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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;

public class A {

    private void work() {
        Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int n = sc.nextInt();
        int[] a = new int[n];
        for (int i = 1; i < n; i++) {
            a[i] = sc.nextInt() - 1;
        }
        sc.close();

        print(a, n - 1);
        System.out.println();
    }

    private void print(int[] a, int k) {
        if (k == 0) {
            System.out.print("1");
        } else {
            print(a, a[k]);
            System.out.printf(" %d", k + 1);
        }
    }

    public static void main(String[] args) {
        new A().work();
    }
}
