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)

import math

#引数nが素数かどうかを判定
def is_prime(n):
    for i in range(2, int(math.sqrt(n))+1):
        if n%i == 0:
            return False
    return True

def getPrimeExp(n):
    array = [True]*(n+1)
    result = []
    for i in range(2, n+1):
        if array[i]:
            array[i] = False
            result.append(i)
            for j in range(2, n+1):
                ij = i**j
                if ij <= n and array[ij]:
                    result.append(ij)
                    array[ij] = False
                elif ij > n:
                    break
            for j in range(i*2, n+1, i):
                array[j] = False

            # for j in range(2, n):
            #     ij = i**j
            #     if ij <= n:
            #         result.append(ij)
            #         array[ij] = False
    return sorted(result)

N = int(input())
if is_prime(N):
    print(1)
else:
    cnt = 0
    primeExp = getPrimeExp(N) 
    n = N
    # print(primeExp)
    for z in primeExp:
        if n%z == 0:
            n = int(n/z)
            cnt += 1
    print(cnt)