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.io.*;
import java.util.*;
public class DivisorSubtraction {
    public static void main(String[] args) throws IOException{
        Scanner in=new Scanner(System.in);
        long n=in.nextLong();
        long d=2;
        for(;d*d<=n;d++)
            if(n%d==0)
                break;
        if(d*d>n)
            d=n;
        long k=0;
        if(d%2==0) {
            k=n/d;
        }
        else{
            k=(n-d)/2+1;
        }
        System.out.println(k);

    }
}