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.
n = int(input())

count = 0
def IsPrime(n):
	d = 2
	while d * d <= n and n % d != 0:
		d += 1
	return d * d > n

def get_count(n, count):
	if n == 0:
		return count
	elif n % 2 == 0 and not IsPrime(n):
		return count + n // 2
	d = 0
	for i in range(2, n // 2 + 1):
		if IsPrime(i) and n % i == 0:
			d = i
			break
	else:
		d = n
	return get_count(n-d, count + 1)

if n % 2 == 0:
	print(n // 2)
elif IsPrime(n):
	print(1)
else:
	print(get_count(n, count))
