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())
count=0
def is_prime(n):
    if n % 2 == 0 and n > 2:
        return False
    for i in range(3, int(math.sqrt(n)) + 1, 2):
        if n % i == 0:
            return False
    return True
while n:
    if n%2 == 0:
        count+=n/2
        break
    else:
        if is_prime(n):
            count+=1
            break
        else:
            for i in range(3,n):
                if n%i==0:
                    n-=i
                    count+=1
                    break
print(int(count))
