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) throws IOException{
        //BufferedReader f = new BufferedReader(new FileReader("uva.in"));
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int n = Integer.parseInt(f.readLine());
        StringTokenizer st = new StringTokenizer(f.readLine());
        int[] a = new int[n];
        HashSet<Integer> invalid = new HashSet<>();
        for(int i = 0; i < n; i++) {
            a[i] = Integer.parseInt(st.nextToken());
            invalid.add(a[i]);
        }
        int[] b = new int[n];
        int temp = 0;
        while(invalid.contains(temp)) {
            temp++;
        }
        invalid.add(temp);
        b[0] = temp;
        for(int i = 1; i < n; i++) {
            if(a[i] != a[i-1]) {
                b[i] = a[i-1];
            } else {
                while(invalid.contains(temp)) {
                    temp++;
                }
                invalid.add(temp);
                b[i] = temp;
            }
        }
        out.print(b[0]);
        for(int i = 1; i < n; i++) {
            out.print(" " + b[i]);
        }
        out.println();
        f.close();
        out.close();
    }
}