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 Julia (1.4.0) (judge verdict: Wrong Answer)

parseInt(x) = parse(Int, x)
parseBigInt(x) = parse(BigInt, x)
parseFloat(x) = parse(Float64, x)
parseBigFloat(x) = parse(BigFloat, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)
using Primes

function main()
    n::Int=parseInt(readline())
    sq::Int=trunc(Int,sqrt(n))
    arr::Vector{Int}=Vector{Int}()
    sosu::Vector{Bool}=[true for i in 1:10^6]
    sosu[1]=false
    for i in 3:10^6
        res=true
        for j in 2:trunc(Int,sqrt(i))+1
            if i%j==0
                res=false
                break
            end
        end
        sosu[i]=res
    end
    ans::Int=0
    for i in 2:10^6
        if !sosu[i]
            continue
        end
        res::Int128=i
        while n%res==0
            ans+=1
            n÷=res
            res*=i
        end
    end
    flag::Bool=true
    for i in 2:10^6
        if n%i==0
            flag=false
        end
    end
    if flag && n>1
        ans+=1
    end
    println(ans)
end
main()