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.BufferedInputStream;
import java.util.LinkedList;
import java.util.Scanner;

public class MA {

	public static void main(String[] args) {
		Scanner s = new Scanner(new BufferedInputStream(System.in));
		int n = s.nextInt();
		int[] arr = new int[n];
		for (int i = 1; i < n; i++) {
			arr[i] = s.nextInt();
		}
		int start = arr[n - 1];
		LinkedList<Integer> b = new LinkedList<>();
		b.add(n);

		while (start > 0) {
			b.add(start);
			start = arr[start - 1];
		}
		while (!b.isEmpty()) {
			System.out.print(b.pollLast());
			if (!b.isEmpty()) {
				System.out.print(' ');
			}
		}
		System.out.flush();
	}

}
