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.Scanner;
public class Helloworld {

	public static void main(String[] args) {
		Scanner s=new Scanner(System.in);
long n ,a=1,i=2;
n=s.nextLong();
long k=(long) Math.sqrt(n);
if(n!=1 && !f(n)) 
	while(n!=1) {	if(n%i==0) { n=g(n,i);
	a*=i;
		}
i++;	}
else if(f(n)) a=n;
System.out.print(a);
				}
		static boolean f(long n)
		{
			long k=(long) Math.sqrt(n);
			for(long i=2;i<=k;i++) if(n%i==0) return false;
			return true;
		}
static long g(long n, long i)
{do n/=i;
while(n%i==0);
return n;	
}

			}
	
	

