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 Router {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int lastRouter = scanner.nextInt();
        int[] ints = new int[lastRouter - 1];
        for (int i = 0; i < ints.length; i++) {
            ints[i] = scanner.nextInt();
        }
        List<Integer> list = route(ints, lastRouter);
        for(int n:list){
            System.out.print(n+" ");
        }
    }
    public static List<Integer> route(int[] array, int lastRouter){
        ArrayList<Integer> list = new ArrayList<>();
        list.add(lastRouter);
        int last = array[array.length-1];
        while(last!=1) {
            list.add(last);
            last=array[last-2];
        }
        list.add(1);
        Collections.reverse(list);
        return list;
    }
}
