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.*;

public class test {
    public static Vector<Vector<Integer>> a = new Vector<Vector<Integer>>();
    public static Vector<Boolean> visited = new Vector<Boolean>();
    public static Vector<Integer> store = new Vector<Integer>();

    public static void dfs(int u) {
        visited.set(u, true);
        store.add(u);
        for (int i = 0; i < a.get(u).size(); i++) {
            if (!visited.get(i)) {
                dfs(a.get(u).get(i));
            }
        }
    }

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        a.add(0, new Vector<Integer>());
        a.add(1, new Vector<Integer>());
        visited.add(0, false);
        visited.add(1, false);
        for (int i = 2; i <= n; i++) {
            a.add(i, new Vector<Integer>());
            a.get(i).add(in.nextInt());
            visited.add(false);
        }
        in.close();
        dfs(n);
        for (int i = store.size() - 1; i >= 0; i--)
            System.out.print(store.get(i) + " ");
    }
}