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 sys
from collections import defaultdict
import math
n=int(sys.stdin.readline())
def getfactors(num):
    ans=0
    if num%2==0:
        return num//2
    fac=-1
    for i in range(2,int(math.sqrt(num))+1):
        #print(num%i)
        #print('a')
        if num%i==0:
            #print(i,'i')
            fac=i
            break
    #print(fac)
    if fac!=-1:
        num-=fac
        ans=1
        ans+=num//2
        return ans
    return 1
    
ans=getfactors(n)
print(ans)

