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.BufferedWriter;
import java.io.FileWriter;
import java.io.IOException;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;

/**
 * Created by abhay.kumar on 19/08/18.
 */
public class Main {

    private static final Scanner scanner = new Scanner(System.in);

    public static void main(String[] args) throws IOException {

        int n = scanner.nextInt();
        Map<Integer, Set<Integer>> graph = new HashMap<>();
        for(int i =2; i<=n; i++) {
            int v = scanner.nextInt();
            if (!graph.containsKey(v)) {
                graph.put(v, new HashSet<>());
            }
            graph.get(v).add(i);
        }
        boolean visited[] = new boolean[n+1];
        List<Integer> res = new LinkedList<>();
        res.add(1);
        dfs(graph, visited, res, 1);
        for (Integer i : res) {
            System.out.print(i +" ");
        }
    }

    private static boolean dfs(Map<Integer, Set<Integer>> graph, boolean[] visited, List<Integer> res, int i) {
        if (i == visited.length-1) {
            return true;
        }
        if (visited[i] || !graph.containsKey(i))  {
            return false;
        }
        visited[i] = true;
        for (Integer val : graph.get(i)) {
            if(!visited[val]) {
                res.add(val);
                if(dfs(graph, visited, res, val)) {
                    return true;
                }
                res.remove(res.size()-1);
            }
        }
        visited[i] = false;
        return false;
    }
}
