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.example.trees;

import java.util.*;

public class BmailComputerNetwork {

    public static class Node {
        int val;
        int parent;

        public Node(int val, int parent) {
            this.val = val;
            this.parent = parent;
        }
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n;
        n = sc.nextInt();
        Map<Integer, Node> mp = new HashMap<>();
        Node root = new Node(1, -1), temp;
        mp.put(1, root);
        for (int i=2; i<=n; i++) {
            mp.put(i, new Node(i, sc.nextInt()));
        }
        temp = mp.get(n);
        List<Integer> ans = new ArrayList<>();
        while(temp.parent != -1) {
            ans.add(temp.val);
            temp = mp.get(temp.parent);
        }
        ans.add(temp.val);
        Collections.reverse(ans);
        for(int i : ans) {
            System.out.printf("%d ", i);
        }
        System.out.println();
    }

}