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())
i=2
while i*i<=n:       # it doesn't make sense to search further than this
 if n%i==0:break
 i+=1
else:i=n
print( 1+(n-i)//2 ) # 3 cases, i=n,i=2(both self explanitory)
                    #and i=random which turns into i=2 after one turn



# // is floor division
 
