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 Haskell (GHC 8.8.3) (judge verdict: Time Limit Exceeded)

import Data.List (group)


factors n = [ x | x <- [ 1 .. n ], n `mod` x == 0 ]

factorize 1 = []
factorize n =
    let
        x = factors n !! 1
    in
        x : factorize (n `div` x)

toInt :: String -> Int
toInt = read

steps' (n, count) set =
    let
        acc = n - head set
    in
        if acc >= 0
            then steps' (acc, count + 1) (tail set)
            else count

steps n = steps' (n, 0) [ 1 .. ]

main = do
    n <- toInt <$> getLine

    print . sum . map steps . map length . group $ factorize n