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.
#!/usr/bin/env python
# coding: utf-8

# In[51]:


n=int(input())


# In[52]:


sub=0

def smallprime(x):
    for i in range(2,x+1):
        if x % i==0:
            return i


def dsub(x):
    global sub
    if x==0:
        print(sub)
        return 
    if  x%2==0:
        sub=sub+x/2
        print(sub)
        return
    else:
        p=smallprime(x)
        sub=sub+1
        dsub(x-p)
    


# In[53]:


dsub(n)


# In[ ]:




