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.Arrays;
import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;
import java.util.TreeSet;

public class C {
	public static void main(String[] args) {
		Scanner sc= new Scanner(System.in);
		int n = sc.nextInt();
		int a[] = new int[n];
		Set<Integer> covered = new HashSet<Integer>();
		for(int i=0;i<n;i++) {
			a[i] = sc.nextInt();
			covered.add(a[i]);
			
		}
		
		TreeSet<Integer> notCovered = new TreeSet<Integer>();
		for(int i=0;i<=n;i++) {
			if(!covered.contains(i)) {
				notCovered.add(i);
			}
		}
		for(int i=n+1;i<=2*n;i++) {
			notCovered.add(i); //do i need this
		}
		int [] lastIndex = new int[n+1];
		Arrays.fill(lastIndex,-1);
		for(int i=0;i<n;i++) {
			lastIndex[a[i]] = Math.max(lastIndex[a[i]],i);
		}
		int b[] = new int[n];
		for(int i=0;i<n;i++) {
			
			b[i] = notCovered.first();
			
			notCovered.remove(notCovered.first());
			if(lastIndex[a[i]]==i) {
				notCovered.add(a[i]);
			}
		}
		StringBuilder sb= new StringBuilder();
		boolean works = true;
		TreeSet<Integer> work = new TreeSet<Integer>();
		for(int i=0;i<=n;i++) {
			work.add(i);
		}
		for(int i=0;i<n;i++) {
			
			if(b[i]<=n) {
				if(work.contains(b[i]))
				work.remove(b[i]);
			}
			if(work.first()!=a[i]) {
				works = false;
				break;
			}
		}
		if(!works) {
			System.out.println(-1);
			return;
		}
		for(int i=0;i<n;i++) {
			sb.append(b[i] + " ");
		}
		System.out.println(sb.toString());
		
	}
}
