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.
a = int(input())
 
def l(p):
    for i in range(2, 100001):
        flag = True
        for y in range(2, round(i**0.5 + 1)):
            if i % y == 0:
                flag = False
            if flag == False:
                break
        if flag == True:
            p.append(i)
    return p
 
p = []
o = l(p)
 
def f(q):
    global o
    k = q
    ans = 1
    for i in o:
        r = 0
        while q % i == 0:
            r += 1
            q //= i
        ans += r
    return ans - 1
print(f(a))
