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.lang.*;
import java.util.*;

public class Main {
	static int[] root = new int[200005];
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		int[] router = new int[n + 1];
		for (int i = 2; i <= n; ++i)
		{
			router[i] = scanner.nextInt();
			root[i] = i;
		}
		root[0] = 0;
		root[1] = 1;
		
		for (int i = 2; i <= n; ++i)
		{
			merge(router[i], i);
		}
		int[] path = new int[n + 1];
		path[0] = 1;
		find(n, path);
		for (int i  = path[0] - 1; i >= 1; --i)
			System.out.print(path[i] + " ");
		scanner.close();
	} // end main
	static void merge(int father, int child)
	{
		root[child] = father;
	}
	static int find(int x, int []path)
	{
		path[path[0]] = x;
		path[0]++;
		if (root[x] == x)
		{
			return x;
		}
		else
		{
			return find(root[x], path);
		}
	}
}