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 ProblemB {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long n = sc.nextLong();
		sc.close();
		long k = n;
		long cnt = 0;
		if(k % 2 == 0) {
			System.out.println(k / 2);
			System.exit(0);
		}
		long p = 3;
		for(long i = p; i <= n; i += 2) {
			if(k % i == 0) {
				p = i;
				break;
			}
		}
		cnt += k / p + (k / p - 1) / 2;
		System.out.println(cnt);
	}
}