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())
subs = 0
while n!=0:
    if n%2 == 0:
        subs+=n//2
        break
        
    for i in range( 3, int(n**0.5)+1, 2):
        if n%i == 0:
            n = n-i
            subs=1
            break
            
    if n>0 and n%2 == 0:
        subs+=n//2
        break
    elif n>0:
        subs+=1
        break
print(subs)