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 prime(n):
    for i in range(2,int(n**0.5)+1):
        if(a[i]==1):
            j=i*2
            while(j<int(n**0.5)+1):
                a[j]=0
                j+=i
n=int(input())
a=[1]*(int(n**0.5)+1)
prime(n)
def findprime(n):
    for i in range(2,int(n**0.5)+1):
        if(a[i]==1 and n%i==0):
            return i
    return n
if(n%2==0):
    print(n//2)
else:
    print(1+(n-(findprime(n)))//2)
                