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 long in;
	public static void main (String[] args) {
	    Scanner sc = new Scanner(System.in);
	    in = sc.nextLong();
	    long f = getFact();
	    long out = 0;
	    if(in % 2 == 1){
	        in -= f;
	        ++out;
	    }
	    
	    out += in / 2;
	    
	    System.out.println(out);
	}
	static long getFact(){
	    for(int i = 2; i <= Math.sqrt(in); ++i){
	        if(in % i == 0){
	            return i;
	        }
	    }
	    return in;
	}
}