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.
def is_prime(num):
    if num > 1: 
        for i in range(2, num//2): 
            if (num % i) == 0: 
               return False
        else: 
           return True
    else: 
       return False

s = 0
n = int(raw_input())
while n != 0:
    for i in range(1,n+1):
        print "aqui"
        if is_prime(i) and (n % i) == 0:
            print "aqui nao"
            n -=i
            s +=1
            break
print s
