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, sys
def smallest(n): 
    while n % 2 == 0: 
        return 2 
        n = n / 2 
    for i in range(3,int(math.sqrt(n))+1,2): 
        while n % i== 0: 
            return i
            n = n / i
    if n > 2: 
        return n 
ans = 0
n= int(input())
if n%2==0:
    print(n//2)
    sys.exit()
while n>0:
    xx = smallest(n)
    n = n-xx
    if n%2==0:
        ans+=1
        print(ans+n//2)
        sys.exit()
    ans+=1
print(ans)
