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 Main {
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int n = input.nextInt();
        int[] a = new int[n+1];
        int[] b = new int[n+1];
        int[] c = new int[n+1];
        int[] s = new int[n+1];
        ArrayList<Integer>[] lists = new ArrayList[n+1];
        lists[0] = new ArrayList<>();
        boolean flag = true; a[0] = 0; c[0] = -1;
        int last = 0;
        for (int i=1;i<=n;i++) {
            lists[i] = new ArrayList<>();
            a[i] = input.nextInt(); c[i] = -1;
            if (a[i] > i) flag = false;
            if (a[i] > a[i-1]){
                s[i] = i-last;
                b[i] = 1;
                last = i;
            }
        }
        if (!flag) System.out.println("-1");
        else {
            int l = 1,lst = 0;
            for (int i=1;i<=n;i++){
                if (b[i] == 1){
                    lists[i].add(lst);
                    lst++;
                    while(lst<a[i]){
                        if(lists[l].size()>=s[l]) l++;
                        else{
                            lists[l].add(lst);
                            lst++;
                        }
                    }
                    lst=a[i];
                }
            }
            for (int i=n;i>=1;i--){
                if(lists[i].size() > 0){
                    int pos=i;
                    lists[i].sort(new Comparator<Integer>() {
                        @Override
                        public int compare(Integer o1, Integer o2) {
                            return o1 - o2;
                        }
                    });
                    int len = lists[i].size();
                    for (int j=0;j<=len-1;j++){
                        c[pos] = lists[i].get(j); pos--;
                    }
                }
            }
            for(int i=1;i<=n;i++) if(c[i] == -1) c[i] = 100010;
            for (int i=1;i<=n;i++) {
                if (i == 1) System.out.print(c[i]);
                else System.out.print(" " + c[i]);
            }
            System.out.println();
        }
    }
}