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(input())
res = 0
flag = False

for d in range(2, int(n ** 0.5) + 1):
  if(n % d == 0):
    flag = True
    n -= d
    res += 1
    break

if(flag):
  res += int(n / 2)
else:
  res = 1

print(res)
 		 		   				 	   										  	