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
import math
n = int(input())
count = 0

if n % 2 is 0:
    print(n//2)
    sys.exit()

primes = [2]

if n in primes:
    print(1)
    sys.exit()
tmp = True
for i in range(2, int(math.sqrt(n)) + 1):
    if n % i is 0:
        tmp = False
        break
if tmp:
    print(1)
    sys.exit()


while True:
    if n % 2 is 0:
        print(count + n//2)
        sys.exit()

    if n is 0:
        break
    #find prime
    temp = False
    for p in primes:
        if n % p is 0:
            count = count + 1
            n = n - p
            temp = True
            break
    if temp:
        continue

    for i in range(primes[-1] + 1, 100000 + 1):
        tt = True
        for j in range(2, int(math.sqrt(i)) + 1):
            if i % j is 0:
                tt = False
                break
        if tt:
            primes.append(i)
            if n % i is 0:
                count = count + 1
                n = n - i
                break
print(count)


