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 CodeForces {

    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);

        int n=sc.nextInt();
        int a[]=new int[n];
        for(int i=0;i<n;i++)
            a[i]=sc.nextInt();
        int b[]=new int[n];
        for(int i=0;i<n;i++)
        {
            if(a[i]==0)
                b[i]=1;
            else
            {
                b[i]=a[i]-1;
            }
        }
        for(int i=0;i<n;i++)
        {
            System.out.print(b[i]+" ");
        }
        System.out.println();
    }

}