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.*;
import java.util.Collection;
import java.util.TreeSet;

public class Main
{

static LinkedHashSet<Integer>adj[];

static LinkedHashSet <Integer>set=new LinkedHashSet<>();
static boolean vis[];
//static int freq[];
//static int level[];
static int com[];
static int q,mx,cnt;static boolean fl=false;
public static void main(String args[])
{
  Scanner ab=new Scanner(System.in);
  
 q=ab.nextInt();

 adj=new LinkedHashSet[q+1];
 for(int i=0;i<=q;i++)
 adj[i]=new LinkedHashSet<Integer>();
   

 for(int i=2;i<=q;i++)
 {

   int u=ab.nextInt();
   
   adj[i].add(u);
   adj[u].add(i);
 }
 
 vis=new boolean [q+1];
 pa.add(1);
 Dfs(1);
 //System.out.println(6538643);
//for(int i=0;i<=q;i++)System.out.println(adj[i]);

        for(int i:set)
        System.out.print(i+" ");
        System.out.println();
    
}
static LinkedHashSet <Integer>pa=new LinkedHashSet<>();
public static void Dfs(int i)
{
vis[i]=true;
if(i==q)
{for(int j:pa)set.add(j);
vis[i]=false;return;}
 
  
  for(int t:adj[i])
  {
  
    if(!vis[t])
    {
     pa.add(t);
     Dfs(t);
     pa.remove(t);
    }
  }
  vis[i]=false;
  
}







}