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 Python (3.8.2) (judge verdict: Wrong Answer)

def factorization(n):
  arr = []
  temp = n
  for i in range(2, int(n**0.5)+1):
    if temp%i==0:
      cnt=0
      while temp%i==0:
        cnt+=1
        temp //= i
      arr.append([i, cnt])
      
    if temp!=1:
      arr.append([temp, 1])
    
    if arr==[]:
      arr.append([n, 1])
    
  return arr

a = factorization(int(input()))
b = [1, 3, 6, 10, 15, 21, 28, 36, 43]

ans = 0

if len(a) == 1 and a[0][0] == 1:
  print(0)
  exit()
  
for i in a:
  for j in range(len(b)):
    if i[1] < b[j]:
      ans+=j
      break
    
print(ans)