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.*;
import java.io.*;

public class main{
    static Read input  = new Read();

    public static void main(String args[]){
        int n = input.nextInt(), all[] = new int[n], ans[] = new int[n];
        boolean used[] = new boolean[n+5];
        for (int i=0;i<n;i++) {
            all[i] = input.nextInt();
            used[all[i]] = true;
        }

        int cur = 1-all[0], low = all[0];

        for (int i=0;i<n;i++){
            while (cur<n+5 && used[cur]==true) cur++;
            if (low==all[i]) {
                ans[i] = cur;
                cur++;
            } else {
                ans[i] = low;
                low = all[i];
            }
        }

        for (int i=0;i<n;i++) System.out.print(ans[i]+" ");

    }

    static class Read{
        BufferedReader br;
        StringTokenizer st;
        public Read(){br = new BufferedReader(new InputStreamReader(System.in));}
        String next(){
            while (st==null || !st.hasMoreElements()){
                try { st = new StringTokenizer(br.readLine()); }
                catch (IOException e) { e.printStackTrace(); }
            }
            return st.nextToken();
        }
        int nextInt(){return Integer.parseInt(next());}
        double nextDouble(){return Double.parseDouble(next());}
        long nextLong(){return Long.parseLong(next());}
        String line(){
            String ans="";
            try {ans = br.readLine(); }
            catch(IOException e) {e.printStackTrace(); }
            return ans;
        }
    }

}