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.*;
import java.io.*;
import java.lang.*;
import java.math.*;

public class Test
{
	public static void main(String args[])
	{
		Scanner sc=new Scanner(System.in);
		
		int n=sc.nextInt();
		int t=n,k=0;
		int arr[] = new int[n+1];
		int arr1[] = new int[n+1];
		arr[1]=1;
		for(int i=2;i<=n;i++)
		{
			arr[i]=sc.nextInt();
		}
		while(t!=1)
		{
			
			arr1[k]=t;
			k++;
			t=arr[t];
		}
		arr1[k]=1;
		for(int i=k;i>=0;i--)
		{
			System.out.print (arr1[i]+" ");
		}	
	}
}

