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 minprime(n):
  if n %2==0:
      return 2
  if n%3==3:
      return 3
  max_t=10**5+9
  for k in range(6,max_t,6):
      if n%(k-1)==0:
          return k-1
      if n%(k+1)==0:
          return k+1
  return n

n=int(input())
print(1+(n-minprime(n))//2)