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 Divisor {
    public static void main(String[] args) throws Exception {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        long n = Long.parseLong(br.readLine());

        long count = 0;
        if( n % 2 != 0 ) {
            n -= solve(n);
            count++;
        }

        long res = count + n / 2;

        System.out.println(res);

    }

    private static long solve(long n) {
        for(long i = 2; i*i <= n; i++) {
            if( n % i == 0 ) {
                return i;
            }
        }

        return n;
    }
}