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)

import math
n = int(input())
a = []
b= []
while n % 2 == 0:
    b.append(2)
    n //= 2
if(len(b)!= 0):
    a.append(b)
    b= [] 
f = 3
while f * f <= n:

    if n % f == 0:
        b.append(f)
        n //= f
    else:
        f += 2
        if(len(b)!= 0):
            a.append(b)
            b= [] 

if(len(b)!= 0):
        a.append(b)
        b= [] 
if(len(a) != 0):
    if(n == a[len(a)-1][0]):
        a[len(a)-1].append(n)
        n  = 1
if (n != 1 ):
    b.append(n)
    a.append(b)

ans =0
for i in range(len(a)):
    ans += int((-1 + math.sqrt(1 + 8 * len(a[i])))/2)

print(ans)