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())

z_2 = 2
handan_1 = 0
while math.sqrt(N) >= z_2:
    if N % z_2 == 0:
        handan_1=1
    z_2+=1

if handan_1 == 0:
    z_s=[0,1]
else:
    z_s = [0]
    while N > max(z_s):
        z_1 = 2
        while True:
            handan = 0
            if N % z_1 == 0 and z_1 not in z_s:
                for i in range(2,z_1+1):
                    if z_1 % i == 0:
                        N = N // z_1
                        z_s.append(z_1)
                        handan = 1
                        break
            if handan == 1:
                break
            z_1 += 1
z_s.remove(0)            
print(len(z_s))