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.*;
import java.util.*;
import java.math.*;
import java.net.*;
import java.applet.*;
import java.awt.*;
import java.awt.event.*;
public class cf
{

    public static void main(String args[])
    {
        Scanner in=new Scanner(System.in);
        int n=in.nextInt();
        int[] a=new int[n-1];
        for(int i=0;i<n-1;i++)
            a[i]=in.nextInt();
        ArrayList<Integer> al=new ArrayList<Integer>();
        al.add(n);
        int i=n-2;
        while(a[i]!=1)
        {
            al.add(a[i]);
            i=a[i]-2;
        }
        System.out.print("1 ");
        for( i=al.size()-1;i>=0;i--)
            System.out.print(al.get(i)+" ");
    }
}