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.*;

public class Main {
	static Scanner sc = new Scanner(System.in);
	static PrintWriter out = new PrintWriter(System.out);

	public static void main(String[] args) throws Exception {
		int n = sc.nextInt(), arr[] = new int[n], mex = 0;
		int ans[] = new int[n];
		Arrays.fill(ans, n + 1);
		Stack<Integer> idx = new Stack<>();
		for (int i = 0; i < n; i++) {
			arr[i] = sc.nextInt();
		}

		boolean flag = true;
		for (int i = 0; i < n; i++) {
			idx.add(i);
			while (mex < arr[i] && !idx.isEmpty()) {
				ans[idx.pop()] = mex++;
			}
			flag &= mex == arr[i];
		}

		if (flag) {
			for (int x : ans) out.print(x + " ");
		} else {
			out.println(-1);
		}

		out.close();
	}
}

class Scanner {
	StringTokenizer st;
	BufferedReader br;

	public Scanner(InputStream system) {
		br = new BufferedReader(new InputStreamReader(system));
	}

	public Scanner(String file) throws Exception {
		br = new BufferedReader(new FileReader(file));
	}

	public String next() throws IOException {
		while (st == null || !st.hasMoreTokens())
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}

	public String nextLine() throws IOException {
		return br.readLine();
	}

	public int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	public double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}

	public Long nextLong() throws IOException {
		return Long.parseLong(next());
	}
}