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 
//package All_in_all;


import java.io.*;
import java.sql.SQLOutput;
import java.util.*;

import static java.lang.Math.abs;
import static java.lang.Math.round;

/**
 * Created by nikitos on 23.08.17.
 */

public class abacaba {

    public StreamTokenizer t;

    public int nextInt() throws IOException {
        t.nextToken();
        return (int) t.nval;
    }

    public String nextString() throws IOException {
        t.nextToken();
        return t.sval;
    }

    private boolean[][] matrix = new boolean[100][100];

    public void start() throws IOException {
        t = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));

        int n = nextInt();

        arr = new int[n + 1];
        for (int i = 2; i <= n; i++) {
            arr[i] = nextInt();
        }

        getPath(n, arr[n]);
        Collections.reverse(order);

        for (Integer cur: order) {
            System.out.print(cur + " ");
        }
    }

    private ArrayList<Integer> order = new ArrayList<>();
    private int[] arr;

    private void getPath(int i, int current) {
        if (current == 0) {
            order.add(1);
            return;
        }

        order.add(i);
        getPath(current, arr[current]);
    }

    public static void main(String[] args) throws IOException {
        new abacaba().start();
    }

}
