Given is a positive integer N. Consider repeatedly applying the operation below on N:

* First, choose a positive integer z satisfying all of the conditions below:
* z can be represented as z=p^e, where p is a prime number and e is a positive integer;
* z divides N;
* z is different from all integers chosen in previous operations.
* Then, replace N with N/z.



Find the maximum number of times the operation can be applied.

Constraints

* All values in input are integers.
* 1 \leq N \leq 10^{12}

Input

Input is given from Standard Input in the following format:


N


Output

Print the maximum number of times the operation can be applied.

Examples

Input

24


Output

3


Input

1


Output

0


Input

64


Output

3


Input

1000000007


Output

1


Input

997764507000


Output

7
from collections import defaultdict
n = int(input())
d = defaultdict(int)
k = 2
while n > 1 and k * k <= n:
    if n % k == 0:
        d[k] += 1
        n //= k
    else:
        k += 1
if n > 1:
    d[n] += 1
ans = 0
for k,v in d.items():
    a = 1
    while v >= a:
        v -= a
        a += 1
        ans += 1
print(ans)