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.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStream;
import java.io.InputStreamReader;

public class sol {

	
	static class Reader {
		
		static BufferedReader reader;
		static StringTokenizer tokenizer;
		
		static void init(InputStream input) {
			reader = new BufferedReader(new InputStreamReader(input));
			tokenizer = new StringTokenizer("");
		}
		
		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 long nextLong() throws IOException {
			return Long.parseLong(next());
		}
		
	}
	
	static long[] merge(long[] a,long[] b) {
		int m = a.length;
		int n = b.length;
		long[] c = new long[m+n];
		int j=0, k=0;
		while(j+k<m+n) {
			if(j>=m) {
				c[j+k]=b[k];
				k++;
			}
			else if(k>=n) {
				c[j+k]=a[j];
				j++;
			}
			else {
				if(a[j]<b[k]) {
					c[j+k]=a[j];
					j++;
				}
				else {
					c[j+k]=b[k];
					k++;
				}
			}
		}
		/*while(j<m) {
			c[j+k]=a[j];
			j++;
		}
		while(k<n) {
			c[j+k]=b[k];
			k++;
		}*/
		return c;
	}
	
	static long[] Msort(long[] unsorted) {
		int l = unsorted.length;
		if(l<=1) {
			return unsorted;
		}
		else {	
			long[] Msorted = new long[l];
			long[] m1 = new long[l/2];
			long[] m2 = new long[l-(l/2)];
			for(int i=0; i<l; i++) {
				if(i<l/2) {
					m1[i] = unsorted[i];
				}
				else {
					m2[i-l/2] = unsorted[i];
				}
			}
			Msorted = merge(Msort(m1),Msort(m2));
			return Msorted;
		}
		
	}
	
	
	static void fillArr(int[] arr, int n) throws IOException {
		for(int i=0; i<n; i++) {
			arr[i] = Reader.nextInt();
		}
	}
	static void darr(int[] arr, int n) {
		for(int i=0; i<n; i++) {
			System.out.print(arr[i]+" ");
		}
		System.out.println();
	}


	
	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		Reader.init(System.in);
		int n = Reader.nextInt();
		int[] a = new int[n];
		int[] b = new int[n];
		boolean[] f = new boolean[n];
		
		for(int i=0; i<n; i++) {
			a[i] = Reader.nextInt();
		}
		for(int i=0; i<n; i++) {
			b[i] = 131072;
		}
		
		int pm=0, j=0;
		for(int i=0; i<n; i++) {
			int cm = a[i];
			if(cm!=pm) {
				
				int k=pm;
				b[i] = k;
				f[i] = true;
				k++;
				while(k<cm) {
					while(f[j])
						j++;
					b[j] = k;
					f[j] = true;
					j++;
					k++;
				}
				
			}
			
			pm = cm;
		}
		
		for(int i=0; i<n; i++) {
			System.out.print(b[i]+" ");
		}
		
	}
}




