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(raw_input())
count = 0
while n != 0:
  found = False
  for d in range(2, int(n**0.5) + 1):
    if n % d == 0: 
      found = True
      break
  
  if not found:
    d = n

  if d == 2:
    count += n // d
    break
  n -= d
  count += 1

print(count)
  			    		 	 	 		 				 		 	 	