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)

"""
~~ Author : Bhaskar
~~ Dated : 01~06~2020
"""

import sys
from bisect import *
from math import floor,sqrt,ceil,factorial as F,gcd,pi
from itertools import chain,combinations,permutations,accumulate
from collections import Counter,defaultdict,OrderedDict,deque
from array import array
INT_MAX = sys.maxsize
INT_MIN = -(sys.maxsize)-1
mod = 1000000007
lcm = lambda a,b : (a*b)//gcd(a,b)
setbit = lambda x : bin(x)[2:].count("1")

def solve():
    n = int(sys.stdin.readline())
    d = Counter()
    while n%2 == 0:
        d[2] += 1
        n //= 2
    i = 3
    while i*i < n:
        if n%i == 0:
            while n%i == 0:
                d[i] += 1
                n //= i
        i += 2
    if n != 1:
        d[n] += 1
    ans = 0
    for k,v in d.items():
        minn = 1
        while v-minn >= 0:
            v -= minn
            minn +=1
            ans += 1
    print(ans)

if __name__ == "__main__":
    try:
        sys.stdin = open("input.txt","r")
    except :
        pass
    solve()