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.io.*;
import java.lang.*;

public class Main {

    static int[] primes;

    public static void main(String[] args) {
        Scanner sc = new Scanner (System.in);

        long n =sc.nextLong();

        computePrimes(Math.sqrt(n));

        int sub = 0;
        long lowestPrime = n;
        while (n != 0) {
            for (int i = 2; i <= Math.min(Math.sqrt(n), lowestPrime); i++) {
                if (n % i == 0 && primes[i] == 1) {
                    lowestPrime = i; break;
                }
            }
            n = n - lowestPrime;
            sub++;
            if (lowestPrime == 2) {
                sub += (n / 2);
                n = 0;
            }
        }

        System.out.println(sub);
    }

    private static void computePrimes(double sqrt) {
        int biggest = (int) sqrt;

        primes = new int[Math.max(10, biggest + 1)];
        primes[2] = 1;
        primes[3] = 1;
        primes[5] = 1;
        outer:
        for (int i = 7; i <= biggest; i = i + 2) {
            for (int j = 3; j <= (int) Math.sqrt(i); j++) {
                if (primes[j] == 1 && i % j == 0) {
                    continue outer;
                }
            }
            primes[i] = 1;
        }
    }

}
