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 

/*
 * Created by cravuri on 10/13/18
 */

import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class BmailComputerNetwork {

   public static void main(String[] args) {
      Scanner sc = new Scanner(System.in);
      int n = sc.nextInt();
      int[] p = new int[n];
      for (int i = 1; i < n; i++) {
         p[i] = sc.nextInt() - 1;
      }
      p[0] = -1;
      int cur = n - 1;
      List<Integer> path = new ArrayList<>();
      while (cur != -1) {
         path.add(cur + 1);
         cur = p[cur];
      }
      Collections.reverse(path);
      System.out.print(path.get(0));
      for (int i = 1; i < path.size(); i++) {
         System.out.print(" " + path.get(i));
      }
      System.out.println();
   }

}
