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

n=int(input()) 
pf={}
for i in range(2,int(n**0.5)+1):
    while n%i==0:
        pf[i]=pf.get(i,0)+1
        n//=i
if n>1:pf[n]=1
#print(pf)

cnt = 1
ans = 0
for i in pf.values():
    tmp = i
    while tmp >= cnt: 
        ans += 1
        tmp = tmp - cnt
        cnt += 1
    cnt = 1
print(ans)