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 
//package com.company;


import java.sql.Array;
import java.util.*;


public class Main {
    public static String myJoiner(ArrayList<Integer> list, char joinerChar) {
        String outputString = "";
        for (int i = 0; i < list.size(); i ++) {
            if (i != list.size() - 1) {
                outputString += String.valueOf(list.get(i)) + joinerChar;
            }
            else {
                outputString += String.valueOf(list.get(i));
            }
        }
    return outputString;
    }
    public static void MainFunction() {
        Scanner inputReceiver = new Scanner(System.in);
        ArrayList <Integer> dynamicArray = new ArrayList<Integer>();
        int n = inputReceiver.nextInt();
        int[] connectedTo = new int[n];
        connectedTo[0] = 1;
        for (int i = 1; i < n; i ++) {
            connectedTo[i] = inputReceiver.nextInt();
        }
        int k = n;
        while (true) {
            dynamicArray.add(k);
            k = connectedTo[k - 1];
            if (k == 1) {
                break;
            }
        }
        dynamicArray.add(1);
        Collections.reverse(dynamicArray);
        for (int i = 0; i < dynamicArray.size(); i ++ ) {
            if (i != dynamicArray.size() - 1) {
                System.out.print(dynamicArray.get(i) + " ");
            }
            else {
                System.out.print(dynamicArray.get(i));
            }
        }
    }
    public static void main(String[] args) {
        MainFunction();
    }
}


