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 MyClass {
    public static void main(String args[]) {
        Scanner scan = new Scanner(System.in);
        long n = scan.nextLong();
        System.out.println(n % 2 == 0 ? n / 2 : 1 + (n - smallestDiv(n))/2);
    }
    public static long smallestDiv(long n){
        long i = 2;
        while(i * i <= n)if(n % i == 0)return i;
                        else ++i;
        return n;
    }
}
