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.io.*;
import java.util.*;
public class A1057 
{
    static HashMap<Integer,ArrayList<Integer>> map;
    static int par[];static boolean vis[];
    static void dfs(int ind)
    {
        vis[ind]=true;
        for(int i:map.get(ind))
        {
            if(!vis[i])
            {
                par[i]=ind;
                dfs(i);
            }
        }
    }
    static void print(int ind)
    {
        if(ind==1)
        {
            System.out.print(ind+" ");
            return;
        }
        print(par[ind]);
        System.out.print(ind+" ");
    }
    public static void main(String args[])throws IOException
    {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        map=new HashMap<>();
        for(int i=1;i<=n;i++)
        {
            map.put(i,new ArrayList<>());
        }
        for(int i=2;i<=n;i++)
        {
            int x=sc.nextInt();
            map.get(i).add(x);
            map.get(x).add(i);
        }
        par=new int[n+1];
        vis=new boolean[n+1];
        dfs(1);
        StringBuffer sb=new StringBuffer("");
        int ind=n;
        print(n);
    }
}
