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.util.LinkedList;
import java.util.Queue;
//Single pair shortest path : Shortest distance from a source(let s )  to all other vertex.
//On unweighted graph, using BFS
//Vertex starts from 0 to n-1

public class Cap{

     public static HashMap<Integer,List<Integer>> adj ;

     public static void graph(int n ){
        adj = new HashMap<>();
        for(int i=1;i<=n;i++){
             List<Integer> l = new ArrayList<Integer>() ;
            adj.put(i,l);
        }
     }
     public static void addEdge(int u, int v){
        (adj.get(u)).add(v);
        (adj.get(v)).add(u);

     }
     public static List<Integer> Nei(int u){
           return adj.get(u);
     }
     public static Stack<Integer> bfs(int u, int v){
        HashSet<Integer> hs = new HashSet<>();
        Queue<Integer> q  = new LinkedList<>();
        HashMap<Integer,Integer> hm = new HashMap<>();

        q.add(u);
        hs.add(u);
        while(!q.isEmpty()){

            int curr = q.remove();
            if(curr==v){break;}
            List<Integer> nor = Nei(curr);
            for(Integer ele : nor){
                if(!hs.contains(ele)){
                   q.add(ele);
                   hs.add(ele);
                   hm.put(ele,curr);
               }
            }
        }
        Stack<Integer> st = new Stack<>();
        st.push(v);

        while( hm.get(v)!=u){
            v = hm.get(v);
            st.push(v);
        }
        st.push(u);
        return st ;

     }

    public static void main(String[] args){
          Scanner in = new Scanner(System.in);
          int n = in.nextInt();
          graph(n);
          int[] ar = new int[n];
          for(int i=0;i<n-1;i++)
             ar[i]= in.nextInt();
          for(int i=0;i<n-1;i++)
             addEdge(ar[i],i+2);
          Stack<Integer> st = bfs(1,n);
          while(!st.isEmpty())
            System.out.print(st.pop()+" ");
    }
}
