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 C649
{
    public static void main(String [] args)
    {
        MyScanner sc = new MyScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        int n = sc.nextInt(); int [] a = new int [n];
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
        }
        boolean ok = true;
        for (int i = 0; i < n; i++) {
            if (a[i] >= i + 2) {
                ok = false; break;
            }
        }
        if (ok) {
            int last = a[n-1]; TreeSet<Integer> set = new TreeSet<>();
            for (int i = 0; i < last; i++) set.add(i);
            int rem = n - set.size();
            for (int i = last + 1; i <= last + rem; i++) set.add(i);
            int [] b = new int [n];
            for (int i = n - 1; i >= 0; i--) {
                int next = a[i];
                int here = a[i]; if (i > 0) next = a[i-1];
                if (next == here) {
                    b[i] = set.last();
                    set.remove(b[i]);
                } else {
                    b[i] = next;
                    set.remove(b[i]);
                }
            }
            Set<Integer> re = new HashSet<>(); boolean good = true;
            for (int i = 0; i < n; i++) {
                if (re.contains(b[i])) good = false;
                re.add(b[i]);
            }
            if (good) {
                for (int i = 0; i < n; i++) out.print(b[i] + " ");
            } else {
                out.println(-1);
            }
        } else {
            out.println(-1);
        }
        out.close();
    }


    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }



    }

}