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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class CodeChef {
    static int mod = (int)1e9+7;
    public static void main(String[] args)  {
        Scanner sc = new Scanner();
        Functions f = new Functions();
            int n = sc.nextInt();
            int[] arr = sc.setIntegerArray(n);
            int[] b = new int[n];
            int min = 999999;
            boolean isPossible = true;
            Set<Integer> set = new HashSet<>();
            for(int i=0;i<n;i++){
                if(arr[i]==0){
                    b[i]=1;
                    set.add(1);
                }
                else{
                    for(int j=0;j<1e9;j++){
                        if(j==arr[i])continue;
                        if(!set.contains(j)){
                            set.add(j);
                            b[i] = j;
                            break;
                        }
                    }
                    min = Math.min(b[i],min);
                    if(arr[i]<min){
                        isPossible = false;
                        break;
                    }
                }

            }
            if(!isPossible) System.out.println(-1);
            else
            for(int ele : b) System.out.print(ele+" ");

        
    }

}
class Scanner {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st = new StringTokenizer("");
    public String next(){
        while (!st.hasMoreTokens())
            try {
                st = new StringTokenizer(br.readLine());
            }catch (IOException e){
                e.printStackTrace();
            }
        return st.nextToken();

    }
    public int nextInt(){
        return Integer.parseInt(next());
    }
    public long nextLong(){
        return Long.parseLong(next());
    }
    public int[] setIntegerArray(int n){
        int[] arr =new int[n];
        for(int i=0;i<n;i++)arr[i] = nextInt();
        return arr;
    }
    public long[] setLongArray(int n){
        long[] arr =new long[n];
        for(int i=0;i<n;i++)arr[i] = nextLong();
        return arr;
    }
}
class Functions extends CodeChef{
    public void sort(int[] a){
        ArrayList<Integer> temp = new ArrayList<>();
        for (int j : a) temp.add(j);
        Collections.sort(temp);;
        for(int i=0;i<a.length;i++)a[i] = temp.get(i);
    }
    public long factorial(int n){
        long fact = 1L;
        for(int i=2;i<=n;i++)fact=  (fact*i)%mod;
        return fact;
    }
    public void sortRev(int[] a){
         sort(a);
         int left = 0;
         int right = a.length-1;
         while (left<right){
             int temp =a[left];
             a[left] = a[right];
             a[right] = temp;
             left++;
             right--;
         }
    }
}