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.
import math
def primeFactors(n): 
    if(n%2==0):
        return 2   
    for i in range(3,int(math.sqrt(n))+1,2): 
        if(n % i== 0): 
            return i 
    if(n > 2): 
        return n 
           
n=int(input())
k=primeFactors(n)
if(k==2):
    print(n//k)
elif(k==n):
    print(1)
else:
    n-=k
    print(1+(n//2))