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.io.PrintWriter;
import java.util.*;

public class Task3 {

    public static void main(String[] args) throws IOException {
        new Task3().solve();
    }

    public void solve() throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);

        int n = Integer.parseInt(f.readLine());
        StringTokenizer tokenizer = new StringTokenizer(f.readLine());
        int[] a = new int[n];
        boolean isAscending = true;
        for (int i = 0; i < n; i++) {
            a[i] = Integer.parseInt(tokenizer.nextToken());
            if (i > 0 && a[i] < a[i - 1]) {
                isAscending = false;
            }
        }
        if (!isAscending) {
            out.println(-1);
            out.close();
        }



        int[] stillIn = new int[n + 1];
        for (int i = 0; i < n; i++) {
            stillIn[a[i]]++;
        }

        int current = -1;
        int[] b = new int[n];
        //System.out.println(Arrays.toString(stillIn));
        for (int i = 0; i < n; i++) {
            if (i != 0 && stillIn[a[i - 1]] == 0) {
                b[i] = a[i - 1];
                if (current <= b[i]) {
                    current = b[i];
                }
            } else {
                current++;
                //System.out.println(current + " " + stillIn[current]);
                while (current <= n && stillIn[current] > 0) {
                    current++;
                }

                b[i] = current;
            }
            stillIn[a[i]]--;
        }

        out.print(b[0]);
        for (int i = 1; i < n; i++) {
            out.print(" ");
            out.print(b[i]);
        }
        out.println();

        out.println();
        out.close();
    }
}
