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 ehabandprefixmexs;

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

public class ehabandprefixmexs {
	public static void main(String[] args) throws IOException {
		BufferedReader fin = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(fin.readLine());
		int[] nums = new int[n];
		HashMap<Integer, Integer> numsLeft = new HashMap<Integer, Integer>();
		HashSet<Integer> skipped = new HashSet<Integer>();
		StringTokenizer st = new StringTokenizer(fin.readLine());
		for(int i = 0; i < n; i++) {
			nums[i] = Integer.parseInt(st.nextToken());
			numsLeft.put(nums[i], numsLeft.getOrDefault(nums[i], 0) + 1);
		}
		int pointer = 0;
		int[] ans = new int[n];
		boolean isValid = true;
		for(int i = 0; i < n; i++) {
			boolean putNum = false;
			if(i != 0) {
				numsLeft.put(nums[i - 1], numsLeft.get(nums[i - 1]) - 1);
				if(numsLeft.get(nums[i - 1]) == 0) {
					numsLeft.remove(nums[i - 1]);
					if(skipped.contains(nums[i - 1])) {
						ans[i] = nums[i - 1];
						putNum = true;
					}
				}
			}
			if(!putNum) {
				while(numsLeft.containsKey(pointer)) {
					skipped.add(pointer);
					pointer ++;
				}
				ans[i] = pointer;
				pointer ++;
				putNum = true;
			}
			if(pointer + 1 < nums[i]) {
				isValid = false;
				break;
			}
		}
		if(isValid) {
			StringBuilder fout = new StringBuilder();
			for(int i = 0; i < n; i++) {
				fout.append(ans[i]).append(" ");
			}
			System.out.println(fout);
		}
		else {
			System.out.println(-1);
		}
	}
}
