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)

import math

n = int(input())
Max = 10**6
count = 0

def sosu(x):
  for i in range(2,int(math.sqrt(n))+1):
    if x % i == 0:
      return False
  return True

if sosu(n):
  print(count +1)
  exit()

alst = [0] * Max
alst[0] = 2
alst[1] = 1
for i in range(2,Max):
  for j in range(i, Max, i):
    alst[j] += 1
    if alst[j] >= 2:
      alst[j] = 2
      break

Prime = []
for i in range(1,Max):
  if alst[i] == 1:
    Prime.append(int(i))

p = len(Prime)
PF = [0]*Max


for i in range(1,p):
  if n%Prime[i] == 0:
    for j in range(20,1,-1):
      if n%Prime[i]**j == 0:
        count += 1
        PF[i] = j
        n = n / Prime[i]
        if sosu(n):
          print(count + 1)
          exit()
          
print(count)