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: Runtime Error)

N=int(input())
if N==1:
    print(0)
else:
    nowN=N
    cnt=[]
    I=[]
    #print(NN)
    cn=0
    if nowN%2==0:
        while nowN%2==0:
            nowN/=2
            cn+=1
        cnt.append([2,cn])
        #print(nowN)
        n=3
    end=N/2
    while n < end:
        cn=0
        if nowN%n==0:
            while nowN%n==0:
                nowN/=n
                cn+=1
            cnt.append([n,cn])
        #print(n,nowN)
        n+=2
        end=int(N/n)
        if nowN==1:
            break
    if nowN==N:
        print(1)
    else:    
        for cn in cnt:
            han=True
            nowcnt=cn[1]
            i=1
            while han:
                nowcnt-=i
                if nowcnt<=i:
                    I.append(i)
                    han=False
                else:
                    i+=1
        ans=0
        for i in I:
            ans+=i
        #print(cnt)
        print(ans)