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.ArrayList;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;

public class Test {

	static Scanner s = new Scanner(System.in);
	
	static int in() {
		int x;
		x = s.nextInt();
		return x;
	}
	
	static ArrayList<ArrayList<Integer>> adj;
	
	static void solve() {
		int n = in();
		adj = new ArrayList<ArrayList<Integer>>();
		for(int i = 0; i <= n; i ++) {
			adj.add(new ArrayList<Integer>());
		}
		for(int i = 2; i <= n; i ++) {
			int p = in();
			adj.get(p).add(i); // it can be undirected, but it doesn't matter
		}
		
		// just BFS with parent array
		int parent[] = new int[n+1];
		boolean vis[] = new boolean[n+1];
		
		Queue<Integer> q = new LinkedList<Integer>();
		q.add(1);
		vis[1] = true;
		parent[1] = -1;
		
		while(!q.isEmpty()) {
			int curr = q.poll();
			for(int a : adj.get(curr)) {
				if(!vis[a]) {
					vis[a] = true;
					parent[a] = curr;
					q.add(a);
				}
			}
		}
		ArrayList<Integer> path = new ArrayList<Integer>();
		int curr = n;
		while(parent[curr] != -1) {
			path.add(curr);
			curr = parent[curr];
		}
		path.add(1);
		for(int i = path.size()-1; i >= 0; --i) {
			System.out.print(path.get(i)+" ");
		}
		
	}
	
	public static void main(String[] args) {

		solve();
	}

}
