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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

import java.util.*;

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);

        int n = in.nextInt();
        int[] a = new int[n];
        TreeMap<Integer, Integer> map = new TreeMap<Integer, Integer>();
        for (int i=0;i<n;i++) {
            a[i] = in.nextInt();
            if (a[i] >= i+2) {
                out.println(-1);
                out.close();
                return;
            }
            if (map.containsKey(a[i])) {
                map.put(a[i], map.get(a[i])+1);
            } else {
                map.put(a[i], 1);
            }
        }

        TreeSet<Integer> set = new TreeSet<Integer>();
        TreeSet<Integer> set_in = new TreeSet<Integer>();
        for (int i=0;i<n+1;i++) {
            set.add(i);
        }
        int tmp_mex = 0;
        int rem_val = 1;
        while (map.containsKey(rem_val)) {
            rem_val++;
        }
        int[] b = new int[n];
        for (int i=0;i<n;i++) {
            if (map.get(a[i]) > 1) {
                map.put(a[i], map.get(a[i])-1);
            } else {
                map.remove(a[i]);
            }
            if (a[i] != tmp_mex) {
                b[i] = tmp_mex;
                set.remove(tmp_mex);
                set_in.add(tmp_mex);
                while (set_in.contains(tmp_mex)) {
                    tmp_mex++;
                }
            } else { // a[i] == tmp_mex
                b[i] = rem_val;
                set.remove(rem_val);
                set_in.add(rem_val);
                while (set_in.contains(rem_val)) {
                    rem_val++;
                }
                while (map.containsKey(rem_val)) {
                    rem_val++;
                }
                // rem_val++;
            }
        }
        StringBuilder sb = new StringBuilder();
        for (int i=0;i<n;i++) {
            sb.append(b[i]);
            if (i != n-1) sb.append(" ");
        }
        out.println(sb);

        out.close();
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

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

    }
}
