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 first_factor(n):
    for num in range(2,int(n**0.5) + 1):
        if n % num == 0:
            return num
    return n
            
a = int(input())
result = 0
now = a
b = a
while a != 0:
    if b != 2:
        b = first_factor(a)
        a -= b
        result += 1
    else:
        result += a//b
        break
        
print(result)