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.List;
import java.util.Scanner;

public class Solution {


    static class Node {
        private final int id;
        public Node prev;

        Node(int id) {
            this.id = id;
        }
    }

    public static void main(String[] args) {

        Scanner input = new Scanner(System.in);
        int[] ids;

        int nodeCount = input.nextInt();
        Node[] nodes = new Node[nodeCount];

        for (int i = 0; i < nodeCount; ++i) {
            nodes[i] = new Node(i + 1);
        }

        int id;
        for (int i = 2; i <= nodeCount; ++i) {
            id = input.nextInt();
            nodes[i - 1].prev = nodes[id - 1];
        }

        List<Node> way = new ArrayList<>();


        Node curr = nodes[nodeCount - 1];
        while(curr != null) {
            way.add(curr);
            curr = curr.prev;
        }

        for (int i = way.size() - 1; i >= 0; --i) {
            System.out.print(way.get(i).id);
            System.out.print(" ");
        }
    }
}
