Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

24

Sample Output 1

3

We can apply the operation three times by, for example, making the following choices:

Choose z=2 (=2^1). (Now we have N=12.)

Choose z=3 (=3^1). (Now we have N=4.)

Choose z=4 (=2^2). (Now we have N=1.)

Sample Input 2

1

Sample Output 2

0

We cannot apply the operation at all.

Sample Input 3

64

Sample Output 3

3

We can apply the operation three times by, for example, making the following choices:

Choose z=2 (=2^1). (Now we have N=32.)

Choose z=4 (=2^2). (Now we have N=8.)

Choose z=8 (=2^3). (Now we have N=1.)

Sample Input 4

1000000007

Sample Output 4

1

We can apply the operation once by, for example, making the following choice:

z=1000000007 (=1000000007^1). (Now we have N=1.)

Sample Input 5

997764507000

Sample Output 5

7

Solution in PyPy3 (7.3.0) (judge verdict: Runtime Error)

import itertools
import copy
n=int(input())
c=0
A=[]
for i in range(2,int(n**0.5+1)):
  if n%i==0:
    a=0
    while(n%i==0):
      n//=i
      a+=1
    A.append(a)
l=len(A)
i=1
while(sum(A)>=l and l>0):
  for j in itertools.combinations_with_replacement(range(l), i):
    for k in j:
      C=deepcopy(A)
      if A[k]==0:
        A[k]=C[k]
        break
      else:
        A[k]-=1
    else:
      c+=1
  B=[]
  for a in A:
    if a!=0:
      B.append(a)
  A=B
  l=len(A)
  i+=1
print(1 if c!=1 and c==0 else c)