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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

import math
from decimal import *
import random

def pf(n):
    rn = int(n)
    ans = {}
    while(n%2==0):
        if(2 not in ans):
            ans[2] = 1
        else:
            ans[2]+=1
        n//=2
    for i in range(3, int(math.sqrt(rn))+1):
        while(n%i==0):
            if(i not in ans):
                ans[i] = 1
            else:
                ans[i]+=1
            n//=i
            if(n==1):
                break
        if(n==1):
            break
    return ans
n = int(input())
d = pf(n)
if(d=={}):
    print(1)
else:
    ans = 0
    for x in d:
        left = 0
        right = int(1e9)
        while(left<right):
            mid = (left+right)//2
            if((mid*(mid+1))//2 > d[x]):
                right = mid
            else:
                left = mid+1
        ans+=(left-1)
    print(ans)