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.
#!/usr/bin/env python3

n = int(input())
cnt = 0

while n > 0:
  if n % 2 == 0:
    n = int(n / 2)
    cnt = cnt + n
    break
  if n % 3 == 0:
    n = int(n / 3)
    cnt = cnt + n
    break
  if n % 5 == 0:
    n = int(n / 5)
    cnt = cnt + n
    break
  if n % 7 == 0:
    n = int(n / 7)
    cnt = cnt + n
    break
  if n % 2 != 0 and n % 3 != 0 and n % 5 != 0 and n % 7 != 0:
    n -= n
    cnt += 1
    continue
print(cnt)
