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.Stack;

public class Main{
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));

        int n = Integer.parseInt(in.readLine());

        int [] p = new int [n+1];

        String [] dat = in.readLine().split(" ");

        for (int i = 2; i <= n; i++){
            p[i] = Integer.parseInt(dat[i-2]);
        }

        Stack<Integer> sol = new Stack<>();

        int current = n;

        while (current != 1){
            sol.add(current);
            current = p[current];
        }

        sol.add(1);

        boolean first = true;

        while (!sol.isEmpty()){
            if (first){
                first = false;
            }else {
                out.write(" ");
            }
            out.write(sol.pop() + "");
        }

        out.write("\n");

        out.close();
    }
}
		 		  	 	 					 					 	 	   	