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 sol(x):
    if x%2==0:
        return 2
    else:
        n=3
        while n*n<=x:
            if x%n==0:
                return n
            else:
                n+=2
        return x
x=int(input())

j=x
ans=0
while x%2==1:
    x-=sol(x)
    ans+=1
print(ans+(x//2))