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 Main {


    public static void main(String[] args) throws IOException {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st;

        int N = Integer.parseInt(br.readLine());
        int[] p = new int[N+1];

        st = new StringTokenizer(br.readLine());
        for(int i = 2; i < N+1; i++)
            p[i] = Integer.parseInt(st.nextToken());

        ArrayList<Integer> path = new ArrayList<>();

        int curr = N;
        path.add(N);

        while(curr != 1) {
            curr = p[curr];
            path.add(curr);
        }

        for(int i = path.size()-1; i > -1; i--)
            System.out.print(path.get(i)+" ");
        System.out.println();
    }

}

				  		 				 	  	   	 			 	 	