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)

#わかったこと　2~N**0.5まで素数関係なく調べればいい
n=int(input())
bunkai=[]

def different_value(e):
    cnt=0
    i=1
    while e-i>=0:
        e-=i
        i+=1
        cnt+=1
    return cnt

def soinsuu(x):
    for i in range(2,int((n)**0.5)+1):
        cnt=0
        while x%i==0:
            x//=i
            cnt+=1
        if cnt==0:
            continue
        bunkai.append([i,cnt])
    if bunkai==[]:
        bunkai.append([n,1])
soinsuu(n)

ans=0
for num,e in bunkai:
    ans+=different_value(e)
if n==1:
    ans=0
print(ans)