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.util.*;
import java.io.*;
public class Main {

	public static void main(String[] args)throws IOException {

		BufferedReader br;
		br = new BufferedReader(new InputStreamReader(System.in));
		//**********************************************************************

		// br = new BufferedReader(new FileReader("input.txt"));
		// PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("output.txt")));

		//**********************************************************************
		int n = Integer.parseInt(br.readLine().trim());
		String inp[] = br.readLine().trim().split(" ");
		int ans[] = new int[n];
		int arr[] = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = Integer.parseInt(inp[i]);
		}
		boolean pre[] = new boolean[100001];
		int vacant = 1;
		boolean vac[] = new boolean[n];
		vac[0] = true;
		for (int i = 1; i < n; i++) {
			if (arr[i] != arr[i - 1]) {
				ans[i] = arr[i - 1];
				pre[arr[i - 1]] = true;
			} else {
				vac[i] = true;
				++vacant;
			}
		}
		int num = arr[n - 1];
		ArrayList<Integer> list = new ArrayList<>();
		for (int i = 0; i < num; i++) {
			if (!pre[i])
				list.add(i);
		}
		// System.out.println(list);
		if (list.size() > vacant)
			System.out.println(-1);
		else {
			int c = 0;
			if (!list.isEmpty()) {
				for (int i = 0; i < n; i++) {
					if (c >= list.size() && vac[i]) {
						ans[i] = list.get(c - 1);
					} else if (vac[i]) {
						ans[i] = list.get(c);
						c++;
					}
				}
			}

			for (int i : ans)
				System.out.print(i + " ");
		}

	}
}
