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.lang.*;
import java.io.*;
import java.util.stream.*; 
 
public final class Codeforces
{	static LinkedList<Integer> adj[];
    static public void getPath(int u , int v, boolean[] visited, List<Integer> list)
    {
        if(u==v)
        {
            for(int p : list)
            System.out.print(p+" ");
            return;
        }
        
        visited[u]=true;
        Iterator<Integer> i = adj[u].listIterator(); 
        while (i.hasNext()) 
        { 
            int n = i.next(); 
            if (!visited[n])
            {
                list.add(n);
                getPath(n,v,visited,list);
                list.remove(list.size()-1);
            }
        } 
    }
    public static void main (String[] args) throws java.lang.Exception
	{
	    
	    Scanner sc = new Scanner(System.in);
	        int N = sc.nextInt();
	        adj = new LinkedList[N+1];
	        for(int i=1;i<N+1;i++)
	        adj[i] = new LinkedList();
	        for(int u=2;u<=N;u++)
	        {
	            int v = sc.nextInt();
	            adj[v].add(u);
	            adj[u].add(v);
	            
	        }
	        boolean[] visited = new boolean[N+1];
	        List<Integer> ans = new ArrayList<Integer>();
	       
	        ans.add(1);
	        getPath(1,N,visited,ans);
	}
}