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

public class aaaaaaaaaaaaaaaa {
	public void run() throws Exception {
		FastReader file = new FastReader();
		int times = file.nextInt();
		int[] x = new int[times];
		for (int i = 0; i < times; i++) x[i] = file.nextInt();
		boolean b = true;
		int[] occ = new int[1000001];
		HashSet<Integer> visited = new HashSet();
		int[] t = new int[times];
		for (int i = 0; i < x.length; i++) visited.add(x[i]);
		ArrayList<Integer> w = new ArrayList();
		for (int i : visited) {
			w.add(i);
			occ[i]++;
		}
		ArrayList<Integer> a=  new ArrayList();
		for (int i = 0; i < occ.length; i++) {
			if (occ[i] != 1) a.add(i);
		}
		HashSet<Integer> q = new HashSet();
		int indA = 0, indW = 0;
		t[0] = a.get(indA);
		indA++;
		for (int i = 1; i < t.length; i++) {
			if (x[i] > i + 1) {
				b = false;
				break;
			}
			if (x[i] != x[0]) {
				if (x[i] == x[i-1]) t[i] = a.get(indA++);
				else t[i] = w.get(indW++);
			}
			else {
				t[i] = a.get(indA++);
			}
		}
		if (!b) System.out.println(-1);
		else {
			for (int i : t) System.out.print(i + " ");
			System.out.println();
		}
	}

	public static void main(String[] args) throws Exception {
		new aaaaaaaaaaaaaaaa().run();
	}

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

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

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}
}
