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.*;

 public class sd{
    
    public static void main(String args[])
{
    Scanner z=new Scanner(System.in);
    int n=z.nextInt();
    int a[]=new int[n-1];
    int i;
    for(i=0;i<n-1;i++)
    {a[i]=z.nextInt();}
    
    int ans[]=new int[n];
    int count=1;
     int node=0;
    ans[0]=n;node=a[n-2];
    
    while(node!=1)
    {   
        ans[count++]=node;
        int pp=node-2;
        node=a[pp];
    }ans[count++]=1;
    for(i=count-1;i>-1;i--)
    System.out.print(ans[i]+" ");
}
}