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.io.*;
public class Main
{
	public static void main (String[] args) throws Exception
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		StringTokenizer t = new StringTokenizer(br.readLine());
		int[] a = new int[n+1];
		a[1] = -1;
		for(int i = 2 ; i <= n ; i++) a[i] = Integer.parseInt(t.nextToken());
		ArrayList<Integer> al = new ArrayList<Integer>();
		int val = n;
		while(val!=-1)
		{
		      al.add(val);
		      val = a[val];
		}
		val = al.size();
		for(int i = val-1 ; i >= 0 ; i--) System.out.print(al.get(i)+" ");
	}
}