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 Test {
    public static void main(String[] args) {

        Scanner input = new Scanner(System.in);
        long n = input.nextLong();

        if (n==0) {
            System.out.println(0);
            return;
        }
        
        long k=0;
        while (n>2) {
            int flag= 1;
            for(long i=2;i<=n/2;i++) {
                if (n % i == 0) {
                    long m = n/i;
                    k+=m-i+1;
                    n=(i-1)*i;
                    flag=0;
                    break;
                }
            }
            if (flag ==1) break;
        }

        k++;

        System.out.println(k);
    }
}
