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.Scanner;

public class Math3 {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner s = new Scanner(System.in);
		long n = s.nextLong();
	
		if (n%2==0) {
			System.out.println(n/2);
		} else {
			long i = 3;
			while(i<Math.sqrt(n)) {
				long m = i-1;
				long f = 1;
				long j = 1;
				while(j<=m) {
					f = f*j;
					j++;
				}
				if(n%i == 0 && f%(m+1)==m ) {
					break;
				}
			}
			System.out.println(((n-i)/2)+1);
		}

	}

}
