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.
//package goku;

import java.io.*;
import java.util.*;

public class goku {

    BufferedReader br;
    PrintWriter out;
    
    long mod = (long) (1e9 + 7), inf = (long) (5e18);
    
    void spiritBomb() {
        int n = ni();
        int a[] = new int[n];
        for(int i = 0; i < n; i++)  a[i] = ni();
        int j = 0;
        boolean not = false;
        int b[] = new int[n];
        Arrays.fill(b, -1);
        for(int i = 0; i < n; i++) {
            if(i == 0) {
                if(a[i] == 1)   b[j++] = 0;
            } else {
                for(int k = a[i]-1; k > a[i-1]; k--) {
                    while(b[j] != -1)   j++;
                    b[j++] = k;
                }
                if(j > i) {
                    not = true; break;
                }
                if(a[i] > a[i-1])   b[i] = a[i-1];
            }
        }
        if(not) {
            out.println(-1);
        } else {
            while(j < n) {
                if(b[j] == -1)
                    b[j] = 500000;
                j++;
            }
            for(int x : b)  out.print(x +" ");
        }
    }
    
    int gcd(int a, int b) {
        if(b == 0)  return a;
        return gcd(b, a % b);
    }
    
    long mp(long b, long e) {
        long r = 1;
        while(e > 0) {
            if( (e&1) == 1 )    r = (r * b) % mod;
            b = (b * b) % mod;
            e >>= 1;
        }
        return r;
    }
    
    // -------- I/O Template -------------
    
    char nc() {
        return ns().charAt(0);
    }
    
    String nLine() {
        try {
            return br.readLine();
        } catch(IOException e) {
            return "-1";
        }
    }
    
    double nd() {
        return Double.parseDouble(ns());
    }
    
    long nl() {
        return Long.parseLong(ns());
    }
    
    int ni() {
        return Integer.parseInt(ns());
    }
    
    StringTokenizer ip;
    
    String ns() {
        if(ip == null || !ip.hasMoreTokens()) {
            try {
                ip = new StringTokenizer(br.readLine());
            } catch(IOException e) {
                throw new InputMismatchException();
            }
        }
        return ip.nextToken();
    }
    
    void kamehameha() {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        spiritBomb();
        out.flush();
    }
    
    public static void main(String[] args) {
        new goku().kamehameha();
    }
    
}
