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())

count = 0

while n:
    if not n&1:
        count += n>>1
        n = 0
    else:
        r = round(n**0.5)+1
        for i in range(3,r,2):
            if n%i == 0:
                count += 1
                n -= i
                break
        else:
            count += 1
            n = 0

print(count)
