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.*;
import java.lang.*;
import java.io.*;
public class hrg
{
			public static void main (String[] args) throws java.lang.Exception
	{
         BufferedReader br=new BufferedReader(new InputStreamReader(System.in)); 
         int t=1;
             //
             // t=Integer.parseInt(br.readLine().trim());
             
             StringBuilder sb=new StringBuilder();
              in1 : while(t-->0){
                  int n = Integer.parseInt(br.readLine().trim());
                  int[] a = new int[n+3];
                  String[] s = br.readLine().trim().split("\\s+");
                  for(int i=1;i<=n-1;i++){
                      a[i]=Integer.parseInt(s[i-1])-1;
                  }
                  Stack<Integer> st = new Stack<>();
                  int i = n-1;
                  st.push(i+1);
                  while(i>0){
                      //st.push(i);
                      st.push(a[i]+1);
                      i=a[i];
                  }
                  while(!st.isEmpty()){
                      sb.append(st.pop()+" ");
                  }
                  
                  
              }
                    
    System.out.println(sb);
	    
	}
	
}