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)

import kotlin.text.Typography.prime

fun main(){
    val n = readLine()!!.split(" ")[0].toLong()
    if(n != 1L) {

        val soinsu = decom(n)
        val kaisuList = MutableList(soinsu.size) { 0 }
        for (i in soinsu.indices) {
            var count = 0
            var a = n
            for (j in 0 until 100000000000) {
                if (a % soinsu[i] != 0L) break
                a /= soinsu[i]
                count++
            }
            kaisuList[i] = count
        }
        var ans = 0
        for (i in soinsu.indices) {
            var a = kaisuList[i].toLong()
            for (j in 1 until 100000000000) {
                a -= j
                if (a < 0) break
                ans++
            }
        }
        if (soinsu.isEmpty()) {
            ans = 1
        }
        println(ans)
    } else {
        println(0)
    }
}

fun prime(from : Long, to : Long = from) : List<Long> {
    return (from..to).filter { i ->
        val max = Math.sqrt(i.toDouble()).toLong()
        (2..max).all { j ->  i % j != 0L }
    }
}

fun decom(value : Long) : List<Long>{
    if (value == 1L) return listOf(1)
    val max = Math.sqrt(value.toDouble()).toLong()
    return prime(2L, max).filter { value % it == 0L }
}