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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;

/**
 * Created by sanco on 10/12/18.
 * CodeForce
 */
public class BmailComputerNetwork {
    public static void main(String[] args) throws IOException {
        BufferedReader bi = new BufferedReader(new InputStreamReader(System.in));
        String routerCount = bi.readLine();
        int n = Integer.valueOf(routerCount);
        String line = bi.readLine();
        line = "1 1 "+line;
        String[] routers = line.split(" ");

        List<Integer> result = makePath(routers,n);
        for(int i=result.size()-1;i>=0;i--){
            System.out.print(result.get(i)+" ");
        }
    }

    public static List<Integer> makePath(String[] routers, int n){
        List<Integer> list = new ArrayList<>();
        list.add(n);
        do{
            n= Integer.parseInt(routers[n]);
            list.add(n);
        }while(n!=1);

        return list;
    }
}
 	  	 	  		  		  	  	 	 			  		