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.
def prost(n):
	if n == 1:
		return True
	for x in range(2, n):
		
		if n % x == 0:
			return False
		else:
			return True
schet = 0
n = int(input())
while not(n==0):
	k = 0
	while(n>=k):
		k = k+1;
		# print(prost(k))
		if (prost(k) and n%k==0):
			last = k
			
	# print(last)
	n = n-last
	# print(n)
	schet = schet+1
print(schet)

