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.
from sys import stdin

def main():
	n = int(input())
	ans = 0
	if n % 2 == 1:
		ans = 1
		d = 3 
		while d*d <= n and n % d != 0:
			d += 2
		if d*d > n:
			d = n
		n = n // d
	
	ans += n // 2

	print(ans)

	return


if __name__ == '__main__':
	main()