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 Main {
    static class node{
        int k,v;
        node(int k,int v){
            this.k = k;
            this.v = v;
        }
        node(){}
    }


     void solve(Scanner in) throws Exception {
        int n = in.nextInt();
        int[] arr = new int[n], ans = new int[n],visited = new int[n+1];
        boolean legal = true;
        Arrays.fill(ans,-1);
        for(int i=0;i<n;i++){
            arr[i] = in.nextInt();
            if(arr[i]>i+1) legal = false;
            if(i==0){
                if(arr[i] == 1){
                    ans[i] = 0;
                    visited[0] = 1;
                }
            }
            else if(arr[i]!=arr[i-1]){
                ans[i] = arr[i-1];
                visited[arr[i-1]] = 1;
                visited[arr[i]] = 1;
            }
        }
        if(legal==false){
            System.out.println(-1);
            return;
        }
        int num = 0;
        for(int i=0;i<n;i++){
            if(ans[i]==-1){
                while(visited[num]==1) num++;
                ans[i] = num;
                visited[num++] = 1;
            }
            System.out.printf("%d%s",ans[i],i==n-1?'\n':' ');
        }

    }

    public static int[] readIntArray(Scanner in,int tokens) {
        int[] ret = new int[tokens];
        for (int i = 0; i < tokens; i++) {
            ret[i] = in.nextInt();
        }
        return ret;
    }


    public static void main(String[] args) throws Exception{
//                Scanner in = new Scanner(System.in);
//         Scanner in = new Scanner(new File("input.txt"));
        Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        new Main().solve(in);

//        int T = in.nextInt();
//        for(int i=1;i<=T;i++){
//            new Main().solve(in);
//        }

    }

}