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.*;
public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n=sc.nextInt();
		int f[]=new int[1000001];
		int b[]=new int[1000001];
		for(int i=2;i<=n;i++) {
			f[i]=sc.nextInt();
		}
		int j=0,qwq=n;
		f[1]=0;
		while(f[qwq]!=0) {
			j++;
			b[j]=qwq;
			qwq=f[qwq];
		}
		System.out.println(1);
		for(int i=j;i>=1;i--) {
			System.out.print(b[i]+ " ");
		}
	}
}

 	   	   		 				  	 	 			 	  	