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 DivisorSubtraction {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        boolean[] primes = sieve(100001);
        long N = scanner.nextLong();
        long prev = N;
        long tot = 0;
        boolean out = false;
        while(N!=0) {
            boolean something = false;
            for (int i = 2; (long) i * (long) i <= N; i++) {
                if (primes[i] && N % i == 0) {
                    if (i == 2) {
                        tot += (N / 2);
                        out = true;
                        break;
                    }
                    N -= i;
                    tot++;
                    something = true;
                    break;
                }
            }
            if (out) break;
            if (!something) {
                tot++;
                break;
            }
        }
        if (tot==0) System.out.println(1);
        else System.out.println(tot);
    }

    public static boolean[] sieve(int N) {
        boolean[] primes = new boolean[N+1];
        Arrays.fill(primes, true);
        primes[0] = primes[1] = false;
        for(int i = 2; i*i <= N; i++) {
            if (primes[i]) {
                for (int j = i*i; j <= N; j += i) {
                    primes[j] = false;
                }
            }
        }
        return primes;
    }

}
