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.Scanner;

public class Main {
	
	public static void main(String[] args)
	{
		Scanner s=new Scanner(System.in);
		
		int n=s.nextInt();
		
		int[] arr=new int[n+1];
		
		for(int i=2;i<=n;i++)
		{
			arr[i]=s.nextInt();
		}
		
		find(arr,n);
		
	}
	
	public static void find(int[] arr,int n)
	{
		ArrayList<Integer> list=new ArrayList<>();
		
		int curr=n;
		
		while(curr!=1)
		{
			list.add(curr);
			curr=arr[curr];
		}
		
		list.add(1);
		
		for(int i=list.size()-1;i>=0;i--)
		{
			System.out.print(list.get(i)+" ");
		}
		
	}
	
}