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 is_prime(n):
    for i in range(2, int(n**0.5)+1):
        if not n%i:
            return False
    return True

n=int(input())
c=0
while True:
    if n%2==0:
        c+=n//2
        break
    if is_prime(n):
        c+=1
        break
    for i in range(2,n):
        if is_prime(i) and n%i==0:
            break
    n-=i
    c+=1
    if n==0:
        break
print(c)