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())
d=2
step=0
while(n!=0 and d<=100000):
    if(n%d==0):
        step=step+1
        n=n-d
        break
    else:
        d=d+1
        continue
if(d==100001):
    step=1
    print(step)
else:   
    step=n//2+step
    print(step)

	   	    			 		 	 						    	 	