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
	{
	  BufferedReader ob = new BufferedReader(new InputStreamReader(System.in));
	  
	  int n = Integer.parseInt(ob.readLine());
	  
	  
	  StringTokenizer st = new StringTokenizer(ob.readLine());
	  
	  int []ar = new int[n+2];
	  for(int i = 2; i <= n; i++){
	      ar[i]  = Integer.parseInt(st.nextToken());
	  }
	  
	 Stack<Integer>stack = new Stack<>();
	 
     int j = n;
     boolean v = true;
     stack.add(n);
     
     while(v){
         if(ar[j] == 1){
             stack.add(1);
             v = false;
         }else{
             stack.add(ar[j]);
             j = ar[j];
         }
     }
   
     while(!stack.isEmpty()){
         System.out.print(stack.pop()+" ");
     }
	}
}
