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.*;

public class CfA {

    static class Reader {
        BufferedReader br;
        StringTokenizer st;

        public Reader() {
            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;
        }
    }

    static long binpow(int a, int b) {
        if (b == 0)
            return 1;
        long res = binpow(a, b / 2);
        if (b % 2 == 1)
            return res * res * a;
        else
            return res * res;
    }

    static long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    static int n, m, x, y, k;
    static int[] a;
    static int[][] dp;

    public static void main(String[] args) throws Exception {
        Reader in = new Reader();
        n = in.nextInt();
        a = new int[n];
        boolean impossible = false;
        HashSet<Integer> set = new HashSet<>();
        HashMap<Integer,Integer> map = new HashMap<>();
        Stack<Integer> stack = new Stack<Integer>();


        for(int i = 0;i < n;i++)
        {
            a[i] = in.nextInt();
            if(a[i] > i+1)
                impossible = true;
            set.add(a[i]);    
            map.putIfAbsent(a[i], i);
        }

        for(int i = 1000000;i >= 0 ;i--){
            if(!set.contains(i))
                stack.push(i);
        }

        int[] b = new int[n];
        b[0] = stack.pop();
        for(int i = 1;i < n;i++)
        {
            if(a[i] > a[i-1])
                b[i] = a[i-1];
            else    
                b[i] = stack.pop();

        }

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

    }


}

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