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 sieve(n):
    ass = []
    is_prime = [True]*(n+1)
    is_prime[0] = False
    is_prime[1] = False

    for i in range(2, int(math.sqrt(n))+1):
        if not is_prime[i]:
            continue
        for j in range(i*2, n+1, i):
            is_prime[j] = False
    for i in range(n+1):
        if is_prime[i]:
            ass.append(i)
    return(ass)

S = sieve(10**5+10)

n = int(input())
if n%2 == 0:
    print(n//2)
else:
    for p in S:
        if n%p == 0:
            break
    print(1+(n-p)//2)
