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 C (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <stdio.h>

long long int checks[1000000];

int main() {
    long long int N, res;
    scanf("%lld", &N);

    size_t pos = 0;
    long long int x = 1, sum = 0;
    while (pos < 1000000) {
        sum += x;
        x++;
        checks[pos++] = sum;
    }

    for (long long int i = 2; i * i <= N; i++) {
        if (N % i != 0) continue;

        long long int acc = 0;
        while(N % i == 0) {
            acc++;
            N /= i;
        }

        for (pos = 0; pos < 1000000; pos++) {
            if (acc < checks[pos]) {
                res += pos;
                break;
            }
        }
    }

    if (N != 1) res++;

    printf("%lld\n", res);
}