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.*;
public class Sample{
    public static final Scanner scan=new Scanner(System.in);
	public static void main(String[] args){
		int n=scan.nextInt();
		int a[]=new int[n+1];
		a[0]=0;a[1]=0;
		for(int i=2;i<=n;i++)
			a[i]=scan.nextInt();
		TreeSet<Integer> ts=new TreeSet<Integer>();
		ts.add(n);
		int i=n;
		while(i>1){
			if(i==a[i]){ts.add(a[i]);i--;}
			else{
				ts.add(a[i]);
				i=a[i];
			}
		}
		Iterator it=ts.iterator();
		while(it.hasNext())
			System.out.print(it.next()+" ");
		
		System.out.println();
	}
}