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 ProblemA {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[] links = new int[n - 1];
        for (int i = 2; i <= n; i++) {
            int link = in.nextInt();
            links[i - 2] = link;
        }
        in.close();
        List<Integer> route = new ArrayList<>();
        route.add(n);
        while (route.get(route.size() - 1) != 1) {
            route.add(links[route.get(route.size() - 1) - 2]);
        }
        for (int i = route.size() - 1; i > 0; i--) {
            System.out.print(route.get(i));
            System.out.print(' ');
        }
        System.out.println(route.get(0));
    }
}
