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.*;

public class Main {

    public static void main(String[] args) {
	    Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[] links = new int[n];
        for (int i = 1; i < n; i++){
          links[i] = in.nextInt();
        }
        int[] out = new int[n];
        out[0] = n;
        int i = 1;
        //String response = Integer.toString(n);
        do {
            //response = String.format("%d %s", links[n-1], response);
            
            n = links[n-1];
            out[i] = n;
            i++;
        } while (n > 1);
        i--;
        while (i >= 0) {
            System.out.print(out[i]);
            System.out.print(' ');
            i--;
        }
        //System.out.println(response);
    }
}