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 
// package PCS;

import java.util.Scanner;

public class BmailNetwork {
    public static void main(String[] args) {
        Scanner reader = new Scanner(System.in);
        int numRouters = reader.nextInt();
        int[] routers = new int[numRouters + 1];
        for (int i=0;i<numRouters - 1;i++) {
            int router = reader.nextInt();
            routers[i+2] = router;
        }
        StringBuilder answer = new StringBuilder();
        int router = numRouters;
        answer.append(new StringBuilder(router + "").reverse().toString() + " ");
        do {
            router = routers[router];
            answer.append(new StringBuilder(router + "").reverse().toString()+ " ");
        } while (router != 1);
        answer.delete(answer.length()-1, answer.length());
        answer.reverse();
        System.out.println(answer);
    }
}
