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.io.*;
import java.util.*;
public class R649C {
    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        StringBuilder out = new StringBuilder();
        int N=Integer.parseInt(in.readLine());
        StringTokenizer tok = new StringTokenizer(in.readLine());
        int[] A=new int[N];
        for (int i=0; i<N; i++)
            A[i]=Integer.parseInt(tok.nextToken());
        int[] ans=new int[N];
        Arrays.fill(ans,-1);
        for (int i=0; i<N-1; i++)
            if (A[i]<A[i+1])
                ans[i+1]=A[i];
        boolean[] exists=new boolean[N+1];
        for (int v:A)
            exists[v]=true;
        List<Integer> cools=new ArrayList<>();
        for (int i=0; i<=N; i++)
            if (!exists[i])
                cools.add(i);
        for (int i=0, id=0; i<N; i++)
            if (ans[i]==-1) {
                ans[i]=cools.get(id);
                id++;
            }
        for (int i=0; i<N; i++)
            out.append(i>0?" ":"").append(ans[i]);
        System.out.println(out);
    }
}