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.*;

public class Solution {
	
		
	public static void main(String [] args)
	{
		
		        Scanner in = new Scanner(System.in);
				int n =in.nextInt();
	
				int [] parents =new int [n-1];
				
				for(int i =0;i<n-1;i++)
				{
					parents[i] =in.nextInt();
				}
				
				int j = n;
				Stack<Integer> path =new Stack<>();
				while(j!=1)
				{
					path.push(j);
					j =parents[j-2];
					
				}
				
				path.push(1);
				
				while(path.isEmpty()==false)
				{
					System.out.print(path.pop()+" ");
				}
				
				
				
				
		
	}

	
	

}
