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.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class C {

    static BufferedReader br;
    static StringTokenizer st;
    static PrintWriter pw;

    static String nextToken() {
        try {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(br.readLine());
            }
        } catch (IOException e) {
            e.printStackTrace();
        }
        return st.nextToken();
    }

    static int nextInt() {
        return Integer.parseInt(nextToken());
    }

    static double nextDouble() {
        return Double.parseDouble(nextToken());
    }

    static long nextLong() {
        return Long.parseLong(nextToken());
    }

    static String nextLine() {
        try {
            return br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return null;
    }

    public static void main(String[] args) {
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(System.out);
        run();
        pw.close();
    }

    private static void run() {
        int n = nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        int[] ans = new int[n];
        boolean[] used = new boolean[n + 1];
        int k = a[0];
        Arrays.fill(ans, -1);
        for (int i = 0; i < n; i++) {
            if (k != a[i]) {
                ans[i] = k;
                used[k] = true;
                k = a[i];
            }
        }
        used[k] = true;
        ArrayList<Integer> g = new ArrayList<>(n * 2);
        for (int i = 0; i < n + 1; i++) {
            if (!used[i]) {
                g.add(i);
            }
        }
        int id2 = 0;
        for (int x :
                g) {
            while (ans[id2] != -1) {
                id2++;
            }
            ans[id2++] = x;
        }
        for (int i = 0; i < n; i++) {
            pw.print(ans[i] + " ");
        }
    }


}
