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: Accepted)

N = int(input())
A = [0 for k in range(int(N**0.5)+1)]

#N=1の処理
if N == 1:
  print(0)
  exit()
ans = 0


prime = [2]
for k in range(3, len(A), 2):
  if A[k] == 0:
    prime.append(k)
    for j in range(k, len(A), k):
      A[j] = 1
for p in prime:
  if N%p == 0:
    break
else: 
  print(1)
  exit()

use = []
for p in prime:
  if p > N:
    break
  if N%p == 0:
    ans += 1
    use.append(p)
    N = N // p
  np = p * p
  while N % np == 0:
    ans += 1
    N = N // np
    np = np * p
    
for u in use:
  while N % u == 0:
    N = N // u
if N > 1:
  ans += 1
print(ans)