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 math
n = int(input())

def primo(l):
	for i in range(2, math.ceil(math.sqrt(l))+1):
		if l%i == 0:
			return False

	return True


if n%2 == 0:
	print(int(n/2))
	exit()


# refl = []
for i in range(3, math.ceil(math.sqrt(n))+1, 2):
	if n%i ==0:
		# refl.append(int(n/i))
		if primo(i):
			print(int(1+((n-i)/2)))
			exit()

print(1)