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.*;
import java.util.Map.Entry;
import java.util.concurrent.atomic.AtomicBoolean;
import java.util.stream.Collectors;

public class Main {

  public static void main(String[] args) {
    MyScanner sc = new MyScanner();
    out = new PrintWriter(new BufferedOutputStream(System.out));

    // Start writing your solution here. -------------------------------------

    int n = sc.nextInt();
    int[] a = new int[n];
    int[] b = new int[n + 1];
    int[] f = new int[n + 1];
    for (int i = 0; i < n; i++) {
      a[i] = sc.nextInt();
      f[a[i]] = 1;
      b[i] = n + 1;
    }
    int l = 0;
    int r = 0;
    for (int i = 0; i <= n; i++) {
      if (f[i] == 0) {
        while (l < n + 1 && b[l] != n + 1) {
          l++;
        }
        if (l < n + 1) {
          b[l++] = i;
        }
      } else {
        while (r < n && a[r] == i) {
          r++;
        }
        b[r] = i;
      }
    }
    for (int i = 0; i < n; i++) {
      out.print(b[i]);
      out.print(" ");
    }

    // Stop writing your solution here. -------------------------------------
    out.close();
  }


  //-----------PrintWriter for faster output---------------------------------
  public static PrintWriter out;

  //-----------MyScanner class for faster input----------
  public static class MyScanner {

    BufferedReader br;
    StringTokenizer st;

    public MyScanner() {
      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;
    }

  }
  //--------------------------------------------------------
}