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 mrc2018 {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int a[] = new int[n+1];
		a[1]=1;
		for(int i=2;i<=n;i++) {
			a[i] = sc.nextInt();
		}
		
		Vector<Integer> v = new Vector<>();
		int temp=n;
		
		while(temp != a[temp]) {
			v.add(temp);
			temp = a[temp];
		}
		
		v.add(1);
		//System.out.print(v.get(0));
		for(int i=v.size()-1;i>=0;i--) {
			System.out.print(v.get(i) + " ");
		}
		
		sc.close();
	}

}
