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
ans = 0
N = int(input())
x = 2
while not N % x:
    ans += 1
    N //= x
    x *= 2
    
while not N % 2:
    N //= 2
    
i = 3

while i*i <= N:
    x = i
    while not N % x:
        ans += 1
        N //= x
        x *= i
        
    while not N % i:
        N //= i
        
    i += 2
    
if N > 1: ans += 1
print(ans)