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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.Random;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Main {
	
	/** Class for buffered reading int and double values */
	static class Reader {
	    static BufferedReader reader;
	    static StringTokenizer tokenizer;

	    /** call this method to initialize reader for InputStream */
	    static void init(InputStream input) {
	        reader = new BufferedReader(
	                     new InputStreamReader(input) );
	        tokenizer = new StringTokenizer("");
	    }

	    /** get next word */
	    static String next() throws IOException {
	        while ( ! tokenizer.hasMoreTokens() ) {
	            
	            tokenizer = new StringTokenizer(
	                   reader.readLine() );
	        }
	        return tokenizer.nextToken();
	    }

	    static int nextInt() throws IOException {
	        return Integer.parseInt( next() );
	    }
		
	    static double nextDouble() throws IOException {
	        return Double.parseDouble( next() );
	    }
	    static long nextlong() throws IOException {
	    	return Long.parseLong( next() );
	    }
	}
	
	  
	public static void main(String[] args) throws IOException {
		Reader.init(System.in);
//		int t= Reader.nextInt();
//		for(int j=0; j<t; j++) {
			int n=Reader.nextInt();
			int[] arr= new int[n];
			for(int i=0; i<n; i++) {
				arr[i]=Reader.nextInt();
			}
			int[] b=new int[n];
			if(arr[0]>0) {
				b[0]=arr[0]-1;
			}
			else {
				b[0]=0;
			}
//			System.out.println(b[0]);
			for(int i=1; i<n;i++) {
				b[i]=arr[i-1];
//				System.out.println(b[i]);
			}
			for(int i=0;i<n; i++) {
				System.out.print(b[i]+" ");
			}
 //		}
	}
}