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())
k = 0
p = 1
for i in range(2,int(n**0.5//1) + 1):
    if n % i == 0:
        if i == 2:
            p = i
        if (i - 1) % 4 == 0 and p == 1:
            p = i
        elif (i + 1) % 4 == 0 and p == 1:
            p = i
        if i != n // i:
            k+=2
        else:
            k+=1
if k == 0:
    print(1)
else:
    print((n - p)//2 + 1)
            

    
    
        
    
