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.io.*;
public class CF1057A {
   public static void main(String[] args) {
      Scanner sc = new Scanner(System.in);
      
      int N = sc.nextInt();
      
      Node[] network = new Node[N];
      for(int i = 0; i < N; i++) {
         network[i] = new Node();
         network[i].id = i + 1;
      }
      
      for(int i = 1; i < N; i++) {
         int to = sc.nextInt() - 1;
         network[i].neighbors.add(to);
         network[to].neighbors.add(i);
      }
      
      int dest = N - 1;
      ArrayList<Integer> path = new ArrayList<Integer>();
      
      Queue<Integer> q = new LinkedList<Integer>();
      boolean[] visited = new boolean[N];
      q.add(0);
      network[0].parent = 0;
      while(!q.isEmpty()) {
         int cur = q.poll();
         visited[cur] = true;
         if(cur == dest) {
            while(network[cur].parent != cur) {
               path.add(network[cur].id);
               cur = network[cur].parent;
            }
            path.add(network[cur].id);
            break;
         }
         for(int i = 0; i < network[cur].neighbors.size(); i++) {
            if(!visited[network[cur].neighbors.get(i)]) {
               int next = network[cur].neighbors.get(i);
               network[next].parent = cur;
               q.add(next);
            }
         }
      }
      Collections.reverse(path);
      for(int i : path) {
         System.out.print(i + " ");
      }
   }
}
class Node {
   public ArrayList<Integer> neighbors = new ArrayList<Integer>();
   public int id;
   public int parent;
}