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 c {
	static final FS sc = new FS();
	static final PrintWriter pw = new PrintWriter(System.out);
	
	static int n;
	static int[] arr, out;
	static TreeSet<Integer> set;
	public static void main(String[] args) {
		n = sc.nextInt();
		arr = new int[n];
		for(int i = 0; i < n; ++i) arr[i] = sc.nextInt();
		
		if(arr[0] > 1) {
			System.out.println(-1);
			return;
		}
		
		set = new TreeSet<>();
		for(int i = 0; i <= n; ++i) {
			if(i != arr[n - 1]) set.add(i);
		}
		
		out = new int[n];
		for(int i = n - 2; i >= 0; --i) {
			Integer yeet = set.ceiling(arr[i]);
			if(yeet == null) {
				System.out.println(-1);
				return;
			}
			
			out[i + 1] = yeet;
			set.remove(yeet);
		}
		
		out[0] = set.pollFirst();
		
		for(int a : out) pw.print(a + " ");
		pw.println();
		pw.flush();
	}
	static class FS {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");
		String next() {
			while(!st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch(Exception e) {}
			}
			return st.nextToken();
		}
		int nextInt() {
			return Integer.parseInt(next());
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
}