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 Divisor2
{
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        long n=sc.nextLong();
        long sum=0;
        int k=0;
        long d=0;
        if(n%2==0)
        {
            sum=n/2;
        }
        else
        {
            for(long i=3;i<=n;i=i+2)
            if(n%i==0)
            {
                for(long j=3;j<i;j=j+2)
                {
                    if(i%j==0)
                    k=k+1;
                }
                if(k==0)
                {
                    d=i;
                    System.out.println(i);
                    sum=1;
                break;
                }
                else
                k=0;
            }

            sum=sum+(n-d)/2;
        }
        System.out.println(sum);

    }
}
