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.
def algo():
    n = int(input())
    i = 0
    while n > 0: 
        if n%2 == 0:
            i += int(n/2)
            n = 0
        else: 
            p = 3
            while n%p != 0 and p < n**(1/2) + 1:
                p += 2
            n -= p
            i += 1
            if p > n**(1/2) + 1:
                n = 0
                i = 1
    print(i)
            
algo()