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;
import java.lang.Math;
import static java.lang.Math.min;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long n = sc.nextLong();
		long resp = 0;
		double i;
		while (n%2!=0){
			long temp = n;
			for(i=2;i*i<=n;i++){
				if(n%i==0){
					temp = 1;
					break;
				}
			}
			n-=temp;
			resp++;
		}
		resp+=n/2;
		System.out.println(resp);
	}
}

  		    		 	  	   	  	 			 	 		