Once upon a time there was only one router in the well-known company Bmail. Years went by and over time new routers were purchased. Every time they bought a new router, they connected it to one of the routers bought before it. You are given the values p_i — the index of the router to which the i-th router was connected after being purchased (p_i < i).

There are n routers in Boogle in total now. Print the sequence of routers on the path from the first to the n-th router.

Input

The first line contains integer number n (2 ≤ n ≤ 200000) — the number of the routers. The following line contains n-1 integers p_2, p_3, ..., p_n (1 ≤ p_i < i), where p_i is equal to index of the router to which the i-th was connected after purchase.

Output

Print the path from the 1-st to the n-th router. It starts with 1 and ends with n. All the elements in the path should be distinct.

Examples

Input

8
1 1 2 2 3 2 5


Output

1 2 5 8 

Input

6
1 2 3 4 5


Output

1 2 3 4 5 6 

Input

7
1 1 2 3 4 3


Output

1 3 7 
import java.io.*;
import java.util.Stack;
import java.util.StringTokenizer;

/**
 * Created by Anton Berezin on 2/18/2017.
 */
public class Routers {

	public static void main(String[] args) throws Exception {
		try (FastScanner fastScanner = new FastScanner();
		     PrintWriter writer = new PrintWriter(new BufferedOutputStream(System.out))) {
			int n = fastScanner.nextInt();
			int[] a = new int[n + 1];
			for (int i = 2; i <= n; i++) {
				a[i] = fastScanner.nextInt();
			}
			Stack<Integer> result = new Stack<>();
			int router = n;
			while (router != 1) {
				result.push(router);
				router = a[router];
			}
			result.push(1);

			while (!result.isEmpty()) {
				writer.print(result.pop() + " ");
			}
			writer.println();
		}
	}

	public static class FastScanner implements AutoCloseable {
		BufferedReader bufferedReader;
		StringTokenizer tokenizer;

		public FastScanner() {
			bufferedReader = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (tokenizer == null || !tokenizer.hasMoreElements()) {
				try {
					tokenizer = new StringTokenizer(bufferedReader.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return tokenizer.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 = bufferedReader.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}

		@Override
		public void close() throws IOException {
			bufferedReader.close();
		}
	}
}
