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())

ans = 0

while(n != 0):
    if n % 2 == 0:
        ans += n // 2
        break
    ans += 1

    p = 3
    tmp = int(n ** 0.5)
    while(p < n):
        if n % p == 0:
            break

        if p > tmp:
            p = n
        else:
            p += 2
    n -= p

print(ans)