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.io.*;
public class Solution{
    public static void main(String[] args)throws IOException{
        FastReader in=new FastReader();
        PrintWriter wr=new PrintWriter(System.out);
        int n=in.nextInt();
        int[] a=new int[n];
        for(int i=0;i<n;i++)a[i]=in.nextInt();
        if(a[0]>1){
            wr.write("-1\n");
            wr.flush();
            System.exit(0);
        }
        int[] ans=new int[n];Arrays.fill(ans,-1);
        int[] map=new int[1000000];
        for(int i=0;i<n-1;i++)if(a[i]!=a[i+1])ans[i+1]=a[i];
        ArrayList<Integer> ar=new ArrayList<Integer>();
        for(int i=0;i<n;i++)map[a[i]]=1;
        for(int i=0;i<1000000;i++)if(map[i]==0)ar.add(i);
        Collections.sort(ar);
        int cnt=0;
        for(int i=0;i<n;i++)if(ans[i]==-1)ans[i]=ar.get(cnt++);
        for(int i=0;i<n;i++)wr.write(ans[i]+" ");
        wr.write("\n");
        wr.flush();
    }
}
class FastReader{
    public static StringTokenizer st;
    public static BufferedReader in;
    public static PrintWriter pw;
    FastReader(){
        in = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        st = new StringTokenizer("");
    }
    public static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
    public static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
    public static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
    public static String next() throws IOException {
        while(!st.hasMoreElements() || st == null){
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }
}