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 trees;

import java.util.Scanner;

public class A1057 {
    
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int a[]=new int[n+2];
        int b[]=new int[n+2];
        int idx=0,c;
        a[1]=1;
        for(int i=2;i<=n;i++){
            a[i]=sc.nextInt();}
        b[0]=n;
        idx++;
        c=a[n];
        
        while(c!=1){
           
            b[idx]=c;
             idx++;
            c=a[c];
            
        }
        
        b[idx]=1;
        idx++;
        for(int i=idx-1;i>=0;i--){
            System.out.print(b[i]+" ");
            
        }
        
    }
    

}
