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.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Stack;
import java.util.StringTokenizer;
import static java.lang.Math.*;

public class A {
	
	static FastScanner sc;
	static PrintWriter pw;
	
	
	public static void main(String[] args) {
		
		new Thread(null ,new Runnable(){
            public void run()
            {
                try{
                    solve();
                } catch(Exception e){
                    e.printStackTrace();
                }
            }
        },"1",1<<26).start();
		
	}
	
	static void solve(){
		sc =new FastScanner();
		pw = new PrintWriter(System.out);
		int n = sc.nextInt();
		Node[] nodes = new Node[n+1];
		for(int i = 1; i <= n; i++){
			nodes[i] = new Node(i);
		}
		for(int c = 2; c <= n; c++){
			int p = sc.nextInt();
			nodes[p].children.add(nodes[c]);			
		}
		Stack<Node> path = new Stack<>();
		dfs(nodes[1], path, nodes[n]);
		int size = path.size();
		int[] p = new int[size];
		int last = size-1;
		while(!path.isEmpty()){
			p[last] = path.pop().val;
			last--;
		}
		
		for(int i = 0; i < size; i++){
			pw.print(p[i]+" ");
		}
		pw.println();
		
		pw.close();
	}
	
	static void dfs(Node start, Stack<Node> path, Node dest){
		path.push(start);
		for(Node child : start.children){
			if(path.peek() == dest){
				return;
			}			
			if(child != dest){
				dfs(child, path, dest);
			}else{
				path.push(dest);
				return;
			}			
		}
		if(path.peek() != dest){
			path.pop();
		}
	}
	
	static class Node{
		int val;
		ArrayList<Node> children = new ArrayList<>();
		
		public Node(int val){
			this.val = val;
		}
	}
	
	static void sort(int[] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
	
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}

	
}

