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: Wrong Answer)


import math

def using_sqrt(p):
    # 2以外の偶数は素数ではないので無視する
    if p % 2 == 0 and p != 2:
        return False
    # 繰り返しの上限を対象の平方根にする
    for divisor in range(2, math.floor(math.sqrt(p))+1):
        if p % divisor == 0:
            return False
    return True

if __name__ == "__main__":
    N = int(input())    
    cnt = 0
    z = 0
    hoge = 0
    for z in range(1, N+1):
        if N % z == 0:
            p = 1
            if (using_sqrt(p)):
                e = 0
                for p in range(1, z):
                    hoge = p**e
                    e += 1
                    if  hoge == z:
                        cnt += 1
                        N = N / z
    print(cnt)