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.Scanner;

public class BmailComputerNetwork {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
			Scanner sc= new Scanner(System.in);
			Scanner sc1= new Scanner(System.in);

		String a= sc.nextLine();
		String aa = sc.nextLine();
		
		String[] tab = aa.split(" ");
		int x=0;
		String tab1[] = new String[Integer.valueOf(a)+1]; 
		int i=0;
		
		tab1[i]=tab[tab.length-1];
		x=Integer.valueOf(tab1[i]);
		i++;

		while(x!=1) {
			
			//System.out.println(x);
			tab1[i]=tab[x-2];
			x=Integer.valueOf(tab1[i]);
			i++;

			
		}
		i--;
		while(i>=0) {
		System.out.print(tab1[i]+" ");i--;
		}System.out.print(a);
	}
}
