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.util.*;
// import java.lang.*;
import java.io.*;

//           THIS TEMPLATE MADE BY AKSH BANSAL.

public class Solution {
    static class FastReader {
        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;
        }
    }

    public static void main(String[] args) throws IOException {
        FastReader sc = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        // ________________________________

        // int t = sc.nextInt();
        // StringBuilder output = new StringBuilder();

        // while (t-- > 0) {

        //     output.append(solver()).append("\n");
        // }

        // out.println(output);
        // _______________________________

        int n = sc.nextInt();
        int[] arr = new int[n];
        Set<Integer> set = new HashSet<>();
        for(int i=0;i<n;i++){
            arr[i] = sc.nextInt();
            set.add(arr[i]);
        }
        // out.println();
        solver(n,arr, set,out);
        // ________________________________
        out.flush();
    }

    public static void solver(int len, int[] arr,Set<Integer> set, PrintWriter out) {
        int[] res = new int[len];
        if(arr[0]>1){
            out.println(-1);
            return ;
        }
        int min = 0;
        int nextt = 0;
        for(int i=0;i<len;i++){
            if(arr[i]>i+1){
                out.println(-1);
                return ;
            }else{
                if(i==0){
                    if(arr[i]==0)res[i] = 1;
                    else {
                        res[i] = 0;
                        min = 1;
                    }
                    nextt = 1+1;
                    // set.add(res[i]);
                    set.remove(Integer.valueOf(arr[0]));
                }
                else{
                    int cur= min;
                    if(cur==arr[i])cur = nextt++;
                    // System.out.println("__"+ cur);
                    while(set.contains(cur)){
                        cur++;
                        nextt++;
                    }
                    res[i] = cur;
                    // set.add(cur);
                    set.remove(Integer.valueOf(arr[i]));
                    min = arr[i];
                }
            }
        }
        for(int i=0;i<len;i++){
            out.print(res[i]+" ");
        }
    }
}