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.*;

public class CodeForces1364C{
	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);
		int n = input.nextInt();
		int[] a = new int[n+10];
		int[] val = new int[n+10];
		int[] vis = new int[n+10];
		for(int i = 1;i<=n;i++){
			a[i] = input.nextInt();
			vis[a[i]] = 1;
		}

		int count = 0;
		for(int i = 1;i<=n;i++){
			if(vis[i] == 0){
				val[++count] = i;
			}
		}

		int pos = 0;
		for(int i = 1;i<=n;i++){
			if(a[i] == a[i-1]){
				System.out.print(val[++pos] + " ");
			}
			else{
				System.out.print(a[i-1] + " ");
			}
		}
	}
}