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)

N = int(input())
nums = []
exps = {}
import math
for p in range(2, N):#int(math.sqrt(N))+1):
  if N % p == 0:
    nums.append(p)
    e = 0
    z = p
    while True:
      if N % z == 0:
        z *= p
        e += 1
      else:
        exps[p] = e
        break
    print(p, exps[p])
    N /= p ** exps[p]
    if N <= 1:
      break
if not len(nums):
  exps[N] = 1
  nums.append(N)

import numpy as np
prod = 0
for p in nums:
  num = 0
  cum = 0
  while True:
    cum += num
    num += 1
    if exps[p] - cum < num:
      break
      
#  print(p, exps[p], num - 1)
  prod += num - 1
print(prod)