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.LinkedHashMap;
import java.util.Map;
import java.util.Scanner;

public class Another {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        Map<Integer, Integer> map = new LinkedHashMap<>();
        map.put(1, 1);
        for (int i = 2; i < n + 1; i++) {
            map.put(i, sc.nextInt());
        }
        ArrayList<Integer> aa = new ArrayList<>();
        StringBuilder a = new StringBuilder();

        int k1 = n, k2 = map.get(k1);
        aa.add(k1);
        aa.add(k2);
        /*a.append(k1);
        a.append(" ");
        a.append(k2);*/

        while (k2 != 1) {
            k1 = k2;
            k2 = map.get(k1);
/*            a.append(" ");
            a.append(k2);*/
            aa.add(k2);
        }
        for (int i = aa.size()-1 ;i >= 0 ;i--){
            a.append(aa.get(i));
            a.append(" ");
        }
        a.deleteCharAt(a.length()-1);
        System.out.println(a.toString());
    }
}