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())

def primes_sieve(size):
    prime = [True] * (size + 1)
    prime[0] = prime[1] = False
    for i in range(2, size + 1):
        if prime[i]:
            for j in range(i * i, size + 1, i):
                prime[j] = False
    return [i for i in range(2, size + 1) if prime[i]]

primes = primes_sieve(int(n**0.5) + 10)

def minPrime(k):
    for p in primes:
        if k % p == 0:
            return p
    return k

ans = 0
if n & 1 == 1:
    n = n - minPrime(n)
    ans += 1
ans += n // 2

print(ans)
