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
n=int(input())
if n%2==0:
    print(n//2)
else:
    i=3
    f=0
    c=0
    while(i<=int(math.ceil(math.sqrt(n)))):
        if n%i==0:
            c+=1
      
            n=n//i
            if n%2==0:
                f=1
                print(c+n//2)
                break
            else:
                i=3
        else:
            i+=1
    if f==0:
        print(c+1)
    
        