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 Bmail {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        int n = scanner.nextInt();
        ArrayList<Integer>[] adj = new ArrayList[n];
        for (int i = 0; i < n; i++) {
            adj[i] = new ArrayList<>();
        }
        for (int i = 0; i < n - 1; i++) {
            int p = scanner.nextInt();
            adj[--p].add(i + 1);
        }
        List<Integer> ans = new ArrayList<>();
        dfs(0, adj, ans, n);
        ans.add(1);
        Collections.reverse(ans);
        for (int node : ans) {
            System.out.print(node + " ");
        }
        System.out.println();
    }

    private static boolean dfs(int cur, ArrayList<Integer>[] adj, List<Integer> ans, int n) {
        if (cur == n - 1) return true;
        for (int node : adj[cur]) {
            if (dfs(node, adj, ans, n)) {
                ans.add(node + 1);
                return true;
            }
        }
        return false;
    }
}
