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.*;

public class bmailComputerNetworkCF {
    public static void main (String[]args) {
        Scanner scan = new Scanner (System.in);

        int routerNumber = scan.nextInt();
        Hashtable <Integer, ArrayList<Integer>> tree = new Hashtable <Integer, ArrayList<Integer>>();

        for (int i = 1; i <= routerNumber; i++) {
            tree.put(i, new ArrayList<Integer>());
        }

        for (int i = 0; i < routerNumber - 1; i++) {
            int cur = scan.nextInt();

            ArrayList<Integer> temp = tree.get(cur);
            temp.add(i + 2);
            tree.put(cur, temp);
        }

        int [] backTrackingArr = new int [routerNumber];

        Queue <Integer> queue = new LinkedList <Integer>();
        queue.add(1);

        while (queue.isEmpty() == false) {
            int cur = queue.poll();

            ArrayList<Integer> children = tree.get(cur);

            for (int i = 0; i < children.size(); i++) {
                queue.add(children.get(i));
                backTrackingArr[children.get(i) - 1] = cur - 1;
            }
        }

        ArrayList<Integer> reversePath = new ArrayList <Integer>();

        int counter = routerNumber - 1;

        while (true) {
            reversePath.add(counter + 1);

            if (counter == 0) {
                break;
            }

            counter = backTrackingArr[counter];
        }

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