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.
while True:
	try:
		prime = []
		mark = [0]*(10**6+2)
			
		def seive():
			prime.append(2)
			N = 10**6
			for i in range(3, N+1, 2):
				if not mark[i]:
					prime.append(i)
					if i*i <= N:
						j = i*i
						while j <= N:
							mark[j] = 1
							j +=(i*2)
		def solution(n):
			#seive()
			if n&1:
				d = n
				i = 3
				while i*i <= n:
					if n%i == 0:
						d = i
						break
					i += 1
				n -= d
				print(1+(n//2))
			else:print(n//2)
				
			
		if __name__ == "__main__":
			n = int(input())
			solution(n)
	except EOFError:
		break