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())

if not n % 2:
  print(n // 2)
else:
  def primes_sieve(limit):
    a = [True] * limit
    a[0] = a[1] = False

    for (i, isprime) in enumerate(a):
      if isprime:
        for n in range(i*i, limit, i):
          a[n] = False

    return a

  sieve = primes_sieve(1000100)

  for i in range(len(sieve)):
    if sieve[i]:
      if not n % i:
        print(((n - i) // 2) + 1)
        exit()
  
  print(1)