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.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {

	private static int[] prev = new int[200010];
	
	public static void main(String[] args) {		
		
		Scanner scan = new Scanner(System.in);
		int i , j , n = scan.nextInt();
		for (i = 2;i <= n;i ++) {
			prev[i] = scan.nextInt();
		}
		List<Integer> list = new ArrayList<>();
		int current = n;
		while (current >= 1) {
			list.add(current);
			current = prev[current];
		}
		Collections.reverse(list);
		for (i = 0;i < list.size();i ++) {
			if (i > 0) {
				System.out.print(" ");
			}
			System.out.print(list.get(i));
		}
		System.out.println();
		
	}
	

    
}







	