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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        FastReader sc = new FastReader();

        int MAX = 1000000;
        int n = sc.nextInt();
        int[] arr = new int[n];
        for (int i = 0; i < n; ++i)
            arr[i] = sc.nextInt();

        Map<Integer, Integer> map = new HashMap<>();
        for (int a : arr) {
            map.put(a, 1 + map.getOrDefault(a, 0));
        }

        TreeSet<Integer> tSet = new TreeSet<>();
        for(int i = 0; i <= MAX; ++i){
            if(!map.containsKey(i))
                tSet.add(i);
        }
        List<Integer> bList = new ArrayList<>();
        int i;
        for(i = 0; i < n; ++i){
            int item = tSet.pollFirst();
            bList.add(item);
            if(tSet.first() < arr[i])
                break;

            int freq = map.get(arr[i]);
            if(freq == 1)
                tSet.add(arr[i]);
            else
                map.put(arr[i], freq - 1);
        }

        /*
        Set<Integer> used = new HashSet<>();
        Queue<Integer> entries = new LinkedList<>();
        int[] brr = new int[n];
        int p = 0;
        int i;
        for (i = 0; i < n; ++i) {
            int b = -1;
            if (entries.size() > 0 && entries.peek() < p) {
                b = entries.poll();
            } else {
                while (used.contains(p) || map.getOrDefault(p, 0) != 0)
                    ++p;
            }
            brr[i] = b;
            used.add(b);
            if (b == p)
                ++p;

            if (brr[i] < arr[i] - 1)
                break;

            if (!used.contains(arr[i]))
                entries.add(arr[i]);



        }*/

        if (i < n) {
            System.out.println(-1);
        } else {
            for (int b : bList)
                System.out.print(b + " ");
            System.out.println();
        }
    }

    private static class FastReader {
        private BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            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;
        }
    }
}
