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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class test{
	
	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		int n=Integer.parseInt(br.readLine());
		int[] arr=new int[n+1];
		StringTokenizer st=new StringTokenizer(br.readLine());
		for(int i=1;i<n;i++) {
			arr[i+1]=Integer.parseInt(st.nextToken());
		}
		int pos=n;
		int[] arr2=new int[n];
		arr2[0]=n;
		int k=1;
		while(pos!=1) {
			pos=arr[pos];
			arr2[k]=pos;
			k++;
		}
		k--;
		while(k>=0) {
			System.out.print(arr2[k]+" ");
			k--;
		}
	}
	
}
