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.*;
import java.math.*;

public class SolA {
	public static void main(String[] args) {
		new SolA().run();
	}

	BufferedReader br;
	StringTokenizer st;
	PrintWriter out;
	boolean eof = false;
	Random rand = new Random(3267347);

	private void run() {
		try {
			br = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
			solve();
			out.close();
		} catch (Throwable e) {
			e.printStackTrace();
			System.exit(566);
		}
	}

	String nextToken() {
		while (st == null || !st.hasMoreTokens()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (Exception e) {
				eof = true;
				return "0";
			}
		}
		return st.nextToken();
	}

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

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

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

	private void solve() throws IOException {
		int n = nextInt();
		int[] a = new int[n];
		for (int i = 1; i < n; i++) {
		    a[i] = nextInt();
		}
		ArrayList<Integer> al = new ArrayList<>();
		int p = n - 1;
		while (p > 0) {
		    al.add(p + 1);
		    p = a[p] - 1;
		}
		al.add(1);
		for (int i = al.size() - 1; i >=0; i--) {
		    out.print(al.get(i) + " ");
		}
	}
}