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.Arrays;
import java.util.List;
import java.util.Scanner;
import java.util.stream.Collectors;

public class BmailComputerNetwork {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int num = sc.nextInt();
        sc.nextLine();
        List<Integer> routerNums = Arrays.stream(sc.nextLine().trim().split(" "))
                .map(Integer::valueOf).collect(Collectors.toList());
        List<Integer> out = new ArrayList<>();
        out.add(num);
        addRouter(out, routerNums, num);
        for (int i = out.size() - 1; i >= 0 ; i--) {
            System.out.print(out.get(i) + " ");
        }
    }

    private static void addRouter(List<Integer> out, List<Integer> routerNums, int rNum) {
        int currentRouterIndex = rNum - 2;
        if (currentRouterIndex < 0) {
            return;
        }
        int parentRouterNum = routerNums.get(currentRouterIndex);
        out.add(parentRouterNum);
        addRouter(out, routerNums, parentRouterNum);
    }
}
