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.*;

/*
polyakoff
*/

public class Main {

    static FastReader in;
    static PrintWriter out;
    static Random rand = new Random();
    static final int oo = (int) 2e9 + 10;
    static final long OO = (long) 4e18;
    static final int MOD = (int) 1e9 + 7;
    static final int N = (int) 1e6;


    static void solve() {
        int n = in.nextInt();

        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = in.nextInt();

        int[] ans = new int[n];
        ArrayDeque<Integer> q = new ArrayDeque<>();
        int last = 0, cur = 0;
        for (int i = 0; i < n; i++) {
            if (a[i] > last) {
                ans[i] = cur++;
                while (cur < a[i])
                    ans[q.pollFirst()] = cur++;
                last = a[i];
            } else
                q.addLast(i);
        }
        while (!q.isEmpty())
            ans[q.pollFirst()] = N;

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


    }

    public static void main(String[] args) throws FileNotFoundException {
        in = new FastReader(System.in);
//        in = new FastReader(new FileInputStream("sometext.txt"));
        out = new PrintWriter(System.out);
//        out = new PrintWriter(new FileOutputStream("output.txt"));

        int T = 1;
//        T = in.nextInt();
        while (T-- > 0)
            solve();

//        Thread thread = new Thread(null, () -> {
//            solve();
//        }, "Main", 1 << 28);
//        thread.start();
//        try {
//            thread.join();
//        } catch (InterruptedException e) {
//            e.printStackTrace();
//        }

//        out.flush();
        out.close();
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        FastReader(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }

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

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

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

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(nextLine());
            }
            return st.nextToken();
        }

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

    static void dbg(Object... args) {
        for (Object arg : args)
            out.print(arg + " ");
        out.println();
    }

}