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.StringTokenizer;

public class Solution {

	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(in.readLine());
		StringTokenizer st = new StringTokenizer(in.readLine());
		int arr[] = new int[n + 1];
		arr[1] = -1;
		for (int i = 2; i <= n; i++)
			arr[i] = Integer.parseInt(st.nextToken());
		int route[] = new int[n + 1], idx = n;
		route[idx--] = n;
		int tmp = arr[n];
		while (tmp != -1) {
			route[idx--] = tmp;
			tmp = arr[tmp];
		}
		boolean f = false;
		StringBuilder sb = new StringBuilder();
		for (idx++; idx <= n; idx++) {
			if(f)
				sb.append(" ");
			sb.append(route[idx]);
			f = true;
		}
		System.out.println(sb.toString());
	}
}
