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.
// package com.company.codeforces;
import com.sun.security.jgss.GSSUtil;

import java.util.*;

public class Solution {
    public static void main(String[] args) {
        Scanner input=new Scanner(System.in);
        int n=input.nextInt();
        int a[]=new int[n];

        HashSet<Integer> set=new HashSet<>();
        for (int i = 0; i <n ; i++) {
            a[i]=input.nextInt();
            set.add(a[i]);
        }
        int res[]=new int[n];
        int ptr=1;
        if (a[0]>1){
            System.out.println(-1);

        }else {
            if (a[0]==0){
                res[0]=1;
                ptr=0;
            }else {
                res[0]=0;
                ptr=1;
            }
            int flag = 0;
            for (int i = 1; i < n; i++) {
                if ((a[i] > i + 1)) {
                    flag = 1;
                    break;
                }

                if (a[i] == a[i - 1]) {
                    int temp = 0;
                    while (set.contains(ptr)) {
                        ptr++;

                    }
                    res[i] = ptr;
                    ptr++;
                    continue;
                } else {
                    res[i] = a[i - 1];
                }


            }
            if (flag==1){
                System.out.println(-1);
            }else {
                for (int i = 0; i <n ; i++) {
                    System.out.print(res[i]+" ");

                }
            }

        }

    }
}
