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.
import math

def prime(n):
    i=2
    while(i<=math.sqrt(n)):
        if(n%i==0):
            return i
        else:
            if(i==2):
                i+=1
            else:
                i+=2
    return n
n=int(input())
r=0
while(n!=0):
    d=prime(n)
    if(d==n):
        r+=1
        break
    else:
        if(n%2==0):
            r=r+n//2
            break
        else:           
            n-=d
            r+=1
print(r)
