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 leastprime(n):   
    for num in range(2,int(math.sqrt(n))+1):
        if n % num == 0:
            return num

def solution(n):
    if n%2 == 0:
        return (int(n/2))
    else:
        cnt = 0
        while (n!=0):
            l = leastprime(n)
            if l:
                n = n - l
                cnt += int(n/2)
                n = 0
            else:
                n = 0
            cnt+=1
        return (int(cnt))

n = input()
n = int(n)
print(solution(n))