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.*;
import java.math.*;

public class Main
{
    private static Scanner s;
    public static void main (String[] args){
        
        s = new Scanner(System.in);
        long num = s.nextLong();
        long count = 0;
        boolean div = true;
        boolean has = false;
        while(div == true){
            if(num % 2 == 0){
                count += num / 2;
                num = 0;
                div = false;
            } else {
                for (int i = 3; (long) i * i <= num; i += 2){
        			if (num % i == 0){
        			    count++;
        				num -= i;
        				i = (int)num;
        				has = true;
        			}
        		}
        		if(has == false){
        		    div = false;
        		    count++;
        		} else has = false;
            }
        }
        System.out.println(count);
    }
}

	 		 	  				  	  			 		   					