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.
def prime(n):
  i=2
  while i*i<=n:
   if n%i==0:return False
   if n%i==0 and n%(n//i)==0:return False
   i+=1
  return True
def sieve(n):
 dp=[False]*(n+2);dp[0]=True;dp[1]=True
 i=2;prime=[]
 while i<=n:
  if not dp[i]:
   prime.append(i)
   for j in range(2*i,n+2,i):
     dp[j]=i
  i+=1
 return prime
primes=sieve(10**5)
n=int(input())
if prime(n):print(1)
else:
 for i in primes:
  if n%i==0:print(1+(n-i)//2);break
