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.Scanner;
public class Mail01 {
    private static final Scanner scanner = new Scanner(System.in);
    public static void main(final String[] args) {
        int n = Integer.valueOf(scanner.nextLine());
        String[] parts = scanner.nextLine().split(" ");
        scanner.close();
        final int[] arr = new int[parts.length];
        for (int i = 0; i < parts.length; i++) {
            arr[i]=Integer.valueOf(parts[i]);
        }
        solve(n,arr);
    }

    private static void solve(final int n, final int[] arr) {
        int x=n;
        final ArrayList<Integer> list = new ArrayList<>();
        list.add(x);
        while(x>1) {
            x = arr[x-2];
            list.add(x);
        }
        final StringBuilder sb = new StringBuilder();
        for (int i = list.size()-1; i >=0 ; i--) {
            sb.append(list.get(i));
            if(i>0)
                sb.append(" ");
        }
        System.out.println(sb.toString());
    }
}