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.
import math

n = int(input())

subs = 0

while(n > 0):
  if (n % 2 == 0):
    subs += n // 2
    n = 0
  else:
    sq = int(math.sqrt(n))
    found = False
    for i in range(2, sq + 1):
      if (n % i) == 0:
        found = True
        break

    if found:
      subs += 1
      n -= i
    else:
      subs += 1
      n = 0

print(subs)