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: Accepted)

import java.lang.Math.sqrt

fun main() = Thread(null, ::abc169d, "(^o^)", 128 * 1024 * 1024).apply { start() }.join()

@OptIn(ExperimentalStdlibApi::class)
fun abc169d() {
    val n = readLine()!!.toLong()

    val primes = primeFactorization(n)

    val answer = primes.map {
        var count = it.value
        (1..1000).takeWhile { i ->
            count -= i
            count >= 0
        }.count()
    }.sum()

    println(answer)
}

private fun primeFactorization(n: Long): Map<Long, Long> {
    val factors = mutableMapOf<Long, Long>()
    var temp = n
    var i = 2L
    while (i * i <= temp) {
        while (temp % i == 0L) {
            factors[i] = (factors[i] ?: 0) + 1
            temp /= i
        }
        i++
    }
    if (temp > 1) factors[temp] = 1
    return factors
}