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 Bmail
{
    public static void main(String args[])
    {
        Scanner sc = new Scanner(System.in);
        int n=sc.nextInt();
        int a1[] = new int[n+1];
        a1[0]=0;
        a1[1]=0;
        for(int i=2;i<=n;i++)
        {
            a1[i]=sc.nextInt();
        }
        Stack<Integer> st = new Stack<Integer>();
        st.push(n);
        for(int i=n;i>1;i=a1[i])
        {
            st.push(a1[i]);
        }
        while(!st.empty())
            System.out.print(st.pop()+" ");
    }
}