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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.Arrays;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Main {
	public static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	public static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
	public static Scanner sc = new Scanner(System.in);
	public static StringTokenizer st;

	public static void main(String[] args) throws NumberFormatException, IOException {
		int n = Integer.parseInt(br.readLine());

		int[] arr = new int[n + 1];
		int[] ans = new int[n + 1];
		boolean[] used = new boolean[n + 1];
		Arrays.fill(ans, -1);

		st = new StringTokenizer(br.readLine());
		for (int i = 1; i <= n; i++) {
			int cur = Integer.parseInt(st.nextToken());
			if (cur > i) {
				System.out.println(-1);
				return;
			}
			arr[i] = cur;
		}

		for (int i = 0; i < n; i++) {
			if (arr[i] != arr[i + 1]) {
				ans[i] = arr[i];
				used[ans[i]] = true;
			}
		}
		used[arr[n]] = true;

		int pos = n;
		for (int i = n - 1; i >= 0; i--) {
			if (ans[i] == -1) {
				for (int j = pos; j >= 0; j--) {
					if (used[j]) {
						continue;
					}
					ans[i] = j;
					used[j] = true;
					pos = j - 1;
					break;
				}
			}
		}

		for (int i = 0; i < n; i++) {
			bw.write(ans[i] + " ");
		}
		bw.write("\n");
		bw.flush();

	}

}