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.
n = int(input())

result = 0
while n != 0:
    i = 2
    if(n % i == 0):
        result += n // i
        break
    else:
        i = 3
        d = n
        while i * i <= n:
            if(n % i == 0):
                d = i
                break
            i += 1
        n -= d
        result += 1

print(result)
 			  	  			   	  		 	 		 					