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 
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		
		 Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();

        int a[] = new int[n+1];

        a[1] =1;
        
        for(int i=2;i<=n;i++)
        {
            a[i] = sc.nextInt();
        }

        sc.close();
        ArrayList<Integer> list = new ArrayList<>();

        list.add(n);
        int val =n;

       // System.out.print(n+" ");

        while(val!=1)
        {
             val = a[val];

            list.add(val);

           // System.out.print(val + " ");

        }

        //System.out.println();
        Collections.reverse(list);
        //System.out.println(list);
        
        for(int i : list)
        {
            System.out.print(i+" ");
        }
        
        System.out.println();
		
	}
}

