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.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class Round_649D2P3 {
    static final FS sc = new FS();
    static final PrintWriter pw = new PrintWriter(System.out);

    public static void main(String[] args) {
        int n = sc.nextInt();
        int[] a = sc.nextArray(n);
        int flag = 0;
        TreeSet<Integer> tree = new TreeSet<>();
        for(int i=0; i<n; i++){
            if(a[i]>i+1){
                flag = 1;
                break;
            }
            tree.add(a[i]);
        }
        if(flag==1){
            System.out.println("-1");
            return;
        }
        String str = "";
        StringBuilder s = new StringBuilder();
        int j=0;
        for(int i=0; i<n; i++){
            if(i>0 && a[i]!=a[i-1]){
                s.append(a[i-1]+" ");
                //str += Integer.toString(a[i-1])+" ";
            }
            else{
                while(tree.contains(j)){
                    j++;
                }
                s.append(j+" ");
                //str += Integer.toString(j)+" ";
                j++;
            }
        }
        System.out.println(s.toString());
    }

    static class FS {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception ignored) {
                }
            }
            return st.nextToken();
        }

        int[] nextArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextLong();
            }
            return a;
        }

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

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