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())
import math
m = int(math.sqrt(n))
a = [False,False]+[True]*(m-1)
primes = []
for i in range(2,m+1):
    if a[i]:
        primes.append(i)
        for j in range(2*i,m+1,i):
            a[j] = False

c = 0
while(n != 0):
    p = n
    for i in primes:
        if n%i == 0:
            p = i
            break
    n -= p
    c += 1
    if n%2 == 0 :
        c += n//2
        break
print(c)
