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.
from sys import stdin

def main():
    N = int(input())

    n = N
    if N % 2:
        primes = erastosthenes(int(N ** 0.5))
        cnt = 1
        for i in primes:
            if not N % i:
                n -= i
                break
        else:
            n = 0
    else:
        cnt = 0
    print(cnt + n // 2)

def erastosthenes(n):
    prime = [0, 1] * ((n + 1) // 2)
    if not n % 2:
        prime += [0]
    prime[1], prime[2] = 0, 1

    i = 3
    while i <= n ** 0.5:
        for j in range(i * i, n + 1, i):
            prime[j] = 0
        i += 2
    prime_list = [2] + [i for i in range(3, n + 1, 2) if prime[i]]
    return prime_list

input = lambda: stdin.readline()
main()
