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.LinkedList;
import java.util.Scanner;


public class BmailComputerNetwork {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub

		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] p = new int[n];
		for(int i=1;i<n;i++)
			p[i] = sc.nextInt()-1;
		LinkedList<Integer> list = new LinkedList<>();
		int num = n-1;
		while(num>0){
			list.addFirst(num+1);
			num = p[num];
		}
		list.addFirst(1);
		for(int x: list){
			System.out.print(x+" ");
		}
	}

}
