<n;i++){
            a[i]=s.nextInt();
            used[a[i]]++;
        }
        for(int i=0;i<n;i++){
            if((i!=0&&a[i]<a[i-1])||a[i]>i+1){
                System.out.println(-1);
                return;
            }
        }
        List<Integer> b=new ArrayList<>();
        int p=0;
        for(int i=0;i<n;i++){
            if(i!=0&&a[i]!=a[i-1]) {
                b.add(a[i - 1]);
                p=Math.max(p,a[i-1]+1);
            }
            else {
                for (; p <= n; p++) {
                    if (used[p] == 0) {
                        b.add(p);
                        break;
                    }
                }
                p++;
            }
            used[a[i]]--;
        }
        System.out.println(help(b));
    }
    public static String help(List<Integer> print){
        StringBuilder ans=new StringBuilder();
        ans.append(print.get(0));
        for(int i=1;i<print.size();i++){
            ans.append(' ');
            ans.append(print.get(i));
        }
        return ans.toString();
    }
}