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 isPrime(n):
    if (n <= 1):
        return False
    if (n <= 3):
        return True
    if (n % 2 == 0 or n % 3 == 0):
        return False
    i = 5
    while (i * i <= n):
        if (n % i == 0 or n % (i + 2) == 0):
            return False
        i = i + 6

    return True

n = int(input())

result = 0
x = 0

def go(k):
    global result, x
    if k==0:
        return
    if k % 2 == 0:
        print(k // 2)
        return
    else:
        if (isPrime(k)): print(1); return
        for i in range(3, int(math.sqrt(n))+1):
            if isPrime(i) and k%i==0:
                #result+=1
                x = i
                break
                #go(k-i)
        print(1+(n-x)//2)


go(n)
#print(result)