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.Arrays;
import java.util.Scanner;

/*
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 * and open the template in the editor.
 */

/**
 *
 * @author 13196480
 */
public class ProbA {
    static Scanner sc = new Scanner(System.in);
    
    public static void main(String[] args) {
        int n = Integer.parseInt(sc.nextLine());
        //int[] routers = new int[n];

        StringBuilder out = new StringBuilder();
        StringBuilder num = new StringBuilder();
        String[] con = sc.nextLine().split(" ");
        //for (int i = 1; i < n; i++ ) connections[i]  = sc.nextInt();

        int current = n;
        while (current != 1) {
            num.append(current).reverse();
            out.append(num+" ");
            //routers[i] = current;
            current = Integer.parseInt(con[current-2]);
            num.delete(0, num.length());
        }
        out.append(current);
        //routers[i] = current;
        //String s = "";
        //for (int j = i; j >= 0; j--) {
        //    s += routers[j] + " ";
        //}
        //out.append(current + " "
        System.out.println(out.reverse().toString().trim());
        
    }
}
