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 
//problem: https://codeforces.com/problemset/problem/1057/A

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

public class Bmail{
    public static void main(String[] args){
        Scanner sObj = new Scanner(System.in);
        int routers = Integer.parseInt(sObj.nextLine());
        Stack<Integer> stkObj = new Stack<Integer>();
        int[] connections = new int[routers + 1];
        for(int i=2; i<=routers; i++){
            connections[i] = sObj.nextInt();
            //System.out.print(" input = " +  connections[i]);
        }
        //System.out.println("Input taken");
        int pos = routers;
        while(connections[pos] != 1){
            //System.out.println("router #" + pos + " connected to router #" + connections[pos]);
            stkObj.push(pos);
            pos = connections[pos];
        }
        stkObj.push(pos);
        stkObj.push(1);
        while(!stkObj.empty()){
            System.out.print(stkObj.pop() + " ");
        }
        //System.out.println("router #" + pos + " connected to router #" + connections[pos]);
    } 
}