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 math import sqrt, ceil

def main():
	n = int(input())
	if not n%2:
		print(n//2)
		return
	stan = False
	for i in range(3, ceil(sqrt(n))):
		if not n%i:
			n -= i
			print(n//2)
			return
	print(1)
	return

main()
