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())
M = 10 ** 5 + 5
pr = [True] * M
pr[0], pr[1] = False, False
for i in range(2, M):
    if pr[i]:
        for j in range(i * 2, M, i):
            pr[j] = False

prime = list(filter(lambda x: pr[x], range(M)))


def calc(n, k):
    if n == 0:
        return k
    else:
        for i in prime:
            if n % i == 0:
                while n % i == 0:
                    k += 1
                    n //= i
        if n == 1:
            return k
        return calc(n, k)


print(calc(N, 0))