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.Arrays;
import java.util.Scanner;
import java.util.Stack;

public class BmailComputerNetwork {
	public static void main(String args[]) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		ArrayList<ArrayList<Integer>> graph = new ArrayList<>();
		for(int i = 0; i<n; i++) {
			graph.add(new ArrayList<>());
			
		}
		
		for(int i = 0; i<n-1; i++) {
			int firstNode = i+1;
			int newNode = sc.nextInt() - 1;
			graph.get(firstNode).add(newNode);
			graph.get(newNode).add(firstNode);
		}
		
		//DFS
		boolean [] visited = new boolean[n];
		Stack<Integer> myStack = new Stack<>();
		
		myStack.push(0);
		while(!myStack.isEmpty()) {
			if(myStack.peek() == n-1){ 
				visited[n-1] = true;
				break;
			}
			if(visited[myStack.peek()]) { 
				myStack.pop();
				continue;
			}
			visited[myStack.peek()] = true;
			for(Integer child:graph.get(myStack.peek())) {
				if(!visited[child]) {
					myStack.push(child);
				}
			}
		}
		
		Stack<Integer> printStack = new Stack<>();
		while(!myStack.isEmpty()) {
			int p = myStack.pop();
			if(visited[p]) {
				printStack.push(p+1);
			}
		}
		while(!printStack.isEmpty()) {
			System.out.print(printStack.pop() + " ");
		}
		
	}
}
