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.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.TreeSet;
import java.util.HashSet;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        CEhabAndPrefixMEXs solver = new CEhabAndPrefixMEXs();
        solver.solve(1, in, out);
        out.close();
    }

    static class CEhabAndPrefixMEXs {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            int[] arr = in.nextIntArray(n);
            int[] ans = new int[n];
            int last = 0;
            HashSet<Integer> set1 = new HashSet<>();
            for (int a : arr) set1.add(a);
            TreeSet<Integer> set = new TreeSet<>();
            for (int i = 0; i <= 1000000; i++) set.add(i);
            for (int i = 0; i < n; i++) {
                if (set.isEmpty()) {
                    out.println(-1);
                    return;
                }
                if (set.first() > arr[i]) {
                    out.println(-1);
                    return;
                }
                if (set.lower(arr[i]) == null && set.higher(arr[i]) == null) {
                    out.println(-1);
                    return;
                }
                int a = (set.lower(arr[i]) == null ? set.higher(arr[i]) : set.lower(arr[i]));
                if (!set1.contains(a)) {
                    ans[i] = a;
                    set.remove(a);
                } else {
                    last = Math.max(a, last + 1);

                    while (set1.contains(last)) {
                        if (set.higher(last) == null) {
                            out.println(-1);
                            return;
                        }
                        a = set.higher(last);
                        last = a;
                    }

                    ans[i] = last;
                    set.remove(last);
                }

                if (set.lower(arr[i]) != null) {
                    out.println(-1);
                }
                set1.remove(arr[i]);
            }
            out.println(ans);
        }

    }

    static class InputReader {
        BufferedReader reader;
        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[] nextIntArray(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; ++i) array[i] = nextInt();
            return array;
        }

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

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(int[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(array[i]);
            }
        }

        public void println(int[] array) {
            print(array);
            writer.println();
        }

        public void close() {
            writer.close();
        }

        public void println(int i) {
            writer.println(i);
        }

    }
}

