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 LeetCode;

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

public class Main {

	static class Reader {
		BufferedReader br;
		StringTokenizer st;

		public Reader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		public int nextInt() throws IOException {
			if (st == null || !st.hasMoreTokens()) {
				st = new StringTokenizer(br.readLine());
			}
			return Integer.parseInt(st.nextToken());
		}

		public float nextFloat() throws IOException {
			if (st == null || !st.hasMoreTokens()) {
				st = new StringTokenizer(br.readLine());
			}
			return Float.parseFloat(st.nextToken());
		}

		public long nextLong() throws IOException {
			if (st == null || !st.hasMoreTokens()) {
				st = new StringTokenizer(br.readLine());
			}
			return Long.parseLong(st.nextToken());
		}

		public double nextDouble() throws IOException {
			if (st == null || !st.hasMoreTokens()) {
				st = new StringTokenizer(br.readLine());
			}
			return Double.parseDouble(st.nextToken());
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public String next() throws IOException {
			if (st == null || !st.hasMoreTokens()) {
				st = new StringTokenizer(br.readLine());
			}
			return st.nextToken();
		}
	}

	static class Pair implements Comparable<Pair> {
		int index, val;

		public Pair(int index, int val) {
			this.index = index;
			this.val = val;
		}

		@Override
		public int compareTo(Pair o) {
			return o.val - this.val;
		}
	}

	static int mod = (int) (1e9 + 7);

	public static void main(String[] args) throws IOException {
		Reader sc = new Reader();
		PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		try {
			int t = 1;
			while (t-- > 0) {
				int n = sc.nextInt();
				long arr[] = new long[n];
				long max = -1;
				for (int i = 0; i < n; i++) {
					arr[i] = sc.nextInt();
					if(max<arr[i])
						max = arr[i];
				}
				max++;
				long maxarr[] = new long[n];
				Arrays.fill(maxarr, -1);
				for(int i=n-2;i>=0;i--) {
					if(arr[i]==arr[i+1])
						maxarr[i] = maxarr[i+1];
					else {
						maxarr[i] = arr[i+1]-1;
					}
				}
				long last = -1;
				long ans[] = new long[n];
				boolean flag = true;
				for(int i=0;i<n;i++) {
					if(i!=0 && arr[i-1]!=arr[i]) {
						if(ans[i-1]<maxarr[i-1] && !(ans[i-1]==maxarr[i-1]-1 && arr[i-1]==maxarr[i-1])){
							flag = false;
//							System.out.println("BREAK "+i);
							break;
						}
						ans[i] = arr[i-1];
						continue;
					}
					long cand = last+1;
					if(cand==arr[i])
						cand++;
					if(maxarr[i]!=-1 && cand>maxarr[i]) {
						ans[i] = max;
					} else {
						ans[i] = cand;
						last = cand;
					}
				}
//				for(int i=0;i<n;i++) {
//					out.print(maxarr[i]);
//					out.print(' ');
//				}
//				out.println();
				if(!flag) {
					out.println(-1);
					break;
				}
				for(int i=0;i<n;i++) {
					out.print(ans[i]);
					out.print(' ');
				}
			}
			out.flush();
		} catch (Exception e) {
			e.printStackTrace();
		}
	}
}