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 Kotlin (1.3.71) (judge verdict: Wrong Answer)

fun main() {
    var n = readLine()!!.toLong()

    val map = mutableMapOf<Long, Int>()
    while (n % 2L == 0L) {
        map[2L] = (map[2L] ?: 0) + 1
        n /= 2L
    }

    var factor = 3L
    while (n >= factor) {
        while (n >= factor) {
            if (n % factor == 0L) {
                map[factor] = (map[factor] ?: 0) + 1
                n /= factor
            } else {
                break
            }
        }

        factor += 2L
    }

    val result = map.map { (_, value) ->
        var count = 1
        var num = 1
        while (true) {
            if (value > num * (num + 1) / 2) {
                count += 1
                num += 1
            } else {
                break
            }
        }

        return@map count
    }.sum()

    println(result)
}