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 = input()
ans = 0

def do(v):
    i = 2
    while i*i<=v:
        if v%i == 0:
            return i
        i+= 1
    return v
d = do(n)
if d == n:
    print 1
    exit()
elif n%2 == 0:
    print n/2
    exit()

ans = 1
n -= d
ans += n/2
print ans

	 	 	 			 		  	 	 		 	 	 	  	 	