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.io.*;
import java.math.BigInteger;
import java.util.*;
public class Main {
	public static void main(String[] args) {
		Scanner sc=new Scanner (System.in);
		int n=sc.nextInt();
		int arr[]=new int [n+1];
		for(int i=2;i<=n;i++) {
			arr[i]=sc.nextInt();
		}
		//System.out.println(Arrays.toString(arr));
		List<Integer>list=new ArrayList<>();
		list.add(n);
		show(list,arr[n],arr);
		list.add(1);
		//System.out.println(list);
		for(int i=list.size();i>0;i--) {
			System.out.print(list.get(i-1)+" ");
		}
	}
	private static void show(List<Integer> list, int x,int arr[]) {
		//System.out.println(1111);
		if(x==1)return;
		else {
			//System.out.println(arr[5]);
			list.add(x);
			show(list,arr[x],arr);
		}
	}
}
 