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())

def PrimeList(limit):
    Plist = []
    for i in range(2,limit+1):
        divcheck = False
        for j in Plist:
            if j*j > i:
                break
            if i%j == 0:
                divcheck = True
                break
        if divcheck == False:
            Plist.append(i)
    return Plist

L = PrimeList(10**5)
count = 0
primecheck = True
for p in L:
    if p*p > n:
        break
    if n%p == 0:
        smallest = p
        primecheck = False

if primecheck == True:
    print(1)
else:
    print(1+int((n-smallest)/2))
