You are given an integer number n. The following algorithm is applied to it:

  1. if n = 0, then end algorithm; 
  2. find the smallest prime divisor d of n; 
  3. subtract d from n and go to step 1. 



Determine the number of subtrations the algorithm will make.

Input

The only line contains a single integer n (2 ≤ n ≤ 10^{10}).

Output

Print a single integer — the number of subtractions the algorithm will make.

Examples

Input


5


Output


1


Input


4


Output


2

Note

In the first example 5 is the smallest prime divisor, thus it gets subtracted right away to make a 0.

In the second example 2 is the smallest prime divisor at both steps.
import java.util.*;
public class Main 
{
	public static void main(String[] args) 
	{
		Scanner sc = new Scanner(System.in);
		long n = sc.nextLong();
		System.out.println(solve(n));
		sc.close();
	}
	static long solve(long n)
	{
		if (n%2==0)
		{
			return n/2;
		}
		for (int i=3;(long)i * i<=n;i+=2)
		{
			if (n%i==0)
			{
				return solve(n-i)+1;
			}
		}
		return 1;
	}
}