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 EdC {

	public static void main(String[] args) throws Exception{
		int num = 998244353;
		// TODO Auto-generated m ethod stub
 		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
 		PrintWriter out = new PrintWriter(System.out);
 		int n = Integer.parseInt(bf.readLine());
//	 		String input1 = bf.readLine().trim();
//	 		String input2 = bf.readLine().trim();
	 	Set<Integer> distinct = new HashSet<Integer>();
	 	int[] array = new int[n+1];
	 	StringTokenizer st2 = new StringTokenizer(bf.readLine());
	 	for(int j=1;j<=n;j++){
	 		array[j] = Integer.parseInt(st2.nextToken());
	 		distinct.add(array[j]);
	 	}
	 	boolean[] filled = new boolean[n+1];	
	 	for(int i = 0;i<=n;i++){
	 		filled[i] = false;
	 	}
	 	int[] b = new int[n+1];
	 	for(int j = 2;j<=n;j++){
	 		if (array[j] != array[j-1]){
	 			b[j] = array[j-1];
	 			filled[j] = true;
	 		}
	 	}
	 	int count = 0;
	 	for(int j = 1;j<=n;j++){
	 		if (filled[j] == false){
	 			while(distinct.contains(count)){
	 				count++;
	 			}
	 			b[j] = count;
	 			count++;
	 		}
	 	}
	 	for(int j = 1;j<=n;j++){
	 		out.print(b[j] + " ");
	 	}
	 	out.println();
	 	out.close();
	 		
	 
	 	
 		
 		
 		
 		
 		
 		
 	}
}
 	
 
//StringJoiner sj = new StringJoiner(" "); 
//sj.add(strings)
//sj.toString() gives string of those stuff w spaces or whatever that sequence is

 		
 		
 		
 		
	


