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.math.sqrt

fun main() {
    val n = nextLong()
    var remain = n
    val root = sqrt(remain.toDouble()).toLong()
    val primes = HashSet<Long>(Int.MAX_VALUE)
    var i = 2L
    var count = 0
    loop@ while (remain > 1 && i <= root && i <= remain) {
        for (prime in primes) {
            if (i % prime == 0L) {
                i++
                continue@loop
            }
        }
        var mod = i
        while (mod <= remain) {
            if (remain % mod == 0L) {
                count++
                remain /= mod
            } else {
                break
            }
            mod *= i
        }
        i++
    }
    println(if (remain == n) 1 else count)
}

val sc = java.util.Scanner(System.`in`)
fun next(): String = sc.next()
fun nextInt() = sc.nextInt()
fun next2Int() = Pair(nextInt(), nextInt())
fun next3Int() = Triple(nextInt(), nextInt(), nextInt())
fun nextIntArray(size: Int) = IntArray(size) { nextInt() }
fun nextLong() = sc.nextLong()
fun nextLine(): String = sc.nextLine()
fun nextList() = nextLine().split(" ")
fun printYesNo(isYes: Boolean) = println(if (isYes) "Yes" else "No")
fun printString(action: StringBuilder.() -> Unit) = println(buildString(action))