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 smallestDivisor(n):
  if (n % 2 == 0):
    return 2

  i = 3
  while(i * i <= n):
    if (n % i == 0):
      return i
    i += 2
    
  return n

n = int(input())
resp = 0
while (n > 0):
  if n % 2 == 0:
    resp += n // 2
    break
  s = smallestDivisor(n)
  n = n - s
  resp += 1
print (resp)
 	  			 	 	  							  	 			