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.io.PrintWriter;
import java.util.*;
import java.util.stream.Collector;
import java.util.stream.Collectors;

public class Main {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt();
        int[] m = new int[n];
        for (int i = 1; i < n; i++) {
            m[i] = in.nextInt();
        }
        List<Integer> path = new ArrayList<>();
        int start = n - 1;
        while (m[start] != 0) {
            path.add(start + 1);
            start = m[start] - 1;
        }
        path.add(1);

        for (int i = 0; i < path.size(); i++) {
            out.print(path.get(path.size() - 1 - i) + " ");
        }
        out.close();
    }
}