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 P1 {
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
	int n = sc.nextInt();
	int a[]=new int[n-1];
	for(int i=0;i<n-1;i++) {
		a[i]=sc.nextInt();
	}
	ArrayList<Integer>al  =new ArrayList<>();
	int c=n;
	al.add(c);
	while(c>1) {
		c=a[c-2];
		al.add(c);
	}
	
	Collections.reverse(al);
	for(int i=0;i<al.size();i++) {
		System.out.print(al.get(i)+" ");
	}
	    }
	 
}
