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 _1057;

import java.util.Scanner;

public class Main {
    public static void main (String args[]){
        
        Scanner scan = new Scanner (System.in);
        
        int n = scan.nextInt();
        
        int node[] = new int[n-1];
        int path[] = new int[n];
        int counter = 0;
        
        for (int i=0; i<n-1; i++) node[i] = scan.nextInt();
        
        int pos = n-2;
        path[counter++] = n;
        
        while (true){
            if (node[pos] == 1) {
                path[counter] = 1;
                break;
            } else {
                path[counter++] = node[pos];
                pos = node[pos]-2;
            }
        }
        
        for (int i=counter; i>=0; i--)
            System.out.print (path[i] + " ");
    }
}
