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.Scanner;

public class solve {
	public static void main(String[] args)
	{
		Scanner sc=new Scanner(System.in);
		int n=Integer.parseInt(sc.nextLine());
		String[] inp=sc.nextLine().trim().split(" ");
		int[] rout=new int[n-1];

		int[] path=new int[n-1];
		for(int i=0;i<n-1;i++)
		{
			path[i]=0;
			rout[i]=Integer.parseInt(inp[i]);
					
		}
		
		int index=n-2;
		int k=0;
		while(index>=0)
		{
			//System.out.println(index);
			path[k]=rout[index];
			index=rout[index]-2;
			k++;
		}
		
		for(int j=n-2;j>=0;j--)
		{
			if(path[j]!=0)
				System.out.print(path[j]+" ");
		}
		System.out.print(n);
		sc.close();
	}
}
