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 Problem_C {
	static final int INF = 1000000;

	public static void main(String[] args) {
		InputReader in = new InputReader();
		StringBuilder out = new StringBuilder();

		int N = in.nextInt();
		int[] A = new int[N];
		for (int i = 0; i < N; i++) {
			A[i] = in.nextInt();
		}
		boolean flag = true;
		for (int i = 0; i < N; i++) {
			if (i + 1 < A[i]) {
				flag = false;
				break;
			}
		}
		if (!flag) {
			System.out.println(-1);
			return;
		}
		int[] B = new int[N];
		Arrays.fill(B, INF);
		int prev = 0;
		for (int i = 0; i < N; i++) {
			if (A[i] != prev) {
				B[i] = prev;
				prev = A[i];
			}
		}
		Queue<Integer> q = new LinkedList<>();
		for (int i = 0; i < N; i++) {
			if (B[i] == INF) {
				q.offer(i);
			}
		}
		int next = 0;
		List<Integer> list = new ArrayList<>();
		for (int i = 0; i < N; i++) {
			if (B[i] == INF) {
				continue;
			}
			list.clear();
			for (; next < A[i] - 1; next++) {
				list.add(q.poll());
			}
			for (int j = 0; j < list.size(); j++) {
				B[list.get(j)] = next - j;
			}
			next++;
		}
		for (int i = 0; i < N; i++) {
			out.append(B[i]).append(' ');
		}
		out.setCharAt(out.length() - 1, '\n');

		System.out.print(out);
	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer st;

		public InputReader() {
			reader = new BufferedReader(new InputStreamReader(System.in));
		}

		public String next() {
			while (st == null || !st.hasMoreTokens()) {
				st = new StringTokenizer(nextLine());
			}
			return st.nextToken();
		}

		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return null;
		}

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