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 a{
    static LinkedList adj[];
    static ArrayList<Integer> arr = new ArrayList();
    public static void main(String []args)
    {
        Scanner sc = new Scanner(System.in);
    
        int n = sc.nextInt();
        adj = new LinkedList[n];    
        for(int i=0;i<n;i++)
        {
            adj[i] = new LinkedList<Integer>();
        }
        for(int i=1;i<n;i++)
        {
            int r = sc.nextInt();
            adj[i].add(r-1);
        }
        boolean b[] = new boolean[n];
        DFS(b,n-1);
        for(int i = arr.size()-1;i>=0;i--)
        {
            System.out.print(arr.get(i)+" ");
        }
    }
    public static void DFS(boolean b[],int v)
    {
        b[v] = true;
        arr.add(v+1);
        Iterator itr = adj[v].iterator();
        while(itr.hasNext())
        {
            int i = (int)itr.next();
            DFS(b,i);
        }
    }
}