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
x = int(input())
inicial = x
cnt = 0

while x>0:
  if x%2 == 0:
    cnt += int(x/2)
    x  = 0
    break
  else:
    for i in range(3,math.ceil(math.sqrt(x))+1,2):
      if x%i == 0:
        x -= i
        cnt += 1
        break
    if inicial == x:
      cnt = 1
      x=0

print(cnt)