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 = float(input())
result = 0;
menor = -1
r = int(math.sqrt(n))

for i in range(2, r+1):
    if(n%i==0):
        result+=1;
        menor = i;
        n=n-i;
        break;
        
    

if(menor==-1):
    result=1;
else:
    result=result+int((n/2));

print(result)

 	  	     	 			 	  				    	  	