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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;

public class BmailComputerNetwork {

	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 t = Integer.parseInt(in.readLine());
		int arr[] = new int[t];
		
		String line[] = in.readLine().split(" ");

		for (int i = 0; i < line.length; i++) {
			int n = Integer.parseInt(line[i]);
			arr[i+1] = n;
		}
		
		StringBuffer sb = new StringBuffer();
		boolean st = true;
		int i = t;
		
		while (st) {
			if (i==1) {
				st = false;
				sb.append(i+"");
			}
			else {
				sb.append(i+" ");
				i = arr[i-1];
			}
		}
		
		String sarr[] = sb.toString().split(" ");
		
		sb =  new StringBuffer();
		
		for (int j = sarr.length-1; j > -1; j--) {
			if (j==0) 
				sb.append((sarr[j])+"");
			else 
				sb.append((sarr[j])+" ");
		}
		
		out.write(sb.toString()+"\n");
		
		in.close();
		out.close();
	}

}