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 sd(n):
    # if divisible by 2
    if (n % 2 == 0):
        return 2;

        # iterate from 3 to sqrt(n)
    i = 3;
    while (i * i <= n):
        if (n % i == 0):
            return i;
        i += 2;

    return n;
n=int(input())
k=sd(n)
if n%2==0:
    print(int(n//2))
else:
    p=n-k
    print(int(p//2)+1)
