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())

if N==1:
    print(0)
    exit()
# N > 1
l=[]
ans=0
for i in range(2,int(N**0.5)+1):
    cnt=0
    while N % i ==0:
        cnt+=1
        N //=i
    if cnt > 0:
        l.append( (i,cnt) )
        ans += int( (-1+(1+8*cnt)**0.5)/2 )
if N > 1:
    l.append((N,1))
    ans +=1

print(ans)