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 Main
{
	public static void main(String[] args) {
	    Scanner sc=new Scanner(System.in);
	    int n=sc.nextInt();
	    int a[]=new int[n+1];
	    int back[]=new int[n+1];
	    Vector<Integer> v=new Vector<>();
	    back[1]=-1;
	    for(int i=2;i<=n;i++){
	        a[i]=sc.nextInt();
	        back[i]=a[i];
	    }
	    int idx=n;
	    while(idx!=-1){
	        v.add(idx);
	        idx=back[idx];
	    }
	    Collections.reverse(v);
	    for(Integer i:v)
	        System.out.print(i+" ");
	}
}
