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())

least_prime_cache = {}
steps_cache = {}
# find all the prime numbers smaller than the end

def find_least_prime(end):
    for i in range(2, int(end ** 0.5 + 1)):
        if end % i == 0:
            return i
    return end

def find_steps(n):
    if n in steps_cache:
        return steps_cache[n]
    if not n % 2:
        return n // 2
    if n not in least_prime_cache:
        prime = find_least_prime(n)
        least_prime_cache[n] = prime
    prime = least_prime_cache[n]
    return 1+find_steps(n - least_prime_cache[n])

print(find_steps(n))