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 {


    static private long get(long n) {
        for (long i = 2; i * i <= n; ++i) {
            if (n % i == 0) {
                return i;
            }
        }
        return n;
    }


    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        long n = scanner.nextLong();
        long counter = 0;

        if (n % 2 != 0) {
            n -= get(n);
            counter++;
        }

        System.out.println(counter + n / 2);
    }
}
