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 Main {
    public static void main(String[] args) throws Exception {
        // Your code here!
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int a[]=new int[n];
        int b[]=new int[n];
        Arrays.fill(b,-1);
        int f=1;
        HashSet<Integer> h=new HashSet<>();
        for(int i=0;i<n;i++)
        {
            a[i]=sc.nextInt();
            
            if(a[i]>i+1)
            {
                f=-1;
            }
            h.add(a[i]);
        }
        if(f==-1)
        System.out.println(-1);
        else
        {
            boolean vis[]=new boolean[100005];
            for(int i=1;i<n;i++)
            {
                if(a[i]!=a[i-1])
                {
                    b[i]=a[i-1];
                    vis[b[i]]=true;
                }
            }
            vis[a[n-1]]=true;
            int p=0;
            for(int i=0;i<n;i++)
            {
                while(vis[p])
                p++;
                
                if(b[i]==-1)
                {
                    b[i]=p;
                    vis[p]=true;
                    p++;
                }
                System.out.print(b[i]+" ");
            }
            
            
            
        }
        
        //System.out.println("XXXXXXXX");
    }
}
