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: Accepted)

main = do
    n <- readLn :: IO Int
    print $ sum $ map (findG . snd) $ pfacTup n

findG n = length $ takeWhile (<=n) $ scanl1 (+) [1..]

sqrtInt :: Int -> Double
sqrtInt = sqrt . fromIntegral

pfacTup :: Int -> [(Int,Int)]
pfacTup n = fAux (takeWhile(<=floor(sqrtInt n))primes) n where
    fAux    _     1 = []
    fAux    []    n = [(n,1)]
    fAux q@(p:ps) n = if n`rem`p==0
        then let e = head (dropWhile (\x-> n`rem`(p^x) == 0) [1..])-1
            in (p,e):(fAux q (n`quot`(p^e)))
        else fAux ps n

primes :: [Int]
primes = f [2..] where f (p:ps) = p:(filter ((/=0).(`rem`p)) ps)